Professional Skills for Mathematics

Professional Skills for Mathematics is an introduction to technical and communication skills utilized in upper level mathematics courses with additional focus on resume building and professional development.

Low-Dimensional Geometry

The course will follow Francis Bonahon's book Low Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots.  This book was written for undergraduates and brings students up to speed on the many developments in the geometry of 3-manifolds over the last 40 years, beginning with rather elementary constructions.  Because the book was written for an undergraduate course, our syllabus will more or less follow the table of contents. 

Analytic Number Theory I

Topics:  Dirichlet series, arithmetic functions, Euler products, Zeta and L-functions functions, functional equations and explicit formulae (for psi and other functions), zero-free regions, Prime Number Theorem, Dirichlet's theorem on primes, exponential sums, Siegel zeros and Siegel's Theorem, Landau-Page Theorem, large sieve, and Bombieri-Vinogradov Theorem

Topics in PDE Dynamics II

Nonlinear dynamics of semilinear and quasilinear PDE models including nonlinear stability/instability, invariant manifolds, bifurcations of coherent states, homoclinics, basic blow-up solutions.


This course is a continuation of the Fall '23 course MATH 8803-LIN, Topics in PDE Dynamics I | School of Mathematics | Georgia Institute of Technology | Atlanta, GA (gatech.edu).

Three-Dimensional Contact Topology

Contact structures on 3-manifolds have become a central part of low-dimensional topology. This course will discuss several techniques to study contact structures with a focus on convex surface theory. We will show how to classify contact structures on certain 3-manifolds and how to study special knots inside contact 3-manifolds.

Mathematical Neuroscience

This course will fill the gap between the computational and engineering aspects of neuroscience covered in BMED 7610 and ECE/BMED6790 by covering mathematical analysis and simulation of neural systems  across single cells, networks, and populations, employing methods from dynamical systems, network  science, and stochastic processes. The topics will include single-neuron excitability and bifurcation,  network structure and synchrony, and statistical dynamics of large neural populations. 

Convex Geometry

In short, I plan to cover major parts of chapters I, II, IV before covering some special topics (time permitting). Possible special topics include polytopes, lattice point enumeration (with applications to integer programming), applications in semidefinite optimization and moment problems in analysis.

Set Theory

This course will provide a rigorous introduction to the modern area of (axiomatic) set theory.

Advanced Analysis

A comprehensive overview of advanced material in analysis. This is a Mother Course with 5 different subtitles; Recommended prerequisites may vary with each offering. 

High-dimensional probability

The goal of this PhD level graduate course is to provide a rigorous introduction to the methods of high-dimensional probability.


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