LatMath 2025

March 6 - 8, 2025

Agenda

SchedulePlenary TalksScientific SessionsPanelsPoster SessionBios

Day 1: Thursday, March 6

Time Event Location
8:30 – All Day Pre-Conference Registration Luskin Center Lobby
10:00 – 12:00 Pre-Conference Events for Students:
10:00 am – 11:30 am: How To Present a Poster
11:30 am – 12:00 pm: Tips for Becoming an Effective Mentee		 Centennial Ballroom AB
12:00 – 1:00 Lunch + Networking Centennial Ballroom CD
1:00 – 1:30 Opening Remarks Centennial Ballroom AB
1:30 – 2:30 Plenary Talk: Federico Ardila Centennial Ballroom AB
3:00 – 5:00 Scientific Sessions:
(4 talks, 25+5 minutes each)
– Combinatorics (Pinnacle)
– Numerical Analysis and Computational Mathematics (Odyssey)
– Mathematical Biology (Pathways)
– Machine Learning (Centennial Ballroom AB)		 Various Locations
5:30 – 8:00 Poster Session + Reception Centennial Ballroom CD

 

Day 2: Friday, March 7

Time Event Location
8:00 – All Day Registration Luskin Center Lobby
8:00 – 9:00 Breakfast Centennial Ballroom CD
9:00 – 10:00 Plenary Talk: Sara Del Valle Centennial Ballroom AB
10:00 – 11:00 Plenary Talk: Johnny Guzman Centennial Ballroom AB
9:00 – 11:00 Math Circle Activity for High School Students Centennial Ballroom CD
11:15 – 12:30 Public Event: Erika Tatiana Camacho Centennial Ballroom AB
12:30 – 2:00 Lunch + Networking Centennial Ballroom CD
2:00 – 3:00 BIG Panel: Career Paths in Math Centennial Ballroom AB
3:00 – 3:15 Opportunities at Math Institutes Centennial Ballroom AB
3:45 – 5:45 Scientific Sessions:
(4 talks, 25+5 minutes each)
– Algebra/Number Theory (Pinnacle)
– Harmonic Analysis, PDEs & Differential Geometry (Odyssey)
– Math Education (Pathways)
– Statistics, Data Analysis (Centennial Ballroom AB)		 Various Locations
6:00 – 7:00 Reading of Testimonios:
Stories of Latinx & Hispanic Mathematicians		 IPAM Lobby

 

Day 3: Saturday, March 8

Time Event Location
8:00 – All Day Registration Lobby
8:00 – 9:00 Breakfast Centennial Ballroom CD
9:00 – 10:00 Plenary Talk: Rodolfo Torres Centennial Ballroom AB
10:15 – 11:15 Concurrent Panels:
– Undergraduate Opportunities: Building a Strong Foundation (Centennial Ballroom AB)
– Graduate School: Training to be a Research Mathematician (IPAM Lecture Hall)		 Various Locations
11:30 – 12:30 Plenary Talk: Carrie Diaz Eaton Centennial Ballroom AB
12:30 – 2:15 Mentoring Luncheon Centennial Ballroom CD
2:30 – 3:30 Concurrent Panels:
– Navigating Your Path: Success Strategies for Early-Career Mathematicians (IPAM Lecture Hall)
– Post-tenure: Now That You Have Tenure, What’s Next? (Centennial Ballroom AB)		 Various Locations
4:00 – 5:00 Plenary Talk: J Maurice Rojas Centennial Ballroom AB
6:00 – 10:00 Banquet (Sponsored by Analog Devices, Inc.) Centennial Ballroom CD

Plenary Talks

LOCATION: Centennial Ballroom AB

Federico Ardila (San Francisco State University)

Intersection theory and combinatorics: variations on a theme

My talk will discuss some beautiful objects at the intersection of combinatorics, geometry, and algebra called “Chow rings of toric varieties”. I will discuss three ways of thinking about them: they can be approached using algebra, polyhedral geometry, or numerical analysis. I will then explain how combinatorialists have recently used these rings to prove several conjectures from the 1970s and 80s about the colorings of a map. My talk will not assume that you know anything about these objects. I will talk about the work of many people, including my joint work with Carly Klivans, Graham Denham, and June Huh.
Watch video of Federico’s talk on YouTube

Sara Del Valle (Los Alamos National Laboratory)

Why population heterogeneity matters for modelling infectious diseases: implications for health equity

The COVID-19 pandemic highlighted significant health disparities among sociodemographic groups in the United States, underscoring the need for modelling approaches that can capture the complex dynamics driving these disparities. Specifically, variations in case incidence, mortality, and disease burden have been observed across historically marginalized racial and ethnic groups, as well as by demographic and geographic regions. Accurately incorporating fine-grained sociodemographic attributes into infectious disease models remains challenging due to complex correlations among individual characteristics within populations. Additionally, embedding mechanistic representations of exposure disparities requires a nuanced understanding of variation in exposure risk across different transmission settings. In this study, we address these challenges by incorporating drivers of exposure risk and detailed sociodemographic data into EpiCast—a large-scale agent-based model of respiratory pathogen spread in the United States. Our findings show that embedding high levels of population heterogeneity into models of infectious disease can reveal inequitable outcomes in disease burden driven by factors such as household size and workplace exposure. This approach can be used to better inform policy interventions to mitigate inequity during future pandemics.
Watch video of Sara’s talk on YouTube

Johnny Guzman (Brown University)

Finite Element Exterior Calculus (FEEC) with smoother spaces

FEEC is now a well developed field of numerical analysis. It borrows from and makes connections with several other areas in mathematics (e.g. algebraic topology, geometric integration). A central topic in FEEC are Whitney forms which were originally developed by H. Whitney to prove de Rham’s Theorem. In fact, Whitney forms were later, independently, discovered in two and three dimensions by J.-C. Nedelec and since then have been used in a wide variety of applications: electro-magnetism, solid mechanics, etc. Whitney forms form a discrete de Rham complex of a simplicial decomposition. The regularity of this complex is in some sense minimal, whereas in some applications forms with more regularity are more natural. In recent years with collaborators, borrowing ideas from the spline community we have developed forms that are smoother that also fit into discrete de Rham complexes. This led us to tackle two questions that were unresolved in our community: 1) Develop a discrete elasticity sequence on a simplicial triangulation in three dimensions and 2) justify why Lagrange elements on special meshes work for Maxwell eigenvalue problems.

 

Erika Tatiana Camacho (Arizona State University)

A Mestiza’s Quest to Find Her Place in Academia and STEM in the Face of Adversity

Dr. Erika Camacho has navigated the challenges of being in STEM and academia at the crossroads between races, nations, languages, cultures and social classes, with multiple identities and contradictions, having Indigenous and Spanish ancestry and everything in between. She will talk about her journey and constant fight against the physical and imaginary borders imposed on her by others, tradition, and disciplinary fields. She will also talk about the price and sacrifices that it took to get to where she is while navigating new worlds and being torn between forces that did not fully accept her. Through the story of her journey, she will illustrate her quest to stay true to herself by gathering the strength to embrace her multiple intersectional identities and learn to be unapologetic for being her, even in the face of adversity. Growing up in East Los Angeles, attaining her PhD from an Ivy League school, playing a pivotal role in NSF HSI Program, becoming a Fulbright Research Scholar, and extending her research to include wet lab work, she understands the struggles that many students and faculty face in attaining their academic and professional goals. Drawing from her personal experiences and the ability to constantly reinvent herself, Dr. Camacho will share her journey of resilience, tenacity, and hard work. She will highlight key decisions that contributed to her continued success and transformation and individuals that were part of her journey.
Watch video of Erika’s talk on YouTube and watch video of her interview here

Rodolfo Torres (University of California, Riverside (UC Riverside))

Almost Orthogonality in Fourier Analysis: From Singular integrals, to Function Spaces, to Leibniz Rules for Fractional Derivatives<h/4>

Fourier analysis has been an extraordinarily powerful mathematical tool since its development 200 years ago, and currently has a wide range of applications in diverse scientific fields including digital image processing, forensics, option pricing, cryptography, optics, oceanography, and protein structure analysis. Like a prism that decomposes a beam of light into a rainbow of colors, Fourier analysis transforms signals into a mathematical spectrum of basic wave components of different amplitudes and frequencies, from which many hidden properties in the data can be deciphered. At the abstract mathematical level signals are represented by functions and their filtering and other operations on them by operators. From a functional analytical point of view, these objects are studied by decomposing them into elementary building blocks, some of which have wavelike behavior too. Decomposition techniques such as atomic, molecular, wavelet and wave-packet expansions provide a multi-scale refinement of Fourier analysis and exploit a rather simple concept: “waves with very different frequencies are almost invisible to each other”. Many of these useful techniques have been developed around the study of some particular operators called singular integral operators. By breaking an operator or splitting the functions on which it acts into non-interacting almost orthogonal pieces, these tools capture subtle cancelations and quantify properties of an operator in terms of norm estimates in function spaces. This type of analysis has been used to study linear operators with tremendous success in the mathematical areas of harmonic analysis, complex analysis, and partial differential equations. More recently, similar decomposition techniques have been pushed to the analysis of new multilinear operators that arise in the study of (para) product-like operations, commutators, null-forms and other nonlinear functional expressions. In this talk we will present some of our contributions in the study of multilinear singular integrals and function spaces, and their applications to the development of the equivalent of the calculus Leibniz rule to the concept of fractional derivatives.

Watch video of Rodolfo’s talk on YouTube

Carrie Diaz Eaton (Bates College)

VECINA: Helping mathematics be a good neighbor

In the Latinx community where I grew up, in Providence, RI, the church served as a hub for the Central and South American immigrant community. I grew up proud of how my dad served his community by helping them negotiate various systems and resources. In the last few years, I have sought to redefine the relationship that my identities have with the mathematics that I do. This journey has included rekindling my relationship with the Latinx community in Providence. In 2022, I co-founded the VECINA project for Visualizing Environmental and Community Information for Neighborhood Advocacy with non-profit organization leaders at the Woonasquatucket River Watershed Council. VECINA seeks to gather, distill, analyze, and make accessible data in a way that is useful for the communities that need it. Combining the power of mathematics, data, and computing with advocacy in my home community has had a profound impact on me as a person, has created a new community for me, and has stretched me as a researcher. At the same time, VECINA has become a model for academic-community partnerships in mathematics and undergraduate community-engaged learning experiences.

Watch video of Carrie’s talk on YouTube

J Maurice Rojas (Texas A&M University)

Breaking Complexity Barriers in Real Algebraic Geometry

Real solutions to large (nonlinear) systems of equations have long been central in many engineering applications, and are now known to be fundamentally important in complexity theory. For instance, recent work has shown that knowing enough about counting solutions implies new separations of complexity classes related to the P vs. NP problem. The key is to pay close attention to the underlying structure of the equations.
We’ll review the connections between solving polynomial equations, algorithmic complexity, fewnomial theory, and combinatorics. We’ll also highlight a recent connection between the abc-Conjecture and speeding up equation solving over the real numbers. We assume no background in algebraic geometry. The main results are joint with Weixun Deng, Alperen Ergur, and Grigoris Paouris.

Watch video of Maurice’s talk on YouTube



Combinatorics

Location: Pinnacle

Organizers: Laura Escobar (Washington University St. Louis), Andrés Vindas-Melendez (Harvey Mudd College)

 

Schedule – Thursday, March 6th

3:00 PM – 3:25 PM Denae Ventura (UC Davis)
3:30 PM – 3:55 PM Javier GonzĂĄlez Anaya (Harvey Mudd College)
4:00 PM – 4:25 PM Mario Sanchez (IAS)
4:30 PM – 4:55 PM Eric Ramos (Stevens Institute of Technology)

Abstracts

Denae Ventura (UC Davis)

Optimization Tools for Computing Colorings of \( [1,\dots,n] \) with Few Monochromatic Solutions on \(3\)-variable Linear Equations

A famous result in arithmetic Ramsey theory says that for many linear homogeneous equations \(\mathbb{E}\) there is a threshold value \(R_k(\mathbb{E})\) (the Rado number of \(\mathbb{E}\)) such that for any \(k\)-coloring of the integers in the interval \([1,n]\), with \(n \ge R_k(\mathbb{E})\), there exists at least one monochromatic solution. But one can further ask, \emph{how many monochromatic solutions is the minimum possible in terms of \(n\)?} Several authors have estimated this function before, here we offer new tools from integer and semidefinite optimization that help find either optimal or near optimal 2-colorings minimizing the number of monochromatic solutions of several families of 3-variable non-regular homogeneous linear equations. In the last part of the paper we further extend to three and more colors for the Schur equation, improving earlier work.

Javier GonzĂĄlez Anaya (Harvey Mudd College)

Moduli spaces of points in flags of affine spaces and polymatroids

We will discuss two novel moduli spaces of labeled points in flags of affine spaces. The first moduli space parametrizes distinct weighted points, with configurations defined up to translation and scaling. The second moduli space allows points to collide freely, without any notion of equivalence between configurations. We will see that the first moduli space admits a toric compactification, which coincides with the polypermutohedral variety of Crowly-Huh-Larson-Simpson-Wang, while the second one is toric and coincides with the polystellahedral variety of Eur-Larson. This is joint work with P. Gallardo and J.L. Gonzalez.

