Georgia Institute of Technology College of Sciences

Spring 2026: 

Math 8803-CHO: This course covers various topics in neural dynamics at the level of single cell and population, and  their connections to biological neural networks. 

Math 8803-TLE: Topics include the Jones polynomial and quantum link invariants,  Topological Quantum Field Theory (ribbon and modular tensor categories), quantum representations of mapping class groups, and skein modules/algebras. 

Math 8803-HOU: The course will cover the following sequence of topics: 

Introduction

Weak Invariance Principles

Longest Increasing Subsequences:  The One Sequence Case

Maximal Eigenvalues of Matrices from the Gaussian Unitary Ensemble

Young Diagrams and the RSK Algorithm 

Convergence of the Shape of RSK Young Diagrams

Spectra of GUE and Related Gaussian Matrices

A Conjecture for Markov Random Words

Two or More Random Words, Longest Common (and Increasing) Subsequences 

Strong Invariance Principles and Rates of Convergence

Quantum Tomography

Quantum Estimation

Math 8803-ZEI: In the first part, we will continue studying representations of classical complex Lie algebras, followed by representations of compact Lie groups and the Peter-Weyl theorem. We will explore applications, including an explicit study of the hydrogen atom from a representation-theoretic perspective. The course then covers the structure of Lie groups, including the classification of compact and complex reductive groups, the topology of Lie groups and homogeneous spaces, and the Bruhat decomposition.

The second part is devoted to advanced topics in modern representation theory: representations of affine Lie algebras, elements of vertex algebra theory, and quantum groups. Topics include highest-weight representations of affine Lie algebras, constructions of vertex algebras with applications to conformal field theory, and quantum groups in the context of knot invariants and quantum topology.