__COVID-19 update 3-31-2022: __

The safety of all IPAM participants and staff is our number one priority, and we will follow all guidelines established by UCLA, LA county, the state of California, and the CDC.

- Our spring long program
**Advancing Quantum Mechanics with Mathematics and Statistics**and all its constituent workshops will meet in-person complemented by a virtual component. - The
**Latinx in the Mathematical Sciences Conference 2022**has been rescheduled. The conference is now set to take place on July 7 – 9, 2022.

Please check this page as well as the UCLA campus web page: https://covid-19.ucla.edu/updates/ for the latest COVID-19 updates.

]]>Congratulations on this great achievement!

]]>Intense interest in 2D materials was sparked by the exfoliation of graphene, a single layer of carbon atoms with hexagonal structure by Geim and Novoselov in 2004. Graphene had previously been theoretically shown by Wallace (1947) to have a linear dispersion near conical Dirac points and later shown to have quasi-particles that propagate by a massless Dirac equation for a two-component wave function (in analogy to Dirac’s relativistic equation with four-component wave functions that propagate at the speed of light). This analogy to Dirac’s relativistic equation has recently motivated the exploration of phenomena such as Klein’s paradox in graphene. A rigorous and general approach by Weinstein and Fefferman to the derivation of the massless Dirac equation for the long wave, low energy wave packets in hexagon structures was presented by Michael Weinstein and an application to the investigation of edge states was presented by Alexis Druhot and Alexander Watson.

Placing a two-dimensional lattice on another with a small rotation gives rise to periodic “moiré” patterns on a superlattice scale much larger than the original lattice analogous to the beating of two waves with slightly different wavelength (see twisted hexagonal lattices below left). This effective large-scale fundamental domain has opened the possibility of discovering new phenomena at the moiré scale that were previously inaccessible at the atomistic scale. An early example was the observation of the fractal Hofstadter butterfly in twisted bilayer graphene by Philip Kim, et al. (2013). Mitchell Luskin and Paul Cazeaux gave presentations describing their general mathematical theory of moiré patterns in relaxed incommensurate 2D heterostructures (see relaxation of twisted bilayer hexagonal lattices below right).

Rafi Bistrizter and Allan MacDonald (2010) developed a low energy continuum model for the electronic structure of twisted bilayer graphene at the moiré scale and showed that the group velocity of electronic quasi-particles is nearly zero at a “magic” angle of approximately 1°, when the interlayer coupling balances the separation of the Dirac cones of the twisted bilayer. This low group velocity and the localization of the electron density led Bistrizter and MacDonald to suggest that correlated electronic phases such as unconventional superconductivity and Mott insulation might be observed in magic angle twisted bilayer graphene. Such an observation (2018) by Pablo Jarillo-Herrero’s group galvanized the scientific world and has led to an intense synergistic development and investigation of new correlated physics models in parallel with experimental investigations.

MacDonald gave an overview of his recent research on the electronic and optical properties of 2D moiré superlattices and Francisco Guinea, another pioneer in the theory of 2D materials, gave a presentation on electron-electron interactions in graphene systems. Theorists and mathematicians gave lectures on Wannier functions for 2D layered materials (Shiang Fang), band-free approaches (Stephen Carr), and momentum space methods for relaxed incommensurate bilayers (Daniel Massatt).

Novel 2D heterostructures beyond twisted bilayer graphene are actively being investigated in the search for new platforms for correlated physics. Zoe Zhu gave theory and computation for twisted trilayer graphene (see figure below) that highlighted the challenges presented by moiré of moiré structures. Experimental results demonstrating correlated phenomena for twisted trilayer graphene were then presented by Ke Wang.

Mathematics and physics at the moiré scale continues to be intensely investigated and has been a major theme in the IPAM long program on Advancing Quantum Mechanics with Mathematics and Statistics. An informal mini workshop will be held during May 18-20, 2022.

]]>UCLA’s Mathematics Department and the Institute for Pure and Applied Mathematics (IPAM) will be hosting a satellite of this year’s workshop at the Luskin Center from 7:30am – 1:00pm. Click **here to Register**!

Prineha Narang has participated as a speaker in IPAM’s 2020 workshop Theory and Computation 2D Materials, a core participant in IPAM’s 2022 spring long program Advancing Quantum Mechanics with Mathematics and Statistics, and an organizer in the Institute’s 2023 fall long program Mathematical and Computational Challenges in Quantum Computing.