Mario Sanchez (IAS)

Symmetric Lattice Paths and Polytope Subdivisions

There are many beautiful connections between lattice paths in a grid and objects in combinatorics, convex geometry, and algebraic geometry. One such connection is the theory of matroid polytopes which associates a polytope to each pair of lattice paths whose properties are described by the relation of the two paths. I will present a symmetric version of this theory which relates symmetric lattice paths to objects called delta matroids. I will discuss how to subdivide these polytopes using lattice path constructions.

Eric Ramos (Stevens Institute of Technology)

Universality theorems for generalized splines

We study generalized splines from the perspective of the representation theory of the category of graphs with contractions. We prove a finite generation result in this context, which implies a kind of universality in the generating set for the module of splines over any graph within a fixed homotopy class. Importantly, these results hold over any Noetherian commutative ring with a chosen finite list of ideals for edge-labels. One can think of our results as expanding upon and explaining many results about generating sets of the module of generalized splines.


Numerical Analysis and Computational Mathematics

Location: Odyssey

Organizer: Claudia Falcon (Wake Forest University)

 

Schedule – Thursday, March 6th

3:00 PM – 3:25 PM Josef Sifuentes (UT Rio Grande)
3:30 PM – 3:55 PM Maricela Cruz (Kaiser Permanente Washington Health Research Institute)
4:00 PM – 4:25 PM David Guinovart (Hormel Institute, University of Minnesota)
4:30 PM – 4:55 PM MayteĂ© Cruz-Aponte (UPR-Cayey)

Abstracts

Josef Sifuentes (UT Rio Grande)

GMRES Convergence and Spectral Properties for Preconditioned KKT Matrices with Extensions to Generalized Block Matrices

Several important preconditioners for saddle point problems yield linear systems for which the GMRES iterative method converges exactly in just a few iterations. However, these preconditioners all involve inverses of large submatrices. In practical computations such inverses are only approximated, and more iterations are required to solve the preconditioned linear system. How many more iterations? In this talk, we present perturbation analysis results for GMRES that leads to rigorous upper bounds on the number of iterations as a function of the accuracy of the preconditioner to the ideal and spectral properties of the constituent matrices. We also derive a thorough analysis of the spectral properties of these common saddle point preconditioners. Generalizations of these preconditioners have been proposed, however their convergence properties have not been described. Our spectral analysis of these generalized systems allow us to finally prove tight convergence bounds for these preconditioned systems.

Maricela Cruz (Kaiser Permanente Washington Health Research Institute)

Assessing Healthcare Interventions via Interrupted Time Series Methods

Assessing the impact of complex interventions on measurable health outcomes is a growing concern in health care and health policy. Interrupted time series (ITS) designs borrow from traditional case-crossover designs and function as quasi-experimental methodology able to retrospectively analyze the impact of an intervention. Statistical models used to analyze ITS data a priori restrict the interruption’s effect to a predetermined time point or censor data for which the intervention effects may not be fully realized, and neglect changes in the temporal dependence and variability. In addition, current methods limit the analysis to one hospital unit or entity and are not well specified for discrete outcomes (e.g., patient falls). In this talk, I present novel ITS methods based on segmented regression that address the aforementioned limitations.

David Guinovart (Hormel Institute, University of Minnesota)

Multipopulation Mathematical Modeling of Vaccination Campaigns for COVID-19

This presentation explores the development and application of advanced mathematical models to study the dynamics of COVID-19 transmission and the effects of vaccination campaigns. Using a multi-population framework, we extend traditional compartmental models, including SIR (Susceptible, Infected, Recovered), to more complex formulations, such as SIRV (Susceptible, Infected, Recovered, Vaccinated) and SIQRDV (Susceptible, Infected, Quarantined, Recovered, Deceased, Vaccinated). These models are designed to incorporate heterogeneities such as demographic stratification and regional variations, offering a flexible platform to investigate pandemic dynamics under diverse conditions. The analysis includes stability assessments, sensitivity evaluations of key parameters, and computational simulations of interventions. By focusing on the mathematical and computational aspects, this work demonstrates how multi-population models can provide critical insights into the effectiveness of vaccination programs and inform public health strategies.

Mayteé Cruz-Aponte (UPR-Cayey)

Metapopulation model framework for Puerto Rico applied to COVID-19

The COVID-19 pandemic has highlighted significant challenges for public health systems worldwide, demonstrating not only the lethality of infectious diseases but also the critical role of public behavior that influence case numbers and mortality rates, particularly in geographically isolated regions like Puerto Rico. This study presents a metapopulation model framework to analyze the transmission dynamics of COVID-19 across Puerto Rico’s municipalities on the main island. By integrating demographic, mobility, epidemiological data, government executive orders, and key events specific to the island, the model captures the interplay between local outbreaks and inter-municipality spread.
The study emphasizes how such models can effectively represent the spatial dynamics of disease transmission, focusing on the pivotal influence of ‘human mobility parameters’ in enhancing the predictive accuracy of SIR-type models. Core components of the framework include evaluating the impact of non-pharmaceutical interventions (NPIs), such as government-imposed mobility restrictions, social events, and vaccination campaigns.
Ultimately, this work aims to provide a robust spatial metapopulation epidemiological modeling framework that accounts for human mobility in Puerto Rico. The framework is designed to support informed public health decision-making, serving as a foundation for simulating future disease scenarios and fostering community awareness and preparedness.


Mathematical Biology

Location: Pathways

Organizers: Janet Best (Ohio State University), Paul Hurtado (University of Nevada, Reno)

 

Schedule – Thursday, March 6th

3:00 PM – 3:25 PM Miriam Nuño (UC Davis)
3:30 PM – 3:55 PM Michael Cortez (Florida State University)
4:00 PM – 4:25 PM Mario Bañuelos (Fresno State)
4:30 PM – 4:55 PM Carina Curto (Brown University)

Abstracts

Miriam Nuño (UC Davis)

Mathematical Optimization of Spatial Distribution in Wastewater-Based Epidemiology for Advancing Health Equity

Dr. Nuño is a professor at UC Davis that specializes in applying statistics and applied mathematics to tackle public health challenges, reduce health disparities, and enhance patient outcomes. Her expertise bridges mathematical modeling, biostatistics, epidemiology, and public health, with a strong focus on developing innovative methodologies for multivariable modeling, clustered longitudinal analysis, observational studies, and big data analytics.

Michael Cortez (Florida State University)

Sensitivity analysis reveals how community composition differentially affects three disease metrics in multi-host communities

In nature, most pathogens can infect multiple host species. Consequently, changes in host community composition (i.e., the gain or loss of a host species from a community) will affect disease levels. Whether the gain or loss of a particular host species increases or decreases disease depends on the characteristics of all host species in the community; these characteristics include the ability of each host species to compete for resources (competitive ability) and the ability of each host species to transmit the disease (host competence). Prior empirical and modeling studies also show that changes in disease levels depend on specific metrics used to measure disease. However, it is unclear when and why disease metrics respond differently.
To determine when disease metrics respond differently, I analyze a multi-host SIR-type model using local sensitivity analysis. I compute explicit formulas for the sensitivities of three commonly used disease metrics: the pathogen basic reproduction number (R0), infected density in focal host (I), and the proportion of infected individuals in a focal host (I/N; infection prevalence). By analyzing those formulas, I show that the three metrics often respond in the same direction to host additions/removals. For example, additions of low competence hosts often decrease all three metrics of disease because the added hosts are poor spreaders of disease. However, I also identify the mathematical conditions when the three metrics can change in different directions. Interpreted biologically, these mathematical condition correspond to (i) density-mediated feedbacks caused by high disease-induced mortality, (ii) density-mediated feedbacks caused by interspecific host competition, or (iii) differences between an individual’s lifetime versus instantaneous production rate of new infections. My work unifies and generalizes prior theory by identifying how differences in host competence and competition between species shape how each disease metric responds to changes in host community composition.

Mario Bañuelos (Fresno State)

Estimating Valley Fever Endemicity with Environmental Parameters

Valley Fever is a lung disease caused by the fungi Coccidioides immitis and Coccidioides posadasii, endemic to arid regions of the southwestern United States. While previous research has examined disease severity and risk factors, few studies have focused on predictive modeling for case forecasting and evolving endemicity. Since transmission occurs from the environment to the host rather than person to person, we hypothesize that environmental conditions significantly impact disease prevalence. Using publicly available data from the past two decades, we developed multiple linear regression, decision tree, random forest, and time series models to predict monthly case rates across six Central California counties. Our results suggest that factors such as air quality and wildfires play a key role in forecasting disease occurrences, providing insights for future studies and public health planning.

Carina Curto (Brown University)

Threshold-linear networks, attractors, and oriented matroids

Threshold-linear networks (TLNs) are common models in theoretical neuroscience that are useful for modeling neural activity and computation in the brain. They are simple, recurrently-connected networks with a rich repertoire of nonlinear dynamics including multistability, limit cycles, quasiperiodic attractors, and chaos. In this talk I will give a brief introduction to TLNs and then show how ideas from oriented matroids provide valuable insights into the connection between network architecture and dynamics.


Machine Learning

Location: Centennial Ballroom AB

Organizer: Guido Montufar (UCLA)

 

Schedule – Thursday, March 6th

3:00 PM – 3:25 PM Oscar Leong (UCLA)
3:30 PM – 3:55 PM Patricio Gallardo (UC Riverside)
4:00 PM – 4:25 PM Angelica Torres (Max Planck Institute for Mathematics in the Sciences)
4:30 PM – 4:55 PM Deanna Needell (UCLA)

Abstracts

Oscar Leong (UCLA)

The Star Geometry of Regularizer Learning

Across many tasks in data science, it is necessary to estimate data from corrupted measurements. Perhaps the most pervasive and commonly used technique to address such problems is variational regularization. This consists of solving an optimization problem where one must minimize the sum of a data fidelity term and a regularizer, a penalty term chosen to encourage certain structure in solutions. While there is a suite of regularizers one could choose from, we currently lack a systematic understanding from a modeling perspective of what types of geometries should be preferred in a regularizer for a given data source. In particular, given a data distribution, what is the “optimal” regularizer for such data? Moreover, what aspects about the data govern whether the regularizer enjoys certain properties, such as convexity? Using ideas from star geometry, Brunn-Minkowski theory, and variational analysis, I show that we can characterize the optimal regularizer for a given distribution and establish conditions under which this optimal regularizer is convex. Moreover, I will discuss how our theory can be applied to recent deep learning-based regularization learning frameworks that incorporate additional measurement information into regularizers, which are especially useful in the context of inverse problems.

 

Patricio Gallardo (UC Riverside)

Applying Machine Learning to Algebraic Geometry

There has been growing interest in applying machine learning techniques to research-level problems in mathematics. In this talk, I will discuss how these methods—such as reinforcement learning —help us better understand their solution spaces. I will highlight ongoing applications in algebraic geometry, including the study of elliptic pairs.

Angelica Torres (Max Planck Institute for Mathematics in the Sciences)

Algebraic varieties for deep learning

In recent years the algebraic techniques have played an increasing role in the understanding of the function space and optimization landscape of Neural Networks. In this talk we will explore the algebraic varieties that appear in the study of the function space of linear and polynomial neural networks. We will start with an introduction to algebraic varieties and then explore how their properties translate into properties of the function space of the Neural Networks.

Deanna Needell (UCLA)

Fairness and Foundations in Machine Learning

In this talk, we will address areas of recent work centered around the themes of fairness and foundations in machine learning as well as highlight the challenges in this area. We will discuss recent results involving linear algebraic tools for learning, such as methods in non-negative matrix factorization that include tailored approaches for fairness. We will showcase our approach as well as practical applications of those methods. Then, we will discuss new foundational results that theoretically justify phenomena like benign overfitting in neural networks. Throughout the talk, we will include example applications from collaborations with community partners, using machine learning to help organizations with fairness and justice goals. This talk includes work joint with Erin George, Kedar Karhadkar, Lara Kassab, and Guido Montufar.


Statistics, Data Analysis

Location: Centennial Ballroom AB

Organizer: David Uminsky (University of Chicago)

 

Schedule – Friday, March 7th

3:45 PM – 4:10 PM Oscar Hernan Madrid Padilla (UCLA)
4:15 PM – 4:40 PM Alejandro Ochoa (Duke University)
4:45 PM – 5:10 PM Ana Maria Kenney (UC Irvine)
5:15 PM – 5:40 PM Marina Meila (University of Washington)

Abstracts

Oscar Hernan Madrid Padilla (UCLA)

Confidence Interval Construction and Conditional Variance Estimation with Dense ReLU Networks

In this talk, we present a residual-based framework for conditional variance estimation, deriving nonasymptotic bounds for variance estimation under both heteroscedastic and homoscedastic settings. We relax the sub-Gaussian noise assumption, allowing the proposed bounds to accommodate sub-Exponential noise and beyond. Building on this, for a ReLU neural network estimator, we derive non-asymptotic bounds for both its conditional mean and variance estimation, representing the first result for variance estimation using ReLU networks. Furthermore, we develop a ReLU network based robust bootstrap procedure (Efron, 1992) for constructing confidence intervals for the true mean that comes with a theoretical guarantee on the coverage, providing a significant advancement in uncertainty.

