Georgia Institute of Technology College of Sciences

Fall 2025: 

Math 8803-BAK: Matroids, which are a way of abstracting the notion of linear independence in vector spaces, lie at the interface of combinatorics and geometry, and in recent years some sophisticated algebra has appeared in connection with matroid theory as well. This course will cover both “classical” topics like cryptomorphic descriptions of matroids and representability over fields, as well as recent topics such as combinatorial Hodge theory, Lorentzian polynomials, and matroids with coefficients.

Math 8803-ETN:  This course will cover the general theory of handlebodies. Topics will include the h-cobordism theorem, classification of surfaces, Heegaard diagrams, 4-manifolds, and Kirby's theorem.

Math 8803-XHE: A treatment of modern developments in Ramsey and Turan theory, with a focus on graph and hypergraph Ramsey numbers and Turan densities.

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-RIE: Introduction to Optimal Transport: existence, duality, dynamical formulation, regularity; Applications: Wasserstein gradient flows, barycenters, functional inequalities, Wasserstein GAN

Math 8803-ZEI: This course starts with the fundamentals of representations of associative algebras and finite groups, providing introduction to the subject. We then explore the representation theory of the symmetric group and its connection to Young tableaux. After that, we move on to Lie groups and Lie algebras, studying their representations with a focus on the classification and structure of finite-dimensional simple complex Lie algebras, as well as the general framework of their finite-dimensional representations. The course wraps up with an examination of the representation theory of GL(n), a key example that ties together many of the concepts introduced earlier.

Math 8803-ZHU: This graduate-level special topics course focuses on the mathematical foundations of machine learning. It covers topics such as statistical learning theory, approximation theory, generalization, and optimization in modern neural networks. The course also includes geometric deep learning, learning benefits and guarantees under invariance, and generative models like GANs and diffusion models. Students will build a strong theoretical understanding of machine learning, preparing them for both research and practical applications.Topic outline: 

1. Introduction to learning theory
2. Approximation
3. Generalization
4. Optimization
5. Geometric machine learning
6. Generative models