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
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