## Seminars and Colloquia by Series

### Detecting gerrymandering with mathematical rigor

Series
Joint School of Mathematics and ACO Colloquium
Time
Thursday, February 6, 2020 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Wesley PegdenMathematics, Carnegie Mellon University

Please Note: (Refreshments will be served at 2:30pm after the lecture.)

In recent years political parties have more and more expertly
crafted political districtings to favor one side or another, while at
the same time, entirely new techniques to detect and measure these
efforts are being developed.

I will discuss a rigorous method which uses Markov chains---random
walks---to statistically assess gerrymandering of political districts
without requiring heuristic validation of the structures of the Markov
chains which arise in the redistricting context.  In particular, we will
see two examples where this methodology was applied in successful
lawsuits which overturned district maps in Pennsylvania and North Carolina.

### A solution to the Burr-Erdos problems on Ramsey completeness

Series
Joint School of Mathematics and ACO Colloquium
Time
Thursday, November 21, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jacob FoxStanford University

A sequence A of positive integers is r-Ramsey complete if for every r-coloring of A, every sufficiently large integer can be written as a sum of the elements of a monochromatic subsequence. Burr and Erdos proposed several open problems in 1985 on how sparse can an r-Ramsey complete sequence be and which polynomial sequences are r-Ramsey complete. Erdos later offered cash prizes for two of these problems. We prove a result which solves the problems of Burr and Erdos on Ramsey complete sequences. The proof uses tools from probability, combinatorics, and number theory.

Joint work with David Conlon.

### Polynomial to exponential transition in Ramsey theory

Series
Joint School of Mathematics and ACO Colloquium
Time
Thursday, February 14, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dhruv MubayiUniversity of Illinois at Chicago

### Graph Colouring Via The Probabilistic Method

Series
Joint School of Mathematics and ACO Colloquium
Time
Thursday, January 21, 2010 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Bruce ReedMcGill University
The term Probabilistic Method refers to the proof of deterministic statements using probabilistic tools. Two of the most famous examples arise in number theory. these are: the first non-analytic proof of the prime number theorem given by Erdos in the 1940s, and the recent proof of the Hardy-Littlewood Conjecture (that there are arbitrarily long arithmetic progressions of primes) by Green and Tao. The method has also been succesfully applied in the field of graph colouring. We survey some of the results thereby obtained. The talk is targeted at a general audience. We will first define graph colouring, explain the type of graph colouring problems which tend to attract interest, and then explain the probabilistic tools which are used to solve them, and why we would expect the type of tools that are used to be effective for solving the types of problems typically studied.

### Quantum Physics and Algebraic Graph Theory

Series
Joint School of Mathematics and ACO Colloquium
Time
Tuesday, October 21, 2008 - 16:30 for 2 hours
Location
Skiles 255
Speaker
Chris GodsilUniversity of Waterloo

Please Note: Refreshments will be served at 4PM in Skiles 236.

The possibility of a quantum computer has lead to much new work in theoretical physics and, naturally enough, this work has raised many new mathematical problems. What is perhaps surprising is that it has lead to interesting problems in algebraic graph theory. For example, questions about the relative power of quantum computer and classical computers lead to questions about the chromatic number of certain graphs. In my talk I will discuss some of these problems, and the progress that has been made.