Seminars and Colloquia by Series

Lost Theorems of Geometry

Series
Graduate Student Colloquium
Time
Friday, January 27, 2023 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Katherine Booth – Georgia Tech

Most of us have been taught geometry from the perspective of equations and how those equations act on a given space. But in the 1870’s, Felix Klein’s Erlangen program was more concerned about the maps that preserved the geometric structures of a space rather than the equations themselves. In this talk, I will present some modern results from this perspective and show details of how to reconstruct the equations that preserve geometric structures.

Topology, algebra, and combinatorics walk into a bar

Series
Graduate Student Colloquium
Time
Friday, November 4, 2022 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Roberta Shapiro – Georgia Tech

One of the most beautiful aspects of math is the interplay between its different fields. We will discuss one such interaction by studying topology using tools from combinatorics and group theory. In particular, given a surface (two-dimensional manifold) S, we construct the curve complex of S, which is a graph that encodes topological data about the surface. We will then state a seminal result of Ivanov: the symmetries of a surface S are in a natural bijection with the symmetries of its curve complex. In the direction of the proof of Ivanov's result, we will touch on some tools we have when working with infinite graphs.

A brief introduction to the circle method and sparse domination

Series
Graduate Student Colloquium
Time
Friday, October 28, 2022 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Christina Giannitsi – Georgia Tech

 In this talk we will go over the Hardly-Littlewood circle method, and the major and minor arc decomposition. We shall then see a toy-example of the High-Low decomposition, and proceed with defining sparse families and sparse domination. We will conclude by explaining why sparse domination is of interest to us  when studying $L^p$ bounds. This talk aims to be accessible to people without a strong background in the area. Some basic concepts of real and harmonic analysis will be useful (e.g. $L^p$ spaces, Fourier transform,  Holder inequality, the Hardy-Littlewood Maximal function, etc)

The Entropy Compression Method

Series
Graduate Student Colloquium
Time
Friday, October 7, 2022 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Abhishek Dhawan – Georgia Tech Math –

The Lovasz Local Lemma is a powerful tool to prove existence of combinatorial structures satisfying certain properties. In a constructive proof of the LLL, Moser and Tardos introduced a proof technique that is now referred to as the entropy compression method. In this talk I will describe the main idea of the method and apply it to a problem easily solved using the LLL. I will also describe recent applications of the idea to various graph coloring problems.

Introduction to tropical geometry and combinatorial algebra/geometry

Series
Graduate Student Colloquium
Time
Thursday, September 8, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Trevor Gunn – Georgia Tech

I will give an introduction to tropical geometry which arises when you take the coordinate-wise logarithm of points in a curve and then take the base of the logarithm to infinity. This gives a combinatorial curve which is basically a bunch of rays starting at the origin. I will also talk a bit about polygons, number theory and geometry.