PUNDiT: (P)racticum for (Und)ergraduates (i)n Number (T)heory

October 16 - 17, 2021


“PUNDiT: (P)racticum for (Und)ergraduates (i)n Number (T)heory” is a 2-day intensive program which will showcase number theory broadly interpreted at the introductory level.  A goal of this program is to expose Southern California students traditionally underrepresented in number theory (such as women and underrepresented minorities) to the beauty of the subject.

The Practicum is introductory in nature and no prior number theory coursework will be assumed.  Students should be familiar with Calculus and Linear Algebra, although this is not required.  The Practicum is designed for students who have completed minimal coursework in upper-division mathematics courses.

PUNDiT will take place on Saturday October 16 and Sunday October 17, and will feature four types of events:

• Tutorial: Two faculty members will rotate to give three lectures over two days to introduce Riemann Surfaces.
• Problem Sessions: Two graduate students will coordinate a series of three hour-long group-work sessions where students will work on problems meant to supplement the tutorials.
• Expository Talks: Four experts in number theory will give one-hour introductory presentations on various topics.
• Panel Discussions: There will be panels on “Opportunities in Number Theory for Undergraduates” and “Opportunities at the NSF-Math Institutes for Undergraduates”.

Tutorial #1: From Pendula to Elliptic Curves (Edray Goins)

Tutorial #2: Riemann Surfaces: number, function theory, and geometry (Caleb Ashley)

Tutorial #3: Character varieties: moduli, Markov equation, and Jabberwocky (Caleb Ashley)


Panel Discussion: Opportunities in Number Theory for Undergraduates
Would you like to continue learning more about topics in algebraic geometry and number theory? What are some next steps available to undergraduates? In this panel, we introduce some opportunities which are well-suited for participants of PUNDiT. We will have representatives from Arizona Winter School (AWS, http://www.math.arizona.edu/~swc/) in Phoenix, AZ; Pomona Research in Mathematics Experience (PRiME, http://research.pomona.edu/prime) in Claremont, CA; and the Research Experience for Undergraduates at the University of Virginia (REU@UVA, https://uva.theopenscholar.com/reu/program) in Charlottesville, VA; and the Virtual Math Seminar on Open Conjectures in Number Theory and Arithmetic Geometry (VaNTAGe, https://sites.google.com/view/vantageseminar).

Panel Discussion: Opportunities at the NSF-Math Institutes for Undergraduates
The Mathematical Sciences Institutes (https://mathinstitutes.org) are comprised of seven U.S.-based institutes that receive funding from the National Science Foundation(NSF), an independent U.S. government agency that supports research and education in all non-medical fields of science and engineering. The Math Institutes aim to advance research in the mathematical sciences, increase the impact of the mathematical sciences in other disciplines, and expand the talent base engaged in mathematical research in the United States. But how can these Institutes benefit me as an undergraduate?

In this panel, we present several opportunities which are available to students during the summers. Many of the institutes offer programs in the form of paid internships and research experiences for undergraduates (REUs). We will have representatives from the Mathematical Sciences Research Institute’s Undergraduate Program (MSRI-UP, http://msri.org/up) in Berkeley, CA; Research in Industrial Projects for Students (RIPS, http://www.ipam.ucla.edu/rips) at IPAM in Los Angeles, CA; Summer@ICERM at the Institute for Computational & Experimental Research in Mathematics in Providence, RI; and the Undergraduate Summer School (USS, https://icerm.brown.edu/summerug/) as part of the Park City Math Institute (PCMI, https://pcmi.ias.edu/upcoming) in Park City, UT.

Organizing Committee

Caleb Ashley (Boston College)
Edray Goins (Pomona College)