Alejandro Ochoa (Duke University)

Improving modeling of linkage disequilibrium in genetically diverse populations

Recent work has improved how we model genetically diverse populations, which include individuals with different as well as multiple ancestries, in some application such as identifying parts of our genomes associated with diseases. However, many important subsequent analyses only model homogeneous populations or occasionally small numbers of discrete populations, which forces researchers to exclude individuals with minority or multiple ancestries, the last of which includes Hispanics and African Americans. In my group’s latest work, we have focused on improving covariance models between nearby parts of the genome, or loci, an effect called linkage disequilibrium in genetics. We consider a new and elegant model of cross covariance between loci that extends the covariance structure at a single locus when there is a relatedness structure between individuals, and present empirical data that supports this model. The new model immediately suggests a new estimator of the cross covariance parameters, which we demonstrate is more accurate than the standard Pearson estimator in data with diverse populations. Lastly, we apply our new model to association test summary statistics, which enables generalizations for diverse populations to the crucial applications of fine mapping, heritability estimation, and polygenic risk scores. Overall, our work is laying the foundation for expanding the models that can be applied to all individuals in a dataset regardless of their ancestry.

Ana Maria Kenney (UC Irvine)

Distilling heterogeneous treatment effects: Stable subgroup estimation in causal inference

Recent methodological developments have introduced new black-box approaches to better estimate heterogeneous treatment effects; however, these methods fall short of providing interpretable characterizations of the underlying individuals who may be most at risk or benefit most from receiving the treatment, thereby limiting their practical utility. In this work, we introduce a novel method, causal distillation trees (CDT), to estimate interpretable subgroups. CDT allows researchers to fit any machine learning model of their choice to estimate the individual-level treatment effect, and then leverages a simple, second-stage tree-based model to “distill” the estimated treatment effect into meaningful subgroups. As a result, CDT inherits the improvements in predictive performance from black-box machine learning models while preserving the interpretability of a simple decision tree. We derive theoretical guarantees for the consistency of the estimated subgroups using CDT, and introduce stability-driven diagnostics for researchers to evaluate the quality of the estimated subgroups. We illustrate our proposed method on a randomized controlled trial of antiretroviral treatment for HIV from the AIDS Clinical Trials Group Study 175 and show that CDT out-performs state-of-the-art approaches in constructing stable, clinically relevant subgroups.

Marina Meila (University of Washington)

Unsupervised Validation for Unsupervised Learning

Scientific research involves finding patterns in data, formulating hypotheses, and validating them with new observations. Machine learning is many times faster than humans at finding patterns, yet the task of validating these as “significant” is still left to the human expert or to further experiment. In this talk I will present a few instances in which unsupervised machine learning tasks can be augmented with data driven validation.
In the case of clustering, I will demonstrate a new framework of “proving” that a clustering is approximately correct, that does not require a user to know anything about the data distribution. This framework has some similarities to PAC bounds in supervised learning; unlike PAC bounds, the bounds for clustering can be calculated exactly and can be of direct practical utility.
In the case of non-linear dimension reduction by manifold learning, I will present a way around the following well-known problem. It is widely recognized that the low dimensional embeddings obtained with manifold learning algorithms distort the geometric properties of the original data, like distances and angles. These algorithm dependent distortions make it unsafe to pipeline the output of a manifold learning algorithm into other data analysis algorithms, limiting the use of these techniques in engineering and the sciences. Our contribution is a statistically founded methodology to estimate and then cancel out the distortions introduced by any embedding algorithm, thus effectively preserving the distances in the original data. This method is based on augmenting the output of a manifold learning algorithm with “the pushforward Riemannian metric”, i.e. with additional metric information that allows it to reconstruct the original geometry.


Algebra/Number Theory

Location: Pinnacle

Organizer: Alex Barrios (University of St. Thomas), Julia Plavnik (Indiana University )

 

Schedule – Friday, March 7th

3:45 PM – 4:10 PM Yariana Diaz (Macalester College)
4:15 PM – 4:40 PM Monique MĂŒller (Indiana University)
4:45 PM – 5:10 PM Roberto Hernandez (Emory University)
5:15 PM – 5:40 PM Juanita Duque-Rosero (Boston University)

Abstracts

Yariana Diaz (Macalester College)

Completely-decomposable subcategories of quiver representations

Persistence theory draws on quiver representations theory and homology to generate an algebraic summary, called a persistence diagram, which details the appearance and disappearance of topological features in a filtration of a topological space. It has applications in topological data analysis, where topological spaces can be inferred from a sampling of data points. When filtering a topological space by two or more parameters, the associated quivers have indecomposable representations which are more complicated to describe or distinguish from one another. This work describes completely-decomposable subcategories of quiver representations, whose objects can be distinguished from one another in a computationally feasible manner.

Monique MĂŒller (Indiana University)

About exact factorization of fusion categories

The concept of exact factorization of fusion categories was introduced by Gelaki in 2017 and is a categorical generalization of the concept of exact factorization of finite groups. We will show some properties of exact factorization of fusion categories and how to construct an exact factorization from two fusion categories and some data. This is a joint work with Héctor Martín Peña Pollastri and Julia Plavnik.

Roberto Hernandez (Emory University)

Rational Points on a Family of Genus 3 Hyperelliptic Curves

Let \(C\) be a smooth projective curve of genus \(g \geq 2\), by Faltings Theorem we know that there are only finitely many rational points on \(C\). We compute the rational points on a family of genus 3 hyperelliptic curves which are curves of the form \(y^2 = f(x)\) where \(f(x)\) is a polynomial of degree \(2g+1\) or \(2g+2\) via the method of Dem’janenko-Manin.

Juanita Duque-Rosero (Boston University)

Invariants of Artin-Schreier curves

Artin-Schreier curves are curves over algebraically closed fields of characteristic \(p\), defined by the equation \(y^p – y = f(x)\), where \(f(x)\) is a rational function. In this talk, I will present progress towards an algorithm for parameterizing moduli spaces of Artin-Schreier curves in characteristic \(p > 2\) by computing invariants of the curves. This is joint work with Heidi Goodson, Elisa Lorenzo García, Beth Malmskog, and Renate Scheidler.


Harmonic Analysis, PDEs & Differential Geometry

Location: Odyssey

Organizers: Mariana Smit-Vega (Western Washington University), Alejandro Velez Santiago (University of Puerto Rico – Rio Piedras)

 

Schedule – Friday, March 7th

3:45 PM – 4:10 PM Rene Cabrera (UT Austin)
4:15 PM – 4:40 PM Tainara Gobetti Borges (Brown University)
4:45 PM – 5:10 PM Samuel PĂ©rez-Ayala (Haverford College)
5:15 PM – 5:40 PM Soledad Benguria Andrews (University of Wisconsin Madison)

Abstracts

Rene Cabrera (UT Austin)

Smoothing estimates of the Landau Coulomb diffusion

The Landau-Coulomb equation is regarded as one of the most studied equations in PDEs. It models the evolution of a particle distribution in the theory of collisional plasma. We focus on the diffusion operator within the equation only. With this diffusion term, this equation contains a reaction term that could rapidly transform “nice” configurations into singularities. In this talk, we’ll give a brief history regarding well posedness of this equation, then present a result regarding the diffusion operator in the Landau-Coulomb equation that provides much stronger regularization effects than its linear counterpart, the Laplace operator. This is work in collaboration with Maria Gualdani and Nestor Guillen.

Tainara Gobetti Borges (Brown University)

A singular variant of the Falconer distance problem

In this talk, we will discuss the following variant of the Falconer distance problem. Let \(E\) be a compact subset of \(\mathbb{R}^d,\,d\geq 1\), and define \(\Box(E)=\{|(y,z)-(x,x)|\colon x,y,z\in E,\,y\neq z\}.\) We showed using a variety of methods that if the Hausdorff dimension of \(E\) is greater than \(d/2+1/4\), then the Lebesgue measure of \(\Box(E)\) is positive, and we have nonempty interior variants of this result when \(d\geq 2\). This problem can be viewed as a singular variant of the classical Falconer distance problem because considering the points \((x,x)\) in the definition of \(\Box(E)\) poses interesting complications stemming from the fact that the set \(\{(x,x)\colon x\in E\}\subset \mathbb{R}^d\) is much smaller than the sets for which the Falconer-type results are typically established. This talk is based on joint work with Alex Iosevich and Yumeng Ou.

Samuel PĂ©rez-Ayala (Haverford College)

Eigenvalue Estimates on Asymptotically Hyperbolic Manifolds

I will talk about sharp upper bounds for the first eigenvalue of the p-Laplacian on asymptotically hyperbolic manifolds. As a consequence, I’ll show that for any minimal conformally compact submanifold \(Y^{k+1}\) within hyperbolic space, the first p-Dirichlet eigenvalue is exactly \(\)\left(\frac{k}{p}\right)^{p}\). I will then talk about lower bounds on the first eigenvalue of \(Y\) in the case where minimality is replaced with a bounded mean curvature assumption and where the ambient space is a general Poincar\’e-Einstein space whose conformal infinity is of non-negative Yamabe type. This is joint work with Aaron Tyrrell.

Soledad Benguria Andrews (University of Wisconsin Madison)

A generalized radial Brezis-Nirenberg problem

Given \(n\in (2,4),\) we study the existence, nonexistence and uniqueness of positive solutions \(u \in H_0^1(0,R)\) of \(−u‘‘(x)−(n−1)\frac{a‘(x)}{a(x)}u‘(x)=λu(x)+u(x)^p,\) with boundary conditions \(u'(0) = u(R) = 0\), under rather general conditions on \(a(x)\). Here, as in the original problem, \(p=(n+2)/(n-2)\) is the critical Sobolev exponent. This is a joint work with Rafael Benguria, PUC, Santiago, Chile.


Math Education

Location: Pathways

Organizer: Cristina Runnalls (Cal Poly Pomona)

 

Schedule – Friday, March 7th

3:45 PM – 4:10 PM Gloriana Gonzalez (University of Illinois Urbana-Champaign)
4:15 PM – 4:40 PM Luis Fernandez (University of Texas Rio Grande Valley)
4:45 PM – 5:10 PM Antonio Estevan Martinez IV (CSU Long Beach)
5:15 PM – 5:40 PM Amanda Ruiz (San Diego State University)

Abstracts

Gloriana Gonzalez (University of Illinois Urbana-Champaign)

Exploring the Intersections of Mathematical Modeling and Design through Geometry

Mathematical modeling has made it into K-12 classrooms, allowing students to solve authentic problems with math. However, there are limited examples of mathematical modeling in the high school geometry curriculum. A human-centered design approach can engage students in math modeling and broaden students’ mathematical problem-solving opportunities. In the talk, I will share examples of geometry lessons created by the FRACTAL research group as part of a project funded by the National Science Foundation. The lessons engage geometry students in solving design challenges that incorporate mathematical modeling and foster interdisciplinary connections. The design-based lessons are situated in authentic contexts including architecture, engineering, and graphic design. Our goal is to empower geometry students so that they can apply math and design-based thinking to solve problems that are relevant to them and their communities.

Luis Fernandez (University of Texas Rio Grande Valley)

Embracing Diversity: Culturally Relevant Approaches to Mathematics Tasks

U.S. K-12 institutions continue to have a more culturally, linguistically, and racially diverse student population, with Hispanic and Asian students increasing in record numbers. As a result, K-12 teachers, including mathematics teachers, are expected more than ever to design, select, and implement mathematical tasks to address the needs of diverse students. Rich mathematical tasks that incorporate culturally relevant assets offer promise in meeting such demands. However, both preservice teachers (PSTs) and in-service teachers often lack sufficient opportunities to engage with and learn how to incorporate such instructional approaches. In response to this, our team of mathematics teacher educators and PSTs engaged in designing mathematical tasks that are rich and culturally relevant to Hispanic students living in the local area. We outline the process we followed to incorporate the authentic experiences of diverse students into mathematical tasks, providing insights into how educators can avoid overgeneralizations about specific cultural practices through critical and respectful discussions.

Antonio Estevan Martinez IV (CSU Long Beach)

Improving Undergraduate Mathematics Education: A Multi-Pronged Approach to Tackle This Thorny Problem

Improving undergraduate mathematics education is a thorny issue that requires a multi-dimensional, or multi-pronged approach to address. From developing new curriculum, to implementing new grading systems, to offering professional development, and more, education researchers have been tackling this challenge for many decades. In this talk, I address three ways I have contributed to the effort of improving undergraduate mathematics education and discuss where I believe the future of undergraduate mathematics is heading.

Amanda Ruiz (San Diego State University)

Reimagining Mathematics Culture

This talk examines how specific characteristics of mathematics culture that mirror those of white supremacy culture can marginalize or harm individuals, shaping who benefits and who is excluded. Focusing on key characteristics such as either/or thinking, one right way, and individualism, we will explore how these dynamics play out and discuss practical steps educators can take to foster greater equity and inclusivity in classrooms, departments, and mathematics communities. The goal is to inspire reflection and provide tools for meaningful change.



BIG Panel: Career Paths in Math: What if You Don’t Want to Follow your PhD Advisor into Academia?

Location: Centennial Ballroom AB

Friday, March 7th | 2:00 PM – 3:00 PM

 

Panel Organizer and Moderator: Fadil Santosa (John Hopkins University)
Panelists: Genetha Gray (Edward Jones), Alex Gutierrez (Google), Alan Lee (Analog Devices)

Description

There are many career paths one may choose with a PhD in mathematics. One of the more obvious is to follow in your advisor’s footsteps and seek a faculty position. But there are many other options as well. In fact, over 50% of PhDs in mathematics will end up in other positions, including business, industry, and government (BIG). This panel will share their experiences based on their own careers in their field.

