Text: Young Tableaux With Applications to Representation Theory and Geometry, William Fulton
Mentee: Katherine Cadzow
Mentor: Mojdeh Tarighat
Grid Homology
Text: Grid Homology for Knots and Links by Ozsváth, Stipsicz, and Szabó
Mentee: Nick Cooney
Mentor: Peter Johnson
Fall 2020
Galois Theory and its Applications
Text: A Book of Abstract Algebra, Charles Pinter
Mentee: Bilal Khan
Mentee: Casia Siegel
Mentor: Will Craig
Group Theory and Rubik’s Cube
Mentee: Sabrina Fuller
Mentor: Alec Traaseth
Classification of Surfaces
Text: A Guide to the Classification Theorem for Compact Surfaces, Gallier and Xu
Mentee: Harsh Padhye
Mentee: Zhijun Cao
Mentor: Alec Traaseth
Analyzing Spaces
Text: Functional Analysis, Bachman and Narici
Mentee: Emma Graham
Mentor: Bruno Braga
Synthetic Topology
Text: Synthetic Topology of Data Types and Classical Spaces, Martin Escardo
Mentee: Joey Rudek
Mentor: Neelav Dutta
Spring 2020
Homological proof of the Brouwer fixed point theorem
Text: Algebraic Topology, Hatcher
Mentee: Thomas Blue
Mentor: Chris Lloyd
Fall 2019
The Geometries of Surfaces
Text: Low-Dimensional Geometry, Bonahon
Mentee: Haoyu Li
Mentor: Ian Runnels
Point-set Topology
Text: Topology, Munkres
Mentee: Dean Sublett
Mentor: Shunyu Wan
Fibered Categories
Text: Categorical Logic and Type Theory, Jacobs
Mentee: Nijat Khanbabayev
Mentor: John Harnois
Character Theory
Text: Linear Representations of Finite Groups, Serre
Mentee: Greg Conneen
Mentee: Spencer Martin
Mentor: Chris Lloyd
Alexander’s Theorem
Text: The Knot Book, Adams
Mentee: Noah Brenny
Mentor: Rostislav Akhmechet
Spring 2019
Gröbner bases and applications in characteristic p
Text: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, David A.Cox, Donal O’Shea, and John B. Little.
Mentee: Abrar Majidi Idrissi
Mentor: Huy Dang
Classification of the Simple Lie Algebras
Text: Introduction to Lie Algebras, Erdmann and Wildon
Mentee: Hisham M Assana
Mentor: Arun Kannan
The Geometry of Free Groups
Text: Geometric Group Theory: An Introduction, Clara Loeh
Mentee: Katherine Andrews
Mentor: Ian Runnels
Hamiltonian ODEs: Deterministic and probabilistic studies
Text: ODEs and Dynamical Systems, Gerald Teschl
Mentee: Yunlu Li
Mentor: Mouhamadou Sy
The Yoneda Embedding and its Applications
Text: Categories for the Working Computer Scientist, Barr and Wells
Mentee: Joseph Snitzer
Mentor: Chris Chung
Real Analysis and Probability Theory
Text: Real Analysis, Folland
Mentee: Chris Pufko
Mentor: Ethan Zell
Representation Theory of Finite Groups
Text: Representations and Characters of Groups, James and Liebeck
Mentee: Jonah Newman
Mentor: Liron Speyer
Exploring Schottky Groups
Text: Indra’s Pearls: The Vision of Felix Klein, Mumford, Series, Wright
Mentee: Aaron Christian
Mentor: Jiajun Yan
Fall 2018
Support vector machines and kernel methods
Text: Foundations of Machine Learning by Mohri, Rostamizadeh, and Talwalkar
Mentee: Dylan Hunt
Mentor: George Seelinger
All groups can be realized as a fundamental group
Text: Algebraic Topology, Hatcher
Mentee: Kyle Hoffmann
Mentor: John Harnois
Topological proof of the Nielsen-Schreier Theorem (a subgroup of a
free group is free)
Text: Algebraic Topology, Hatcher
Mentee: Mia Shaker
Mentor: Chris Lloyd
Difference between algebraic bases and Schauder bases
Text: Real Analysis: Modern Techniques and Their Applications, Folland
Mentee: Yifei Yang
Mentor: Joseph Eisner
Wirtinger presentations of fundamental groups of knot complements
Text: Algebraic Topology, Hatcher
Mentee: Zach Baugher
Mentor: Rostislav Akhmechet
Theorem: Let G be a finitely generated group with two different
finite generating sets S and S’. Then G with the word metric induced
by S is quasi-isometric to G with the word metric induced by S’
Text: Office Hours with a Geometric Group Theorist, Clay and Margalit
Mentee: Sam Dulin
Mentor: Ian Runnels
Constructing hyperbolic structures on closed surfaces (of genus g)
Text: Low-dimensional geometry: from euclidean surfaces to hyperbolic knots, Bonahon
Mentee: Andrew Zazzera
Mentor: Jiajun Yan
Brownian Motion and its Applications
Text: Brownian Motion by Peter Morters and Yuval Peres
Mentee: Xinru Cheng
Mentor: Ethan Zell
Summer 2018
An Introduction to Computability Theory and ‘Universal Programs’
Text: Computability: An introduction to recursive function theory, N.J. Cutland