RTG in Algebra, Algebraic Geometry, and Number Theory


Graduate directed reading for undegraduates

Program description

This quarter-long program was modeled after the GULP program run by the local AWM Chapter (and loosely on the Directed Reading Program network). It consists of small groups of advanced undergraduate students who are curious about algebra, algebraic geometry, or number theory. Each group will explore a topic in one of these subjects under the mentorship of one of our graduate students. At the end of the quarter, the mentees will give a short presentation of what they learned to the faculty, postdocs, etc in the group.

By participating in this program, undergraduates get to learn more about a topic in algebra, algebraic geometry, or number theory; gain experience presenting mathematical ideas to their peers; and bond with a graduate student who has experience working as a mathematician.
At the same time, the graduate students get the opportunity to practice pedagogical skills using material familiar to them.
The faculty in the group would be happy to advise/help with curriculum design.

Past topics

Spring 2023
  • Basic Representation Theory (Rusiru Gambheera, Bharatha Rankothge)
  • Elliptic Curves (Bryan Hu)
  • (Geometric) Class Field Theory (Shubhankar Sahai)
  • Lie Theory (Suhas Gondi, Abhik Pal, Runqiu Xu)
  • The mathematics of modern cryptography (Jun Bo Lau)
  • p-adic numbers following Gouvea's book (Steve Huang)
Spring 2022
  • Algebraic curves (Jacob Keller, Shubham Saha)
  • Category theory and functional computer programming (Paul Orland)
  • Computational aspects of algebra, algebraic geometry and number theory (Daniel Kongsgaard, Jun Bo Lau)
  • Ergodic theory and number theory (Juno Seong, Srivatsa Srinivas)
  • 'Introduction to commutative algebra' by Atiyah and MacDonald (JJ Garzella)
  • 'Primes of the form x^2 + ny^2' by Cox (Tom Grubb, Alex Mathers)
  • Bhargava's Cube Law and Quaternion Algebras (Poornima B, Bryan Hu, Finn McGlade)
  • 'Rational points on elliptic curves' by Silverman and Tate (Rusiru Gambheera, Bharatha Rankothge)
  • Representation theory (Abhik Pal, Adu Vengal)
Spring 2021
  • Algebraic curves and Riemann surfaces (Shubham Sinha)
  • Algebraic number theory (Nandagopal Ramachandran)
  • Commutative algebra (JJ Garzella)
  • First course in p-adic numbers (Alex Mathers)
  • Galois groups and fundamental groups (Jun Bo Lau)
  • Introduction to elliptic curves (Bryan Hu)
  • Modular forms (Rusiru Gambheera)
  • Representation theory of quivers (Tanny Libman)
Spring 2020
  • Baby tropical geometry (Thomas Grubb)
  • Computational algebraic geometry (Peter Wear)
  • Galois representations (Zeyu Liu)
  • (Infinity) Category theory (Jacob Keller)
  • Using proof verification software (Alex Mathers)
  • 27 lines on a cubic surface (Shubham Sinha)
Spring 2018
  • Algebraic curves (Samir Canning)
  • Elliptic Curves (Peter Wear)
  • Ergodic theory with applications to number theory/geometry (Taylor McAdam, Jaqueline Warren)
  • Error correcting codes (Thomas Grubb, Zach Higgins)
  • Modular forms (Zach Higgins, Francois Thilmany)
Spring 2017
  • Intro to Riemann surfaces (Iacopo Brivio)
  • Elementary algebraic geometry (Daniel Smith)
  • Bernoulli Numbers and Zeta Functions (Robert Snellman)
  • Introduction to Lie algebras (François Thilmany)
  • Cox's "Primes of the Form x^2+ny^2" (Peter Wear)
Spring 2016
  • Representation theory of finite groups (Zonglin Jiang)
  • Serre's "Course in Arithmetic" (Peter Wear)

© 21 November 2017 Alina Bucur