 

Undergraduate Opportunities: Building a Strong Foundation for Your Future

Location: Centennial Ballroom AB

Saturday, March 8th | 10:15 AM – 11:15 AM

 

Panel Organizer and Moderator: Marco V. Martinez (North Central College)
Panelists: Cristina Eubanks-Turner (Loyola Marymount University), John Rock (Cal Poly Pomona), Cristina Villalobos (University of Texas Rio Grande Valley)

Description

When you first start off in college there are many opportunities available to you. How and what should you choose from among all the options to build the strongest foundation for the next step in your career. This panel will discuss the value of internships, REUs or other research experiences on campus, and obtaining good references. This panel will also discuss the benefits of graduate studies, how to search for a graduate program, and applying to graduate school.

Graduate School: Training to be a Research Mathematician

Location: IPAM

Saturday, March 8th | 10:15 AM – 11:15 AM

 

Panel Organizer: Bianca Viray (University of Washington)
Panel Moderator: Anthony VĂĄrilly-Alvarado (Rice University)
Panelists: Johnny Guzman (Brown University), Jose Israel Rodriguez (University of Wisconsin – Madison), Mariana Smit Vega Garcia (Western Washington University)

Description

In graduate school, particularly the time after the core coursework, it can be easy to feel unmoored and hard to know if you are doing “the right things”. This panel will focus on demystifying this process, giving guidance on ways to uncover the hidden curriculum, to build and support your community, to push yourself to grow mathematically and as a researcher, and to take care of yourself on the journey.

Navigating Your Path: Success Strategies for Early-Career Mathematicians

Location: IPAM

Saturday, March 8th | 2:30 PM – 3:30 PM

 

Panel Organizer and Moderator: Nancy Rodriguez (University of Colorado, Boulder)
Panelists: Claudia Falcon (Wake Forest University), Paul Hurtado (University of Nevada, Reno), Joaquin Moraga (UCLA)

Description

There are many challenges and obligations when you first start off in your career as a research mathematician. This panel will discuss some of the many expectations on early-career mathematicians such as grant writing, setting priorities (e.g. the art of saying no), how to give good talks, strengthening your CV, and negotiating job offers. The panel will also discuss the importance of networking, finding mentors and developing a community by establishing collaborations with others.

Post-tenure: Now That You Have Tenure, What’s Next?

Location: Centennial Ballroom AB

Saturday, March 8th | 2:30 PM – 3:30 PM

 

Panel Organizer and Moderator: Roummel Marcia (UC Merced)
Panelists: Alvina J. Atkinson (AMS), Hector Ceniceros (UC Santa Barbara), Eun Heui Kim (South Dakota State University)

Description

For many academics, tenure is the culmination of many years of hard work and preparation. But there is also academic life post-tenure, which many do not plan as carefully. This panel will explore possibilities and challenges facing faculty who have achieved tenure. Topics will include advancing to full professor, balancing research with service commitments, exploring new research and teaching directions and administrative roles, and developing leadership skills.


Isiaha Akatlzin Rodriguez

Pregnancy, Diabetes, and Differential Equations: The Population Dynamics of Gestational Diabetes

Gestational Diabetes Mellitus (GDM) is a condition that causes high blood sugar levels in pregnant women, with an observed increased risk of pregnancy complications and developing Diabetes Mellitus (DM) post-pregnancy. Approximately 10.5 pregnancies per 100 deliveries were affected by GDM in 2020, according to the CDC, representing an increase from 4.5 pregnancies per 100 deliveries in 2000. Overall, it affects 5-9\% of pregnant women annually in the US. Despite its prevalence and increasing risk for DM, little mathematical modeling has been done to understand the population flow of women diagnosed with GDM into the diabetic population. Understanding the dynamics of a non-diabetic non-pregnant population into a newly diabetic population may serve as a foundation for researching effective interventions at the population level, before, during, and after pregnancy to reduce both the incidence of GDM and DM. We developed a model of pregnant women, focusing exclusively on women without diabetes who develop GDM. Using primarily CDC data to estimate initial parameter values, and assuming a fixed population growth rate, we observed the non-diabetic population converges to roughly 55.5 million and the diabetic population to approximately 470 thousand. The model also captures the dynamic of pregnant women who develop gestational-diabetes-related complications, and the increased risk factor of developing DM from previous GDM. Equilibrium analysis was conducted to determine the steady state of the solution to the system of ODEs, and we were able to show the positivity and uniform boundedness of the solution. Additionally, sensitivity analysis was conducted on uncertain parameters.

Tahmineh Azizi

Unraveling Cancer: Insights from Mathematical Modeling

Cancer remains one of the most pressing challenges in modern medicine, affecting millions of lives worldwide. Mathematical modeling has emerged as a valuable tool in the study of cancer, offering insights into its complex dynamics, progression, and treatment. By representing biological processes using mathematical equations, researchers can simulate and analyze various aspects of cancer growth, metastasis, and response to therapy. These models incorporate factors such as genetic mutations, cell proliferation, angiogenesis, immune response, and microenvironmental interactions to provide a comprehensive understanding of tumor behavior. Mathematical modeling also facilitates the exploration of novel treatment strategies, optimization of drug dosing regimens, and prediction of treatment outcomes. Moreover, it enables researchers to integrate data from diverse sources, including clinical studies, imaging techniques, and molecular profiling, to improve diagnostic accuracy and personalized medicine approaches. Through this work, we aim to bridge the gap between theoretical research and clinical practice, contributing to the ongoing efforts to improve cancer treatment outcomes.

Tosin Babasola

Bifurcation Analysis of the Impact of Media Campaigns on HIV Epidemic

HIV remains a global public health challenge, requiring multifaceted strategies to curb its spread and impact. Media campaigns have emerged as a powerful tool to raise awareness, promote behavior change, and encourage access to antiretroviral therapy (ART). In this work, we investigate the impact of media campaigns on influencing HIV transmission dynamics. To achieve this, we formulate an HIV transmission model that incorporates the influence of media campaigns and explore the relationship between these campaigns and disease spread. To further understand the transmission dynamics, we conduct a bifurcation analysis using center-manifold theory and establish the conditions for the occurrence of a backward bifurcation. A model simulation and sensitivity analysis are then performed using Latin hypercube sampling to demonstrate the role of the effective contact rate in driving the proliferation of the HIV epidemic.

Jose Colchado

Taxman Game’s Optimal Second Move

The taxman game begins with a list of integers from 1 to some integer N . The player may only select a number with proper divisors left on the list, which the taxman then collects. When no numbers with proper divisors left on the list remain, the taxman collects all remaining numbers, and whoever has the largest sum of numbers wins. Previous research shows that the player’s optimal first move is the largest prime on the list, and their optimal second move is the largest square of a prime on the list if N ≀ 1000 except for N = 8, 20, and 120 . We show that this is the optimal second move for all N > 120. Beyond the second optimal move, no clear ”optimal” move exists, making further moves impractical. Instead, we analyze Chess’s strategic framework to develop a generalized algorithm for any N.

Mont Cordero

The Tropical Degree Of A Tropical Root Surface

The field of tropical geometry arose from the desire to convert an algebraic variety \(V\) into a piecewise linear combinatorial structure Trop \(V\) that retains a lot of information about \(V\), such as degree, dimension, etc. We study tropical surfaces that arise from the root systems of type \(A\) rather than from the tropicalization of an algebraic variety. Our main result is that the tropical root surface of \(A_{n-1}\) has degree \(frac{1}{2}n(n-1)(n-2)\).}

Alvaro Cornejo

Equatorial Flow Triangulations of Gorenstein Flow Polytopes

Generalizing work of Athanasiadis for the Birkhoff polytope and Reiner and Welker for order polytopes, in 2007 Bruns and Römer proved that any Gorenstein lattice polytope with a regular unimodular triangulation admits a regular unimodular triangulation that is the join of a special simplex with a triangulated sphere. These are sometimes referred to as equatorial triangulations. We apply these techniques to give purely combinatorial descriptions of previously-unstudied triangulations of Gorensten flow polytopes. Further, we prove that the resulting equatorial flow polytope triangulations are usually distinct from the family of triangulations obtained by Danilov, Karzanov, and Koshevoy via framings. We find the facet description of the reflexive polytope obtained by projecting a Gorenstein flow polytope along a special simplex.

Isabel Corona Guevara

Stepwise Bayesian active learning for sparse polynomial chaos expansion

Polynomial chaos expansion (PCE) is a surrogate modeling approach that approximates a model’s response using an orthogonal basis of polynomials. Active learning is a machine learning approach in which a subset of data points is strategically selected from a pool to train the model. The goal is to select the most informative points to enhance performance while keeping the size of the training set low. In this work, state-of-the-art sparse Bayesian learning techniques are employed to construct a sparse PCE, integrated with Bayesian active learning (BAL) strategies to adaptively identify the training set. We introduce a step-wise BAL algorithm, where data points are iteratively added to or removed from the training set at each iteration. The proposed methods are tested on several numerical examples, comparing the performance of BAL-based models with those built using randomly selected training sets. The results demonstrate that the BAL techniques achieve superior performance with fewer training points, highlighting their effectiveness in enhancing model efficiency and accuracy.

Elsie Cortes

Using Encoder-Decoder Neural Networks to Model Optical Cloaking Devices

We use an encoder-decoder neural network to solve the forward and inverse scattering transmission problems in 2D multilayered media. This allows us to predict how waves scatter and identify the optimal parameters needed to design optical cloaking devices. By fine-tuning these parameters, we aim to manipulate light in a way that renders objects invisible. Our approach demonstrates the potential of deep learning in advancing optical cloaking technology and the design of metamaterials with controllable scattering properties. We show results for designing cloaks defined by circular boundaries and discuss extensions to more exotic boundary shapes, and how we might find more optimal cloaking device constructions.

Maria Luisa Daza Torres

Bayesian sequential approach to monitor COVID-19 variants through test positivity rate from wastewater

We present a statistical model to enhance the monitoring of COVID-19 outbreaks by correlating SARS-CoV-2 RNA concentrations in wastewater with the test positivity rate (TPR). To capture the non-autonomous nature of the prolonged pandemic, we introduce an adaptive scheme that can effectively model changes in viral transmission dynamics over time. The TPR is modeled through a sequential Bayesian approach with a Beta regression model using SARS-CoV-2 RNA concentrations measured in WW as covariable.
This approach allows us to compute the TPR based on wastewater measurements and to incorporate changes in viral transmission dynamics through the adaptive scheme. Our results demonstrate that the proposed model provides a more comprehensive understanding of COVID-19 transmission dynamics compared to relying solely on clinical case detection. The model can inform public health interventions and serve as a powerful tool for monitoring COVID-19 outbreaks.

Baboucarr Dibba

Hierarchical Neural Networks with Delay

The first goal of this talk is to introduce a new type of p-adic reaction–difusion cellular neural network with delay. We study the stability of these networks and provide numerical simulations of their responses.

Juan Felipe Osorio Ramirez

Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis

We introduce a novel kernel-based framework for learning differential equations and their solution maps that is both data-efficient and computationally efficient. Our approach is mathematically interpretable and backed by rigorous theoretical guarantees, including quantitative a priori worst-case error bounds. Furthermore, numerical benchmarks demonstrate significant improvements in both computational complexity and accuracy, achieving a reduction in relative error by one to two orders of magnitude compared to state-of-the-art methods.

Marilin Guerrero Laos

The Inhomogeneous Diffusion Equation of Wentzell Type With Discontinuous Data

Let Ω ⊂ R^N (N ≄ 3)) be a bounded domain with a Lipschitz continuous boundary Γ. We study the existence and uniqueness of weak solutions for a non-homogeneous parabolic diffusion problem in Ω, given by the equationu t − Au = f. Here, A is a second-order differential operator with measurable and bounded principal coefficients, not necessarily symmetric, and measurable and unbounded lower-order coefficients.
We consider non-homogeneous Wentzell-type boundary conditions on Γ, expressed as N*_v(u) − Bu = g, where N*_v(u) represents the conormal derivative of u and B is a second-order operator with similar characteristics to A.
Additionally, under minimal assumptions, we obtain a priori estimates for the weak solution of the parabolic problem. These estimates depend on the norms of the data and the initial condition, allowing us to analyze the behavior and regularity of the solution under the specific Wentzell-type boundary conditions.

Alex Gutierrez Diaz

Stackelberg Network Interdiction for Vulnerability Analysis in the U.S. Leading-Edge Chip Supply Chain

This poster highlights the analysis of the U.S.’s leading chip supply chain to determine the most critical inter-country company relations in terms of their overall disruption potential. We develop a directed graph model consisting of the key players in the U.S.’s leading chip supply chain and define metrics to assess the model’s weaknesses based on revenue and geographical distance. We employ an attack-defense network interdiction model and use its dual formulation to identify the minimal set of player relations causing the highest levels of disruption based on objective maximization and minimization of revenue and distance respectively.

Kimberly Herrera

Determining Quasiperiodicity with Cup Products

Gakhar and Perea showed that quasiperiodic time series are those whose sliding window point clouds are dense in tori. The topological structure of these time series can be captured via persistence diagrams, however there exist time series with persistence diagrams which have seems to have the same topological features as quasiperodic functions but whose sliding window point clouds are not dense in a torus; we consider these “fake quasiperiodic” functions. To distinguish between the quasiperiodic functions and the “fake quasiperiodic” functions, we propose an algorithm that incorporates both persistent cohomology and cup products, which assigns the to a persistence diagram what we call a quasiperiodic score. This algorithm achieves a more precise detection of quasiperiodicity and demonstrates the robustness when applied to various dissonant signals even when different kinds of noise was added.