Welcome to UCLA, Prineha!

]]>The MSEC Fellowship, established in 2021, reflects a joint commitment by Mathematically Gifted & Black (MGB) and SIAM to promote long-term engagement of MSEC Fellows within SIAM and continued success within the wider applied mathematics and computational sciences community. This program recognizes the achievements of early career applied mathematicians—especially those belonging to racial and ethnic groups historically excluded from the mathematical sciences in the United States—and provides professional activities and career development. We would like to congratulate the following IPAM affiliates who are among the inaugural class of esteemed fellows:

**Samy Wu Fung** (Colorado School of Mines), participated as a speaker in IPAM’s 2020 workshop High Dimensional Hamilton-Jacobi PDEs.

**Iván Ojeda-Ruiz **(Texas State University), participated in the 2011 NSF Mathematics Institutes’ Modern Math Workshop at SACNAS.

**Joan Ponce** (University of California, Los Angeles), participated in the 2018 Latinx in Mathematical Sciences Conference (LATMath).

Congratulations on this great achievement!

]]>Tim Austin has participated as a core participant in IPAM’s 2018 long program Quantitative Linear Algebra, and a speaker for the workshop Random Matrices and Free Probability Theory.

Congratulations, Tim Austin!

Ostrowski Foundation Press Release

]]>The Society for Industrial and Applied Mathematics (SIAM) has announced the 2022 Class of SIAM Fellows. Twenty-six esteemed members of the SIAM community were nominated by their peers and chosen for their exemplary research as well as outstanding service to the community. We would like to congratulate the following IPAM affiliates who are among the nominees:

**Sharon F. Arroyo (**The Boeing Company), speaker for IPAM’s 2021 workshop, Deep Learning and Combinational Optimization.

**Weizhu Bao **(National University of Singapore), speaker for numerous IPAM programs including the 2012 workshop, Computational Methods for Multiscale Modeling of Materials Defects

**Abba Gume**l (Arizona State University), speaker for IPAM’s 2020 workshop, Mathematical Models in Understanding COVID-19.

**Eldad Haber** (The University of British Columbia), speaker for numerous IPAM programs and core participant for IPAM’s 2020 long program, High Dimensional Hamilton-Jacobi PDEs.

**Lek-Hang Lim** (University of Chicago), speaker for numerous IPAM programs and core participant for IPAM’s 2021 long program, Tensor Methods and Emerging Applications to the Physical and Data Sciences.

**Daniel Kressner **(Ecole Polytechnique Fédérale de Lausanne)**, **speaker for IPAM’s 2021 workshop, Tensor Methods and their Application in the Physical and Data Science.

**Jose Nathan Kutz** (University of Washington), speaker for numerous IPAM programs including the 2019 workshop, Interpretable Learning in Physical Science.

**Peter B. Monk** (University of Delaware), speaker for IPAM’s 2010 workshop, Metamaterials: Applications, Analysis and Modeling.

**Houman Owhadi** (California Institute of Technology), speaker for numerous IPAM programs and core participant for IPAM’s 2020 long program, High Dimensional Hamilton-Jacobi PDEs.

**Keith Promislow** (Michigan State University), speaker for numerous IPAM programs including the 2020 workshop, Mathematical Models in Understanding COVID-19.

**Leonard Schulman** (California Institute of Technology), speaker for IPAM’s 2009 workshop, Quantitative and Computational Aspects of Metric Geometry.

**Amit Singer** (Princeton University), speaker for numerous IPAM programs including the 2019 workshop, Geometry of Big Data.

**Gabriele Steidl** (Technische Universität Berlin), core participant for IPAM’s 2019 long program, Geometry and Learning from Data in 3D and Beyond.

**Hongkai Zhao** (Duke University), speaker for numerous IPAM programs and core participant for IPAM’s 2019 long program, Geometry and Learning from Data in 3D and Beyond.

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- Richard Baraniuk – speaker at IPAM’s 2003 workshop Theoretical and Computational Aspects, and 2015 workshop Computational Photographyand Intelligent Cameras.
- Lou Durlofsky (Stanford University) – organizer, core and speaker at IPAM’s 2017 long program Computational Issues in Oil Field Applications.
- Guillermo Sapiro (Duke University) – organizer for IPAM’s 2019 workshop Geometry of Big Data.
- Karen Willcox (University of Texas at Austin) – speaker at IPAM’s 2017 workshop HPC and Data Science for Scientific Discovery and 2018 tutorials Science at Extreme Scales: Where Big Data Meets Large-Scale Computing Tutorials.

