## Seminars and Colloquia by Series

### Topology, algebra, and combinatorics walk into a bar

Series
Time
Friday, November 4, 2022 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Roberta ShapiroGeorgia 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
Time
Friday, October 28, 2022 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Christina GiannitsiGeorgia 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
Time
Friday, October 7, 2022 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Abhishek DhawanGeorgia 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.

Series