Victoria Kala

A Thermomechanical Hybrid Incompressible Material Point Method

We present a novel hybrid incompressible flow/material point method solver for simulating the combustion of flammable solids. Our approach utilizes a sparse grid representation of solid materials in the material point method portion of the solver and a hybrid Eulerian/FLIP solver for the incompressible portion. We utilize these components to simulate the motion of heated air and particulate matter as they interact with flammable solids, causing combustion-related damage. We include a novel particle sampling strategy to increase Eulerian flow accuracy near regions of high temperature. We also support control of the flame front propagation speed and the rate of solid combustion in an artistically directable manner. Solid combustion is modeled with temperature-dependent elastoplastic constitutive modeling. We demonstrate the efficacy of our method on various real-world three-dimensional problems, including a burning match, incense sticks, and a wood log in a fireplace.

John Lentfer

The sign character of the triagonal fermionic coinvariant ring

We determine the trigraded multiplicity of the sign character of the triagonal fermionic coinvariant ring \(R_n^{(0,3)}\). As a corollary, this proves a conjecture of Bergeron (2020) that the dimension of the sign character of \(R_n^{(0,3)}\) is \(n^2-n+1\). We also give an explicit formula for double hook characters in the diagonal fermionic coinvariant ring \(R_n^{(0,2)}\). Finally, we give a multigraded refinement of a conjecture of Bergeron (2020) that the dimension of the sign character of the \((1,3)\)-bosonic-fermionic coinvariant ring \(R_n^{(1,3)}\) is \(\frac{1}{2}F_{3n}\), where \(F_n\) is a Fibonacci number.

Gyivan Lopez-Campos

Borsuk and VĂĄzsonyi problems through Reuleaux polyhedra

The Borsuk conjecture and the VĂĄzsonyi problem are two attractive and famous questions in discrete and combinatorial geometry, both based on the notion of diameter of bounded sets. In this poster, we present an equivalence between the critical sets with Borsuk number 4 in \(\mathbb{R}^3\) and the minimal structures for the VĂĄzsonyi problem by using the well-known Reuleaux polyhedra. The latter lead to a full characterization of all finite sets in \(\mathbb{R}^3\) with Borsuk number 4.
The proof of such equivalence needs various ingredients, in particular, we proved a conjecture dealing with strongly critical configuration for the VĂĄzsonyi problem and showed that the diameter graph arising from involutive polyhedra is vertex (and edge) 4-critical. This is a joint work with DĂ©borah Oliveros and Jorge RamĂ­rez AlfonsĂ­n.

Thomas Martinez

Affine Deodhar Diagrams and Rational Dyck Paths

Given a bounded affine permutation f, we introduce affine Deodhar diagrams for f, similar to affine pipe dreams introduced by Snider. We explore combinatorial moves between these diagrams and use these moves to establish a bijection between Deodhar diagrams and restricted Dyck paths for a special class of bounded affine permutations. This resolves an open problem posed by Galashin and Lam.

Haily Martinez

Congruences in arithmetic progression for lecture hall partitions

In 1997 Bousquet-Melou and Erikkson proved a finite version of Euler’s “odd = distinct” partitions theorem and thus lecture hall partitions were discovered. For positive integers n and m, this finite version can be stated as follows: p(n│odd parts,none larger than 2m-1)=LH_m(n), where LH_m denotes the lecture hall partitions of n with length m. This presentation will discuss families of Ramanujan-like congruences in arithmetic progression for the lecture hall partitions. For example, for all integers
k>0, LH_3 (15k-1)≡0(mod 5)
LH_4 (105k-1)≡0(mod 7)
LH_3 (3465k-7)≡0(mod 11)
These results have similarities to congruences for p(n,d), the function enumerating the partitions of n into at most d parts, established by Kronholm in 2005.

Efren Mesino Espinosa

Generalized Quasi-linear Fractional Venttsel’-Type Problems Over Non-Smooth Regions

We investigate the solvability and establish a priori estimates for the generalized elliptic quasi-linear fractional problem involving the regional fractional p-Laplace operator with Neumann or Robin boundary conditions. First, we prove the existence and uniqueness of weak solutions for the problem, and we show that such solutions are globally bounded. Moreover, we establish a priori estimates for the difference of weak solutions of our problem. Additionally, we present results on inverse positivity and a weak comparison principle.

Cesar Meza

Generic torus orbit closures in matrix Schubert varieties

T-varieties are affine varieties equipped with an action of a torus T. The complexity of a normal T-variety is the codimension of the largest T-orbit. In this poster, we focus on the complexity of a specific class of T-varieties called matrix Schubert varieties. Introduced by Fulton in 1992, matrix Schubert varieties consist of square matrices satisfying certain constraints on the ranks of their submatrices. The cross product of n-by-n diagonal invertible matrices is a torus that acts on certain affine subvarieties of a matrix Schubert variety. Building up from results by Escobar–MĂ©szĂĄros and Donten-Bury–Escobar–Portakal, we show that for a fixed n, the complexity of these subvarieties of a matrix Schubert variety with respect to this action can be any integer between 0 and (n − 1)(n − 3), except 1.

Kayode Oshinubi

Accounting for spatial variation in climatic factors predicts spatial variations in mosquito abundance in the desert southwest

Mosquito population dynamics are particularly sensitive to local weather conditions, and previous studies have demonstrated that mosquito-borne disease outbreaks can be spatially concentrated. In this study, we build a climate-driven model of mosquito population dynamics, and we compare whether predictions of mosquito abundance at the county-scale are improved by accounting for sub-county climate variation. First, we built a simple mechanistic model of mosquito population dynamics that is influenced by both daily temperature and 30-day accumulated precipitation. Then, we use clustering algorithms to divide Maricopa County into clusters with similar variation in temperature and precipitation, combining zip codes into clustered communities. Our goal is to evaluate the effectiveness of this cluster-based modeling for predicting mosquito abundance in Maricopa County. Therefore, we compare two clustering techniques: one based only on neighbor distance, and the method based on time series of climate data. We then use MCMC to fit the mechanistic model using averaged climate data in each cluster. We show how the simple, climate-forced modeling does a good job at estimating detailed mosquito abundance trajectories throughout a ten-year period. Most importantly, we discovered that this spatial variation in climate improves the fit of the model to the data, emphasizing how small-scale variation cause heterogeneities in mosquito population dynamics. This study demonstrates that constructing models at a small scale improves explanation of mosquito population dynamics and we anticipate that such modeling efforts will also aid in using weather forecasts to predict mosquito populations, aiding in efforts to control the spread of infectious disease.

Kimberly Savinon

An a posteriori error field calculation of the finite element method

Many computer simulations use numerical methods to estimate the solutions of PDE systems. Some of the most popular methods are finite difference methods (FDM), finite element methods (FEM), and finite volume methods (FVM). In application settings, the analytical solution is not available, so there is an unknown numerical error. Auxiliary computations may be used to assess this error, known as a posteriori error estimates. There are many varieties of such error estimates; one class of interest computes entire fields of error that can be used to create a detailed picture of the error over the computational domain. Direct error field calculations are not common or well-understood for FEM. It will be shown how to adapt techniques developed with FDM and FVM to compute a posteriori error fields using FEM. A computational example will be provided to illustrate the quality of the error field even where the solution lacks differentiability and yields a complex error structure that is difficult to capture.

Kevin D Silva Perez

Diffusion over Bronchial Trees: Construction and Approximation Results

In this paper following the results and notions held in [1] about a ramified domain class with fractal boundary Γ∞, we construct a pair of successions an ↘ H d(Γ∞), bn ↗ H d(Γ∞) such that 0 < bn ≀ H d(Γ∞) ≀ an < ∞. On the other hand, we extend the fine regularity theory for weak solutions in a parabolic diffusion problem (1) with variation in the pa- rameters (a, Ξ ) and Dirichlet and Robin boundary conditions (in the generalized sense) on a d-set with certain fractal properties, where sobolev spaces can be defined W1,p, for an appropriate d.
u_t – Δu + αu = f(x,t) en Ω × (0,∞).
(∂u/∂Μ) + ÎČu = g(x,t) en Γ∞ × (0,∞).
u = 0 en (∂Ω \ Γ∞) × (0,∞).
u(x₀,t) = u₀ en (Ω \ (∂Ω \ Γ∞)) × (0,∞).
Moreover, if a < a∗, then Ω is a (Δ,ÎŽ)-domain, and in this case we use the results of [2] to check that the weak solutions are Holder continuous over Ω, and by taking a = a∗, Ω is weakened to the point of not being a (Δ,ÎŽ)-domain, and consequently we prove that the solutions can be globally bounded. Thus, from functional methods we state existence, uniqueness and boundedness results for the solutions of the above class of diffusion prob- lems, and we point out some applications of interest.

Antonio Torres

Slicing Convex Polytopes

We investigate the sections of convex polytopes obtained by intersecting them with affine hyperplanes. Our work focuses on establishing tight bounds on the maximum number of vertices attainable in these slices, as well as analyzing the sequence of vertex counts from all possible slices and the gaps within that sequence. In particular, we emphasize key polytopes such as the cyclic polytope and hypercubes.


Main Organizers

Mario Bañuelos (Fresno State)

Mario Bañuelos is an Associate Professor of Mathematics at California State University, Fresno (Fresno State). He is from the small, agricultural town of Delano, California and a first-generation college student. He earned his B.A. in Mathematics from Fresno State and obtained his Ph.D. in Applied Mathematics from the University of California, Merced. His research group focuses on machine learning approaches for genomics, disease prediction, and mathematical biology. He is committed to bringing more research opportunities to the Central Valley as well as positively impacting the community through culturally-sustaining research and teaching.

Selenne Bañuelos (CSUCI/IPAM)

Dr. Selenne Bañuelos is the Associate Director at IPAM and an Associate Professor of Mathematics at Cal. State Univ. Channel Islands. She earned her B.S. from UCSB and her Ph.D. from USC. Her research focuses on differential and difference equations, dynamical systems, and mathematical biology, with her latest collaboration modeling combination treatments of phage and antibiotics for multi-drug-resistant infections. Dr. Bañuelos is Co-Editor-in-Chief of La Matematica, the official journal of the AWM. She is a Linton-Poodry SACNAS Leadership Fellow, an MAA Project NExT Fellow, and a recipient of the 2020 MAA Henry L. Alder Award. She has served as Co-PI on several institutional-level NSF grants. Born and raised in Boyle Heights, Los Angeles, she is deeply committed to creating and organizing opportunities that expand access to STEM education for women and historically underrepresented minorities.
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Cynthia Flores (CSUCI)

Dr. Cynthia Flores is an American Latina mathematician and Associate Professor at California State University Channel Islands. She is dedicated to expanding opportunities for exceptional undergraduates in STEM through research, mentorship, and innovative teaching. She earned her BS and MS in mathematics from California State University Northridge and completed her PhD at the University of California Santa Barbara in 2014, specializing in dispersive partial differential equations. She is a recipient of the NSF PRIMES award and has served as a Co-PI on multiple NSF-funded projects, including AGEP, PUMP, and HSI-SMART. She also collaborates with community partners to design undergraduate research projects such as the NASA Undergraduate Research Challenge. Inspired by her mentors, she strives to create meaningful research and learning experiences that empower students in the mathematical sciences community.
Juan Meza

Juan Meza (UC Merced)

Juan C. Meza, Ph.D., is currently serving as the Associate Director for the Simons Laufer Mathematical Sciences Institute. Prior to this, he served as Division Director at the National Science Foundation’s Division of Mathematical Sciences (2018-2022) and as Dean of the School of Natural Sciences at the University of California, Merced (2011-2017). As the Dean, he served as the primary executive officer for the School of Natural Sciences and was responsible for establishing a vision and strategy for the School; recruiting, retaining, and supporting talented faculty; and advancing diversity in all academic and administrative areas. Juan also holds a position as Professor of Applied Mathematics, where his current research interests include nonlinear optimization with an emphasis on methods for parallel computing.
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Tony VĂĄrilly-Alvarado (Rice University)

Tony VĂĄrilly-Alvarado is a Professor of Mathematics at Rice University, in Houston TX. He earned his AB in Mathematics from Harvard University and his Ph.D. Mathematics from UC Berkeley in 2009. His research focuses on arithmetic algebraic geometry, although he also dabbles in applications of algebraic geometry to coding theory and inverse problems. He received an NSF CAREER grant in 2014, and in 2020 was named a Fellow of the American Mathematical Society.

Plenary Speakers

Federico Ardila (San Francisco State University)

Federico Ardila-Mantilla is a Colombian-American mathematician, educator, and musician. He has received the NSF CAREER Award and Simons Fellowship for his research, the MAA National Haimo Award for his teaching, and the AMS “Mathematics Programs that Make a Difference” Award for his service work. Federico investigates objects in algebra, geometry, topology, and applications by understanding their underlying combinatorial structure. His interests include polytopes, matroids, hyperplane arrangements, Lie and Coxeter combinatorics, Hopf algebras, and tropical geometry. He was an Invited Speaker in the International Congress of Mathematicians 2022, a Clay Lecturer in 2024, and a Member of the Institute for Advance Study in Princeton in 2024-25. Federico is committed to fostering an increasingly just, equitable, and welcoming community of mathematicians. He has advised more than 50 thesis students, codirected the MSRI-UP program for students from underrepresented groups, coorganized the first Latinx in Math Conference in 2015, directs the SFSU-Colombia Combinatorics Initiative, and hosts over 200 hours of combinatorics lectures online.