Andy Lucas has participated as a speaker in IPAM’s 2020 workshop Theory and Computation for 2D Materials.

Congratulations, Andy Lucas!

2022 APS Medal & Society Prizes Documentary.

American Physical Society Press Release.

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Eitan Tadmor, Distinguished Professor at the University of Maryland, College Park, received the 2022 AMS-SIAM Norbert Wiener Prize in Applied Mathematics for his original contributions to applied and numerical analysis with applications in fluid dynamics, image processing, and collective dynamics. The prize also recognizes the significant impact of his fundamental work in theory and computation of nonlinear partial differential equations.

Eitan Tadmor was one of the founding members of IPAM in 2000 along with Mark Green and Tony Chan. Eitan has participated as a speaker in IPAM’s 2000 The Office of Naval Research Meeting, the 2003 summer school on Modern Applied Mathematics for the Atmospheric and Oceanic Sciences, and 2005 conference titled International Forum on Multiscale Methods and Partial Differential Equations.

Congratulations Eitan Tadmor on this great achievement!

American Mathematical Society Press Release

]]>On September 14, 2015, a worldwide effort of countless of scientists that had started one hundred years earlier with Einstein’s formulation of the Theory of General Relativity (GR) came to a climax with the LIGO and Virgo’s historic detection of GWs from a pair of colliding black holes (BHs). GWs are dynamical changes in the curvature of spacetime. Their astrophysical and cosmological sources are cataclysmic events, such as coalescing binary systems of BHs and supernovae explosions. Less than two years after the first detection, LIGO and Virgo observed GWs from a pair of neutron stars (NSs), ushering a new era of multi-messenger astrophysics (MMA). The most recent LIGO-Virgo-KAGRA (LVK) GW transient catalog includes a total of 90 detections of compact binary coalescences (CBCs). These observations provide physicists with a plethora of new physical information, from testing GR in the strong field regime to using new ways of measuring the expansion of the universe to exploring the properties and dynamics of matter in extreme densities.

Because of the extreme sensitivity of the detectors and the complexity of the physics involved, the extraction of physical information from the data is very challenging. The process that leads from signal detection to their physical interpretation requires a synergy of expertise encompassing instrumental science, mathematics, fundamental physics, astrophysics, and computer science.

Construction of accurate theoretical models is one of the main requirements to identify and interpret the observed GW signals. This involves a deep mathematical knowledge and a synergy between analytic and numerical techniques to solve the field equations of GR. In the presence of matter, such as in NSs, GR must be combined with additional physics, such as magnetohydrodynamics (MHD).

Confident detection of GW signals and the extraction of their physical information are computationally intensive. Therefore, the development of fast and robust tools to increase the speed of these processes is crucial for the GW community and bound to become even more critical as the sensitivity of current detectors improves and next-generation detectors come online.

Machine learning (ML) is a common tool for all these topics.

The aim of this IPAM long program was to connect these many facets of GW science and MMA by bringing together some of the foremost mathematicians, physicists and computer scientists working in the GW community. The program was designed with a structure mimicking the complex process that leads from first mathematical principles in GR to the physical interpretation of GW observations. Thus the program consisted of four workshops (WSs), each addressing one of the main aspects of the GW science:

- WS I “Computational Challenges in Multi-Messenger Astrophysics” focused on the physics of source dynamics of future detections of GW signals and the generation of accurate GW templates.
- WS II “Mathematical and Numerical Aspects of Gravitation” focused on the mathematics of the equations governing relativistic systems.
- WS III “Source Inference and Parameter Estimation in Gravitational-Wave Astronomy” focused on current, state-of-the-art approaches for parameter estimation in MMA.
- WS IV “Big Data in Multi-Messenger Astrophysics” focused on the development of ML techniques for a more efficient handling of GW data sets, reduction of detector noise, identification of astrophysical signals, and increase in detection confidence.

Given the interconnection between the topics covered in the four WSs, this document has been organized into the following sections: Mathematics of spacetime, numerical relativity (NR), GW data analysis, and physical interpretation of GW observations.

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