Geometry & Topology RTG

University of Notre Dame

Directed Readings

Emulating an activity initiated at the University of Chicago in the early 2000s, every academic year we pair PhD students with sophomores/juniors interested in learning material beyond their regular classes. Each pair decides, with some faculty oversight, on a topic and a book. The goal is for the pair to cover as much as possible of that book in detail, and more importantly, for the undergraduate to experience how one learns new mathematics. The RTG grant provides funding for purchasing books for all the people involved in this experience.

Mentor Student Topic
Kyle Gannon Nathaniel Vaduthala T. Tao: An Introduction to measure Theory
JD Quigley Ting Gong F. Jarviz: Algebraic Number Theory
J. Neukirch: Algebraic Number theory
Aaaron Tyrrell Enhao Feng M.Spivak: Calculus on Manifolds
Jens Kjaer Mark Sun A. Karlin, Y.Peres: Game Theory Alive
Xiaoxiao Li Kyle Duffy M. Taylor: Measure Theory and Integration
Taylor Ball Kyle Weingarten S. Roman: Advanced Linear Algebra
Tim Campion Alex Kokot P. Aluffi: Algebra. Chapter 0
L. Nicolaescu Mikhail Sweeney H. McKean: Probability-The Classical Limit Theorems
Mentor Student Topic
Jens Kjaer Rathin Katcham A. Bonato, R. J. Nowakowski: The Game of Cops and Robbers
Jose Pastrana Misha Sweeney J. Franks: A (Terse) Introduction to Lebesgue Integration
Samuel Perez-Ayala Sam Booth V. Barbu: Differential Equations
James Quigley Anthony Napolitano T. R. Shemanske: Modern Cryptography and Elliptic Curves: An Introduction
Eric Wawerczyk Tim Stavetski W. G. Chinn, N. E. Steendrod: First Concepts of Topology
Laura Wells Sophia Kardadi C. Adams: The Knot Book
Leandro Lichtenfelz Nathaniel Vadutha M. Spivak: Calculus on Manifolds
Mentor Student Topic
Laura Wells Rathin Katcham C. Adams: The Knot Book
J.D. Quigley Christian Hokaj Alvaro Lozano-Robledo: Elliptic Curves, Modular Forms, and their L-functions
Kyle Gannon Danny O'Connor C.E. Silva: Invitation to Ergodic Theory
Lendro Lichtenfelz Maciej Olszewski J.W. Milnor: Topology from a Differentiable Viewpoint
Jeremy Mann Katie Gallagher Barden & Thomas: Introduction to differentiable manifolds
Erin Bela Caitlyn Booms Cox, Little, O'Shea: Ideals, varieties, algorithms