Erika Tatiana Camacho (University of Texas San Antonio)

Dr. Erika Tatiana Camacho is the BerriozĂĄbal Endowed Chair and professor in UTSA’s mathematics and NDRB departments. Camacho has a long and very successful career in and outside of academia as a mathematical biologist, researcher, educator, mentor and leader in racial and gender equity. She is one of two researchers in the world leading the mathematical work on photoreceptor degeneration and one of the few mathematicians with a wet lab where she is focusing on metabolic adaptation and protective stress responses in diseased and aging retinas. Camacho was a Fulbright Research Scholar at the Institut de la Vision-Sorbonne UniversitĂ© in Paris 2022-2023 and a Full Professor in SoMSS at Arizona State University 2007-2023. Between 2019-2022 she was Program Director co-Lead of the NSF HSI Program and Program Director of the ADVANCE and the Racial Equity in STEM Education programs. Her leadership, scholarship, and mentoring have won her numerous national and regional recognitions including named a 2024 AMS Fellow and AWM Fellow, the 2019 AAAS Mentor Award, 2014 PAESMEM award from the White House, 2022 NSF Director’s Award for Superior Accomplishment, 2023 M. Gweneth Humphreys Award, 2020 SACNAS Presidential Award, 2018 AAHHE Outstanding Latino/a Faculty Award, and 2013-2014 MLK Visiting Assistant Professor of Mathematics at Massachusetts Institute of Technology (MIT).

Sara Del Valle (Los Alamos National Laboratory)

 
Carrie Diaz Eaton

Carrie Diaz Eaton (Bates College)

Dr. Carrie Diaz Eaton is an Associate Professor of Digital and Computational Studies at Bates College, and co-founder and PI of the Institute for a Racially Just, Open, and Inclusive STEM education (RIOS Institute). Dr. Diaz Eaton is a proud first generation Peruvian-American mother who deeply values the complex interplay at the intersection of their identities, professional activism in STEM education, and her work. Dr. Diaz Eaton’s research explores the intersection of mathematics, computation, and social justice, often addressing how structural inequities manifest in educational systems. They are a leading voice in national conversations on open education, ethics in computational science, and collaborative practices that bridge traditional academic boundaries.

Johnny Guzman (Brown)

Johnny GuzmĂĄn is a professor of applied mathematics at Brown University. He earned his PhD from Cornell University and before that earned his BS from California State University-Long Beach. His research focuses on numerical methods for partial differential equations. Johnny was raised in Southern California.

J Maurice Rojas (Texas A&M)

J. Maurice Rojas was born in Los Angeles, of Colombian immigrant parents. His degrees are from UCLA (B.S. math/applied science) and UC Berkeley (M.S. computer science and Ph.D. applied mathematics), and his Ph.D. advisor was Fields Medalist Steve Smale. Maurice is an AMS Fellow and has had visiting appointments at NSF (computer science directorate), Technical University of Munich (as a von Neumann professor), Johns Hopkins, and was an NSF CAREER Fellow and NSF Postdoctoral Fellow earlier in his career. Maurice is now executive associate head of teaching operations, and a full professor, in the mathematics department at Texas A&M University. He works at the intersection of algebraic geometry, algorithmic complexity, and number theory.

Rodolfo Torres (UC Riverside)

Rodolfo H. Torres is a Distinguished Professor of Mathematics and Vice Chancellor for Research and Economic Development at the University of California, Riverside (UCR). Before arriving to UCR he was University Distinguished Professor of Mathematics at the University of Kansas. Torres did his undergraduate studies at the Universidad Nacional de Rosario, Argentina, received his PhD from Washington University and held postdoctoral positions at New York University and the University of Michigan. He was elected to the inaugural class of Fellows of the American Mathematical Society and featured in 2017 in the Calendar of Latinxs and Hispanics in Mathematical Sciences. Torres’ research focuses on Fourier analysis and applications in partial differential equations, signal analysis, and biology.


Session Organizers

Alex Barrios (University of St. Thomas)

Alex Barrios is a number theorist specializing in Diophantine geometry, using algebraic and geometric techniques to tackle number-theoretic questions. Part of his research focuses on bridging the gap between theoretical and computational aspects of elliptic curves. In addition, Dr. Barrios is passionate about introducing undergraduates to original research in number theory and co-directs the Pomona Research in Mathematics Experience (PRiME). Raised in Miami, FL, and of Colombian descent, Dr. Barrios began his studies at Miami Dade Community College before earning a Sc.B. in mathematics from Brown University. He completed his M.S. and Ph.D. in mathematics at Purdue University and is now an assistant professor of mathematics at the University of St. Thomas in St. Paul, MN.
Janet Best

Janet Best (Ohio State University)
Laura Escobar

Laura Escobar (Washington University St. Louis)

Laura Escobar grew up in Bogotá, Colombia, where she completed her bachelors in mathematics at Universidad de los Andes. Afterwards, she did a masters at San Francisco State University with Federico Ardila as her advisor. She completed her Ph.D. in 2015 at Cornell University and her advisor was Allen Knutson. She was a JL Doob Research Assistant Professor at UIUC and an Einstein fellow at TU Berlin. Also, she was a postdoctoral fellow during the Fall 2016 Thematic Program in “Combinatorial Algebraic Geometry” at The Fields Institute for Research in Mathematical Sciences. After some time as a professor at Washington University in St. Louis, she is now an Associate Professor at UC Santa Cruz.
Claudia Falcon

Claudia Falcon (Wake Forest University)

Claudia Falcon is an Assistant Professor in the Department of Mathematics at Wake Forest University. She grew up in Havana, Cuba, and moved to the US in high school. She earned her BS and Ph.D. in Applied Mathematics from the University of North Carolina at Chapel Hill. Her research focuses on fluid dynamics and partial differential equations. She directs the Fluid Dynamics Lab at Wake Forest, where she mentors students in interdisciplinary research with applications to environmental problems such as erosion. She is also the founder of the WFU’s Girls Talk Math chapter, a math and media summer camp.
Paul Hurtado

Paul Hurtado (University of Nevada, Reno)

Dr. Hurtado is an Associate Professor in Mathematics & Statistics at the University of Nevada, Reno, and a faculty member in the Ecology, Evolution, and Conservation Biology graduate program. He serves on the Society for Mathematical Biology’s DEI Committee. Raised in Pueblo, CO, he studied Math, Biology, and Chemistry at the University of Southern Colorado (now Colorado State University-Pueblo). He participated twice in the Mathematical & Theoretical Biology Summer Institute at Cornell, where he later earned a Ph.D. in Applied Mathematics. He was a Postdoc at the Mathematical Biosciences Institute and Aquatic Ecology Laboratory at Ohio State. Dr. Hurtado’s research uses techniques from dynamical systems, probability, stochastic processes and statistics to develop and analyze mathematical models to tackle questions in population ecology, infectious disease and immunology, including any interesting mathematical questions that emerge from these applications.

Guido Montufar (UCLA)

Guido Montufar is a Professor of Mathematics and Statistics & Data Science at UCLA. He obtained degrees in Mathematics and Physics from the TU Berlin and the Dr. rer. nat. in Mathematics from Leipzig University as an IMPRS Fellow at MPI MiS. His research spans topics of mathematical machine learning and deep learning. He has received recognitions including the NSF CAREER award, the Sloan Research Fellowship, and the ERC Starting Grant. He serves as the Research Group Leader of Mathematical Machine Learning at MPI MiS. Guido grew up in Panama, Guatemala, and Colombia, before moving to Germany and the USA.

Julia Plavnik (Indiana University)

Julia Plavnik is an Argentinian mathematician. She earned her Ph.D. in Mathematics from Universidad Nacional de CĂłrdoba, Argentina. Her research is on quantum symmetries. Julia’s latest work is on the classification and construction of tensor, fusion, and modular categories. She is also very interested in link invariants, cohomological aspects of non-commutative algebras, such as Hopf algebras, and the mathematical foundation of topological phases of matters. Julia is a principal investigator in the Simons Collaboration on Global Categorical Symmetries and an NSF CAREER grant. She received the 2022 Outstanding Faculty Mentor Award from CEWIT, IU. In 2023, Julia was awarded a Humboldt Research Fellowship for Experienced Researchers to visit UniversitĂ€t Hamburg. Julia has a 6-year-old daughter.
Cristina Runnalls

Cristina Runnalls (Cal Poly Pomona)

Dr. Cristina Runnalls is an Associate Professor of Mathematics & Statistics at Cal Poly Pomona, where she has worked since 2018. She earned her B.A. in Mathematics at Fresno State, and her M.S. in Mathematics and Ph.D. in Mathematics Education at the University of Iowa. Her research focuses broadly on addressing issues of access and opportunity for culturally and linguistically diverse students in mathematics, grounded within a framework that acknowledges the powerful social, cultural, and political influences in the classroom. Within this thread, she works extensively with both pre-service and in-service teachers to help support their math classrooms towards becoming a more socially just and rehumanizing space.
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Mariana Smit-Vega Garcia (Western Washington University)

Mariana Smit Vega Garcia earned her undergraduate degree from the Universidade de SĂŁo Paulo, in Brazil, and her Ph.D. in Mathematics from Purdue University in 2014. She was a post-doc at the University of Duisburg-Essen in Germany and at the University of Washington. In 2018, she joined Western Washington University as an Assistant Professor, being promoted to Associate Professor in 2021, and Professor in 2024. Dr.Smit Vega Garcia works in the areas of mathematical analysis and combinatorics. Her research has been funded by the NSF through grants from 2021-2025 and 2024-2027, and she was awarded the 2024 Karen Edge Fellowship. She was also awarded the 2023 Peter J. Elich Excellence in Teaching Award.
David Uminsky

David Uminsky (University of Chicago)

David Uminsky is the Executive Director of the Data Science Institute and Senior Research Associate at the University of Chicago since 2020. Previously, he was Associate Professor of Mathematics and Executive Director of the Data Institute at the University of San Francisco (USF). His research interests include machine learning, signal processing, pattern formation, and dynamical systems. David is an Associate Editor for the Harvard Data Science Review and was named a 2015 Kavli Frontiers of Science Fellow. He founded USF’s BS in Data Science and directed its MS program from 2014-2019. Before USF, he was an NSF and UC President’s Fellow at UCLA and won the Chancellor’s Award for outstanding postdoctoral research.
Alejandro Velez Santiago

Alejandro Velez Santiago (University of Puerto Rico – Rio Piedras)

Alejandro VĂ©lez-Santiago is an associate professor of Mathematics at the University of Puerto Rico – RĂ­o Piedras (UPRRP). He did both his BS and Ph.D. in Mathematics at the UPRRP. His research focuses in the areas of Partial Differential Equations (PDEs) and Analysis, mainly on the solvability and regularity theory of various boundary value problems over non-smooth regions. He also works on operator semigroups, fractal geometry, and potential theory (among others).

Andrés Vindas-Melendez (Harvey Mudd College)

AndrĂ©s R. Vindas MelĂ©ndez, Ph.D., is a Costa Rican-American mathematician raised in Lynwood, South East Los Ángeles, California. A first-generation college graduate, he serves as an Assistant Professor of Mathematics at Harvey Mudd College. Previously, he held a National Science Foundation Postdoctoral Fellowship and was a Lecturer at UC Berkeley and was a Postdoctoral Scholar at the Mathematical Sciences Research Institute (now SLMath). He participated in SLMath’s Fall 2023 program on Algorithms, Fairness, & Equity and was a research scholar at ICERM focusing on Data Science & Social Justice during the Summers of 2022 and 2023. Vindas MelĂ©ndez earned his Ph.D. from the University of Kentucky, where he also received a graduate certificate in Latin American, Caribbean, and Latinx Studies. His research interests include algebraic, enumerative, and geometric combinatorics, as well as applications of mathematics and data science for social justice. He is dedicated to fostering a supportive community that enhances confidence in mathematics.


Session Speakers

Soledad Benguria Andrews

Soledad Benguria Andrews (University of Wisconsin Madison)

Soledad Benguria is Teaching Faculty at University of Wisconsin – Madison. She earned her Licenciatura en Matematicas from Pontifi cia Universidad Catolica de Chile and her Ph.D. in Mathematics from University of Wisconsin – Madison. Her research focuses on differential equations and several complex variables. Her latest project is on a generalization of a radial model of the Brezis-Nirenberg problem. Soledad grew up in Santiago, Chile.
CABRERA_RENE

Rene Cabrera (UT Austin)

My name is Ren®e Cabrera. I am originally from Alhambra, a city located east of Los Angeles, California. I completed my undergraduate studies at UCLA, where I earned a Bachelor of Science in Mathematics. I then attended the California State University, Los Angeles, where I pursued a master’s degree in math. Subsequently, I attended the University of Massachusetts, Amherst, where I defended my dissertation under the guidance of Professor Nestor Guillen. Currently, I am a postdoctoral researcher at the University of Texas at Austin, collaborating with Maria Gualdani and Matias Delgadino. My research focuses on the analysis of partial differential equations, calculus of variations, and optimal transport. I love teaching math to undergraduate students. One of my favorite classes to teach is analysis. My dream is to pursue a career as a professional research mathematician, as a professor, to contribute to math and to impart knowledge to students.
Michael Cortez

Michael Cortez (Florida State University)

Michael Cortez is an Associate Professor in the Department of Biological Science at Florida State University. He earned is BS in Chemistry and Mathematics at Hope College and his Ph.D. in Applied Mathematics from Cornell University. His research focuses on developing differential equation models to answer questions in ecology, epidemiology, and evolution. His latest projects use models to explore how the biodiversity of host communities affects disease dynamics and how adaptation in prey or their predators alters the population-level dynamics of predator-prey systems.
Maricela Cruz

Maricela Cruz (Kaiser Permanente Washington Health Research Institute)

Maricela Cruz is an Assistant Biostatistics Investigator at Kaiser Permanente Washington Health Research Institute and Affiliate Assistant Professor at the University of Washington Department of Biostatistics. Her research primarily focuses on developing novel statistical methods to assess and evaluate the impact of healthcare interventions in observational settings.
Mayteé Cruz-Aponte

Mayteé Cruz-Aponte (UPR-Cayey)

Mayteé Cruz-Aponte serve as Coordinator of the Natural Sciences Program at UPR Cayey, and formerly held the position of Director of the Department of Mathematics-Physics. She earned her BS in Computational Mathematics from UPR Humacao, her MS in Mathematics from University of Iowa and her Ph.D. in Applied Mathematics for Life and Social Sciences, with an emphasis in mathematical epidemiology, from Arizona State University. Her research focuses on mathematical models of infectious diseases, specifically examining the effectiveness of interventions in controlling or eradicating disease spread. She has published multiple articles with colleagues and undergraduate students in her Biomathematics Computational Laboratory and has mentored over 60 research assistants.
Carina Curto

Carina Curto (Brown University)

Carina Curto is a Professor of Applied Mathematics and Brain Science at Brown University. She received an A.B. in Physics from Harvard University in 2000 and a Ph.D. in Mathematics from Duke University in 2005. During her postdoctoral years at Rutgers and NYU, she transitioned to research in theoretical and computational neuroscience. Before moving to Brown, Curto was a professor at the University of Nebraska-Lincoln (2009-2014) and at Penn State University (2014-2024). Her research focuses on theory and analysis of neural networks and neural codes, motivated by questions of learning, memory, and sequence generation in cortical and hippocampal circuits. Curto’s work uses and develops tools in applied algebra, geometry, topology, and dynamical systems.

Yariana Diaz (Macalester College)

Yariana Diaz is a Postdoctoral Fellow at Macalester College in Saint Paul, MN, USA. She earned a Ph.D., M.S., and Certificate in College Teaching from The University of Iowa. She graduated from Amherst College with a double major in Mathematics and Music (B.A.). Yariana’s research is centered on quiver representation theory and, often, its applications to topological data analysis. A recent project of hers expands on existing methods in persistent homology for an application to climate science. Yariana grew up in Ashland, Massachusetts. She enjoys singing in choir and cooking in her free time.
DuqueRosero_Juanita

Juanita Duque-Rosero (Boston University)

Juanita Duque-Rosero is a Colombian mathematician, working as a Research Assistant Professor at Boston University. She earned a Ph.D. in mathematics from Dartmouth College, an M.S. from Colorado State University, and a B.A. from the University of the Andes. She researches computational arithmetic geometry, focusing on triangular modular curves and explicit methods for rational points on curves.
Luis Fernandez

Luis Fernandez (University of Texas Rio Grande Valley)

Luis M. FernĂĄndez, Ph.D., is an Assistant Professor of Mathematics Education in the School of Mathematical and Statistical Sciences at UTRGV. Dr. FernĂĄndez is focused on developing resources and facilitating professional development opportunities for educators, equipping them with the tools to leverage Emergent Bilingual skills for both English acquisition and content comprehension simultaneously. Moreover, he delves into the underlying causes of apparent disparities in college students’ mathematical proficiency, such as the necessity for developmental courses and more equitable modes of instruction such as Specifications Grading in Calculus. In essence, Dr. FernĂĄndez’s work reflects his commitment to advancing educational equity and excellence, particularly in the realm of mathematics education for EBs in the RGV area and elsewhere.
Patricio Gallardo

Patricio Gallardo (UC Riverside)

Patricio Gallardo is an assistant professor in the Department of Mathematics at the University of California, Riverside. He earned his PhD in mathematics from Stony Brook University. His research focuses on families of algebraic and geometric objects, incorporating both geometric and computational perspectives. His latest projects describe the moduli of n-labeled points in affine space and explore the interface between machine learning techniques and geometric problems. Patricio grew up in Colombia and has lived in New York, Georgia, Missouri, and California.
Tainara Gobetti Borges

Tainara Gobetti Borges (Brown University)

Tainara Borges is a Ph.D. student at Brown University, expected to graduate in May 2025. She earned her B. Sc. in Mathematics at UFRGS, in Porto Alegre, Brazil, and an M. Sc. in Mathematics from IMPA in Rio de Janeiro, Brazil. Her research focuses on harmonic analysis and geometric measure theory with a special interest in bilinear averaging operators over spheres or more general compact smooth surfaces and their connections to geometric problems like singular variants of the Falconer distance problem.
Javier GonzĂĄlez Anaya

Javier GonzĂĄlez Anaya (Harvey Mudd College)

Javier GonzĂĄlez Anaya is currently a Visiting Assistant Professor at Harvey Mudd College. In Fall 2025, he will join the Mathematics Department at Santa Clara University as an Assistant Professor. Previously, he held the same position at UC Riverside, after earning his Ph.D. from the University of British Columbia in Vancouver, Canada. Prior to that, he completed his MSc and “Licenciatura” at the National Autonomous University of Mexico (UNAM) in Mexico City. His research is in algebraic geometry and its connections to combinatorics and machine learning. Javier was born and raised in Mexico City.
Gloriana Gonzalez

Gloriana Gonzalez (University of Illinois Urbana-Champaign)

Gloriana GonzĂĄlez is Professor and University Scholar at the University of Illinois Urbana-Champaign. She earned her B.A. in Mathematics Education from the University of Puerto Rico, her M.S. from Cornell University, and her Ph.D. from the University of Michigan. She taught middle school and high school mathematics in Massachusetts and Puerto Rico. Her research focuses on problem-based instruction in math classrooms. She is interested in geometry teaching and learning. With support from the National Science Foundation, her current project engages math teachers in designing and implementing geometry lessons using a human-centered design approach. She was a Visiting Scholar at the Design School Kolding in Denmark which sparked her interest in applying geometry to sustainable fashion design.
David Guinovart

David Guinovart (Hormel Institute, University of Minnesota)

David Guinovart is an accomplished Assistant Professor at the Hormel Institute, leveraging his background in mathematics and computer science to advance bioscience research. Originally from Cuba, he earned his Bachelor’s in Mathematics from the University of Havana and a Ph.D. in Applied Mathematics from the University of Central Florida (UCF). His research focuses on mathematical modeling in epidemiology, cell proliferation, and material science. He has taught at the University of Havana, UCF, and the University of Delaware. At the Hormel Institute, he integrates mathematical techniques with cancer research

Roberto Hernandez (Emory University)

Roberto Hernandez is a Mexican-American first-generation student from Cudahy, California. In spring 2020, he earned his B.A. in Pure Mathematics from California State University, Fullerton. After graduating from California State University, Fullerton, he started the Ph.D. program at Emory University and is currently working in arithmetic geometry. He is committed to creating a more diverse and inclusive community in mathematics and creating opportunities for under-privileged, under-represented students of color.
Ana Maria Kenney

Ana Maria Kenney (UC Irvine)

Ana Maria Kenney is an Assistant Professor in the Department of Statistics at UC Irvine. She works at the interface of statistics, interpretable machine learning, and large-scale optimization to advance biomedical research and clinical decision making in several domains including cardiovascular genetics and early cancer screening. She completed a postdoc at UC Berkeley and previously received a dual title Ph.D. at Penn State in Statistics and Operations Research. Ana grew up in the Central Valley (Atwater/Winton area) and started her academic journey at Merced Community College before graduating from Stan State.
Oscar Leong

Oscar Leong (UCLA, Stats)

Oscar Leong is an Assistant Professor of Statistics and Data Science at the University of California, Los Angeles (UCLA). He earned his BA in Mathematics from Swarthmore College and his Ph.D. in Computational and Applied Mathematics from Rice University, where he was an NSF Graduate Research Fellow. Prior to joining UCLA, he was a von Karman Instructor in the Computing and Mathematical Sciences Department at the California Institute of Technology. His research interests lie in the mathematics of data science and the theory and application of machine learning for inverse problems.
Oscar Hernan Madrid Padilla

Oscar Hernan Madrid Padilla (UCLA Stats)

Oscar Hernan Madrid Padilla is a Tenure-track Assistant Professor in the Department of Statistics at University of California, Los Angeles. Previously, from July, 2017 to June, 2019, he was Neyman Visiting Assistant Professor in the Department of Statistics at University of California, Berkeley. Before that, he earned a Ph.D. in statistics at The University of Texas at Austin in May 2017 under the supervision of Prof. James Scott. His undergraduate degree was a B.S in Mathematics completed at CIMAT (in Mexico) in April 2013. His research interests include: High-dimensional and nonparametric statistics, change point detection, network problems, deep learning, and causal inference, and causal inference.
Antonio Estevan Martinez IV

Antonio Estevan Martinez IV (CSU Long Beach)

Antonio Martinez is an associate professor of mathematics education at California State University, Long Beach. He earned his B.A. in Mathematics at California State University, Sacramento, his M.S. in Applied Mathematics at San Diego State University (SDSU), and his Ph.D. in Mathematics Education at UC San Diego/SDSU. His research areas span active learning practices, university and departmental change, course coordination, and computational thinking. In 2024, Antonio was awarded an NSF grant to study computer science and mathematics undergraduate students’ thinking to investigate the cognitive strategies of the students as they solve problems at the intersection of both domains.
Marina Meila

Marina Meila (University of Washington)

Marina Meila is Professor of Statistics at the University of Washington and Senior Fellow of the University of Washington’s eScience Institute. Her long term interest is in statistical learning, particularly the discovery of geometric and combinatorial structure in data, efficient algorithms, and developing guarantees and validation methods for unsupervised learning with minimal or no assumptions about the data generating process. She has collaborated with scientists in applied inverse problems,materials science and theoretical chemistry. Meila holds a MS degree in Electrical Engineering from the Polytechnic Institute of Bucharest, and a PhD in Computer Science and Electrical Engineering from the Massachusetts Institute of Technology.

Monique MĂŒller (Federal University of Sao Joao del-Rei, Brazil/Indiana University, Bloomington)

Monique MĂŒller is an Associate Professor of Mathematics at Federal University of Sao Joao del-Rei (Brazil) and now is serving as a postdoc at Indiana University at Bloomington. She earned her PhD in Mathematics from National University of Cordoba (Argentina). Her research focuses on algebra, Hopf algebras, fusion categories and their representations.
Deanna Needell

Deanna Needell (UCLA, Math)

Deanna Needell earned her PhD from UC Davis before working as a postdoctoral fellow at Stanford University. She is currently a full professor of mathematics at UCLA, the Dunn Family Endowed Chair in Data Theory, and the Executive Director for UCLA’s Institute for Digital Research and Education. She has earned many awards including the Alfred P. Sloan fellowship, an NSF CAREER and other awards, the IMA prize in Applied Mathematics, is a 2022 American Mathematical Society (AMS) Fellow and a 2024 Society for industrial and applied mathematics (SIAM) Fellow. She has been a research professor fellow at several top research institutes including the SLMath (formerly MSRI) and Simons Institute in Berkeley. She also serves as associate editor for several journals including Linear Algebra and its Applications and the SIAM Journal on Imaging Sciences, as well as on the organizing committee for SIAM sessions and the Association for Women in Mathematics.
Miriam Nuño

Miriam Nuño (UC Davis)

Dr. Miriam Nuño is a Professor of Biostatistics at UC Davis, leading the Soφia (Statistical Solutions for Public Health) research team, dedicated to advancing public health and reducing health disparities through innovative statistical and mathematical methodologies. Her expertise lies at the intersection of mathematical modeling, biostatistics, epidemiology, and public health, with a strong focus on leveraging data-driven approaches to inform policy and improve healthcare outcomes. Dr. Nuño earned her Ph.D. from Cornell University and completed postdoctoral training at the Harvard T.H. Chan School of Public Health and UCLA. She has authored and contributed to over 160 peer-reviewed publications.
Alejandro Ochoa

Alejandro Ochoa (Duke University)

Alejandro Ochoa is an Assistant Professor at Duke University’s Department of Biostatistics and Bioinformatics, and part of the Duke Center for Statistical Genetics and Genomics. He did a postdoc in John Storey’s lab at Princeton University, where he started his research on statistical genetics. He earned his Ph.D. in Molecular Biology from Princeton University, focused on probabilistic protein domain prediction and malaria. He earned bachelors degrees in Mathematics and Biology from the Massachusetts Institute of Technology. His current interests are in developing methods to correctly analyze diverse genomes. Alex was raised in Ciudad Juarez, Mexico, and loves languages and music. In high school he participated in the Mexican Math Olympiad.
Samuel PĂ©rez-Ayala

Samuel Pérez-Ayala (Haverford)

Samuel Pérez Ayala is a Visi1ng Assistant Professor at Haverford College. He holds a B.S. in Mathema1cs from the University of Puerto Rico, Río Piedras, and a Ph.D. from the University of Notre Dame. His research interests include spectral geometric theory and conformal geometry. More recently, Samuel has contributed to the study of Poincaré-Einstein manifolds, a field that has gained prominence due to its relevance in string theory, par1cularly in the context of the AdS/CFT correspondence.

Eric Ramos (Stevens Institute of Technology)

 

Eric Ramos is an Assistant Professor of Mathematics at the Stevens Institute of Technology. Prior to this he was an Assistant Professor at Bowdoin College, as well as an NSF sponsored postdoc at the Universities of Oregon and Michigan. He received his BS and MS in Mathematics from Carnegie Mellon University, and his Ph.D. from the University of Wisconsin under the guidance of Jordan Ellenberg. Eric’s research work lives at the intersection of combinatorics, algebra, and topology. More recently, He has also begun incorporating AI systems and simulation into his work. Eric grew up in Northeastern New Jersey, where he still lives to this day with his wife and dog.
Amanda Ruiz

Amanda Ruiz (San Diego State University)

 

Dr. Amanda Ruiz earned her PhD in mathematics from Binghamton University and joined the University of San Diego in 2014 after a teaching and research postdoctoral fellowship at Harvey Mudd College. Her work bridges combinatorics and equity in STEM, with a focus on inclusive mathematics education. Her scholarship includes the book Middle School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice and research on the cultural capital of first-generation STEM students. A dedicated educator, she fosters critical conversations on math accessibility and equity.
Mario Sanchez

Mario Sanchez (IAS)

Mario Sanchez is a postdoctoral fellow at the Institute for Advanced Study visiting for the special year on Algebraic Geometry and Combinatorics. He was previously a postdoctoral fellow at Cornell University. He obtained his BA in mathematics from Swarthmore College and his Ph.D in Mathematics from UC Berkeley. His research focuses on combinatorics arising from algebraic geometry, convex geometry, and homological algebra. His most recent interest is in studying subdivisions of polytopes as a way of approaching derived categories of toric varieties. He was born in LA and raised in Pomona, CA.
Josef Sifuentes

Josef Sifuentes (UT Rio Grande)

 

Dr. Josef Sifuentes is a native Texan who majored in Math, Computational and Applied Math, and Art as an undergraduate at Rice University and stayed to complete a Ph.D. in Computational and Applied Math there. He has worked as a research scientist at the Courant Institute at NYU is currently faculty in the School of Mathematical and Statistical Sciences at UTRGV. His research interests are in numerical methods in linear algebra and applied mathematics more generally. Dr. Sifuentes has worked to promote undergraduate involvement in research, having directed, co-directed and served as a research mentor in several REU programs. His dedication to mentoring and teaching was recently recognized when he won the University of Texas System Wide Regents Outstanding Teaching Award. He also really likes BBQ and coffee.
Angelica Torres

Angelica Torres (Max Planck Institute for Mathematics in the Sciences)

AngÂŽelica Torres is a postdoctoral researcher at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany. She completed her undergraduate studies at the Universidad Nacional de Colombia and earned her Ph.D. in Mathematics from the University of Copenhagen. Her research focuses on applied algebraic geometry, with an emphasis on using algebraic techniques to model phenomena across scientific disciplines. Currently, she is particularly interested in the intersection of algebraic geometry and deep learning where she is studying properties of the gradient flow Neural Networks.
Denae Ventura

Denae Ventura (UC Davis)

Denae Ventura is a chancellor postdoctoral fellow at University of California, Davis, where she works with Prof. JesÂŽus De Loera. She earned her Ph.D. in Mathematics from UNAM in QuerÂŽetaro, MÂŽexico under de mentorship of Dr. Adriana Hansberg. Her research focuses on graph theory, discrete geometry and discrete optimization. She is particularly interested in Ramsey theory and extremal graph theory. Her latest project is on arithmetic Ramsey theory where she minimizes monochromatic solutions to given linear equations in k-colorings of the integers in [1,n]. Shortly after earning her Ph.D. in 2023, she was awarded with the chancellor postdoctoral fellowship. Denae grew up in San Luis Potosi, Mexico.


Panel Organizers/Moderators

Cristina Villalobos

Roummel Marcia (UC Merced)

Roummel Marcia is Professor of Applied Mathematics at University of California, Merced. He earned his B.A. from Columbia University and his Ph.D. from UC San Diego. His research includes nonlinear optimization, numerical linear algebra, machine learning, signal processing, and computational biology. At UC Merced, he is currently serving as the chair of Department of Applied Mathematics and is supervising seven Ph.D. students, whose research includes quantum sensing, ultrasound imaging, computational genomics, low-count signal recovery,modeling of pulsing corals, fractional calculus, and power grids.
Marco V. Martinez

Marco V. Martinez (North Central College)

Dr. Marco V. Martinez is a Professor of Mathematics and Actuarial Science at North Central College (NCC). Marco was a Graduate Research Assistant at the National Institute for Mathematical and Biological Synthesis (NIMBioS). His research interests fall under two broad categories. First, he uses mathematical and statistical tools to develop strategies to preserve biodiversity. Second, he analyzes large datasets to identify academic interventions that enhance student retention and graduation rates. He has also worked closely with NCC’s nationally recognized First-Generation Program, working one-on-one with students to help them invest in their careers and strategically manage family and work obligations to achieve their goal of graduating from college
Nancy B. Rodriguez

Nancy B. Rodriguez (University of Colorado, Boulder)

Nancy Rodriguez is an Associate Professor of Applied Mathematics at the University of Colorado, Boulder. She earned her doctoral degree from UCLA under the mentorship of Andrea Bertozzi. From 2011 to 2014, she was an NSF Postdoctoral Fellow at Stanford University. Her research focuses on nonlinear partial differential equations (PDEs), particularly in areas related to urban crime, segregation, biological aggregation, chemotaxis, and ecology. Her work has advanced the theoretical understanding of non-local PDEs and provided valuable insights into crime dynamics and prevention, social segregation, and pest control. Beyond academia, she enjoys outdoor activities such as biking, hiking, skiing, and anything that allows her to connect with nature.
Fadil Santosa

Fadil Santosa (Johns Hopkins)

Fadil Santosa is Professor of Applied Mathematics and Statistics at Johns Hopkins University. He is also serving as the Yu Wu and Chaomei Chen Department Head. Prior to joining Johns Hopkins, he was Professor in the School of Mathematics at the University of Minnesota, and served as Director of the Institute for Mathematics and its Applications from 2008 to 2017. He completed his BS in Mechanical Engineering at the University of New Mexico, and his PhD in Theoretical and Applied Mechanics at the University of Illinoi Urbana Champaign. His current research interests are in optimal experiment design for inverse problems and in modeling graphene-based photonic devices. He holds two US patents. He is SIAM Fellow, Fellow of the American Mathematical Society, and was awarded the SIAM Prize for Distinguished Service to the Profession in 2023.
Bianca Viray

Bianca Viray (Univ. Washington)

 


Panelists

Alvina J. Atkinson

Alvina J. Atkinson (AMS)

Dr. Alvina J. Atkinson serves as the Program Manager for the Inclusive Graduate Education Network Mathematics Initiative and Professor of Mathematics at Georgia Gwinnett College (GGC). Her leadership roles include having served as a department chair, assistant dean, and co-founder/ co-director of the GGC Mathematics in Action Scholars Program. She also directed the GGC STEM Academy. Dr. Atkinson actively supports the mathematics community by serving as a member of the Council on General Education for the University System of Georgia, as Southeast VP for the American Mathematical Association of Two-Year Colleges, as a board member of the National Association of Mathematicians, and as deputy editor of Math Horizons, a publication of the Mathematical Association of America.
Hector Ceniceros

Hector Ceniceros (UC Santa Barbara)

Hector Ceniceros is a Professor of MathemaEcs at the University of California at Santa Barbara (UCSB). He earned his bachelor’s degree in physics and mathemaEcs from the NaEonal Polytechnic InsEtute in Mexico and his masters and Ph.D. degrees in mathemaEcs from the Courant InsEtute of MathemaEcal Science of New York University. He had faculty and research posiEons at UCLA and Caltech, prior to joining UCSB in 2000. His primary research is in numerical analysis and machine learning applied soU materials and fluids. He was elected fellow of the American MathemaEcal Society in 2019.
Cristina-Eubanks Turner

Christina Eubanks-Turner (Loyola Marymount University)

Christina Eubanks-Turner is a Professor of Mathematics at Loyola Marymount University (LMU). Her interests are in commutative algebra, graph theory, mathematics education, and broadening participation in the mathematical sciences. Eubanks-Turner received her Ph.D. and M.S. from the University of Nebraska-Lincoln in 2008 and 2004, respectively, and her B.S. degree from Xavier University of Louisiana in 2002. She joined the LMU faculty in 2013.
Genetha Gray

Genetha Gray (Edward Jones)

 

Dr. Genetha Gray is a technical leader in the Data Science group at Edward Jones where her team focuses on developing models to improve the client experience. Prior to joining Jones, she managed a research group at Salesforce tasked with enhancing the employee experience through data and held a people analyAcs posiAon at Intel where her work included studying the representaAon of women in the tech workforce. She started her career in the High Performance CompuAng Division at Sandia NaAonal Labs. She has a Ph.D. in Computational & Applied Math from Rice University and co-authored a text book on environmental modeling with her Dad.
Alex Gutierrez

Alex Gutierrez (Google)

Alex Gutierrez is a Staff Data Scientist at Google, where he has worked since 2019. He earned a BS in Mathematics from Arizona State University and a Ph.D. in Mathematics from the University of Minnesota. In his current role, he uses a mixture of tools he learned in his academic training (e.g., optimization, estimation theory) along with others developed on the job (e.g., time series forecasting).
Eun Heui Kim

Eun Heui Kim (South Dakota State University)

 
Alan Lee

Alan Lee (Analog Devices)

Alan Lee, Chief Technology Officer at ADI, drives the company’s long-term technology strategy, working closely with global business units and manufacturing to enhance ADI’s competitive edge. He identifies and cultivates new business, technology, and research opportunities while advancing foundational capabilities. With over 20 years in technology, Alan previously served as Corporate VP of Research and Advanced Development at AMD, where he founded AMD Research and led extreme-scale computing initiatives. He has also held leadership roles at Intel, IBM, and a fintech startup. Alan chairs the CTO Committee for the SIA and the CTO Council for GSA, has served on multiple boards, and actively supports educational initiatives through non-profits.
Joaquin Moraga

Joaquin Moraga (UCLA)

JoaquŽın Moraga is a tenure-track Assistant Professor at the University of California, Los Angeles. He got his BS and his MSc in Mathematics at Universidad de ConcepciŽon. He got his Ph.D. in Mathematics at the University of Utah under the advice of Christopher Hacon. From 2019 to 2022, he was a postdoc at Princeton University under the mentorship of JŽanos KollŽar. Since 2022, he has been at UCLA. Moraga works in Algebraic Goemetry, more precisely, birational geometry, toric geometry, and singularity theory.
John Rock

John Rock (Cal Poly Pomona)

I joined the Department of Mathematics and Statistics at Cal Poly Pomona in Fall 2011. I earned my PhD in Mathematics in 2007 from the University of California, Riverside, under the guidance of Dr. Michel Lapidus. Before coming to Cal Poly Pomona, I was an Assistant Professor at CSU Stanislaus (2007-2011). I am currently the Graduate Coordinator for my department’s graduate program. My research interests have been in fractal geometry, complex analysis, and measure theory, but lately my writing endeavors have been focused on mathematical pedagogy. This includes “Row Integration by Parts (RIP)” in calculus and notions of arbitrarily close in real analysis, complex analysis, and topology.
Jose Israel Rodriguez

Jose Israel Rodriguez (University of Wisconsin – Madison)

Jose Israel Rodriguez is an Assistant Professor at the University of Wisconsin—Madison. He earned his BS in Mathematics from the University of Texas at Austin and his Ph.D. in Mathematics from University of California, Berkeley. His research focuses on applied algebraic geometry and algebraic statistics. Some of the applications he is currently interested in include economic fragility, polynomial neural networks in machine learning, and maximum likelihood estimation for phylogenetics. His work is partially supported by the Alfred P. Sloan Foundation and Wisconsin Alumni Research Foundation.
Cristina Villalobos

Cristina Villalobos (University of Texas Rio Grande Valley)

Cristina Villalobos holds the Myles and Sylvia Aaronson Endowed Professorship in the School of Mathematical and Statistical Sciences at the University of Texas Rio Grande Valley. Currently, she serves as the interim Dean of the Honors College and is the Founding Director of the Center of Excellence in STEM Education. Her research areas lie in optimization, optimal control, and STEM education. Her recognitions at the national level for mentoring and STEM leadership can be summarized with the 2020 Presidential Award for Excellence in Science, Mathematics, and Engineering Mentoring. She was born and raised in the Rio Grande Valley, is a first-generation college graduate, and received her B.S in Mathematics from UT-Austin and her Ph.D. in Computational and Applied Mathematics from Rice University.