Coordinator: Brendon Rhoades
Email: bprhoades (at) math.ucsd.edu
Office: 7250 APM
Colloquium Location: Zoom
Colloquium Time: Tuesdays, 1:00-1:50 pm

Description: This is a weekly colloquium meant to give students a fun and informative introduction to ideas in research mathematics.

Grading: You are required to attend each colloquium *while it is taking place* (this is *not* an asynchronous class) with your camera on. You may miss at most one colloquium to receive credit.

Schedule

1/11/2022: Brendon Rhoades
Title: Shoving boxes into corners
Abstract: A *partition* is a way to shove a finite collection of square boxes into a corner. We will explain some combinatorial, algebraic, and geometric applications of box shoving.

1/18/2022: Lutz Warnke
Title: The probabilistic method in combinatorics
Abstract: The probabilistic method is a power tool for tackling many problems in discrete mathematics and related areas. Roughly speaking, its basic idea can be described as follows. In order to prove existence of a combinatorial structure with certain properties, we construct an appropriate probability space, and show that a randomly chosen element of this space has the desired property with positive probability. In this talk we shall give a gentle introduction to the Probabilistic Method, with an emphasis on examples.

1/25/2022: Jonathan Novak
Title: Polya's random walk theorem
Abstract: A random walk is said to be recurrent if it returns to its starting point with probability one: otherwise it is called transient. It is a remarkable result of George Polya that a simple random walk on the integer lattice in d-dimensions is recurrent in dimensions one and two, but transient in dimensions three and up: a drunkard stumbling around a city grid will certainly return home, but if he can fly he might not be so lucky. I will explain this fundamental law of nature using elementary generating function methods together with a dash of classical analysis.

2/1/2022: No Seminar

2/8/2022: Anthony Sanchez
Title: What are translation surfaces?
Abstract: A translation surface is a collection of polygons with edge identifications given by translations. In this introductory talk, we go over some examples of translation surfaces and hint at some of the connections that this simple definition has to many areas of mathematics including dynamical systems, group theory, low dimensional topology, and hyperbolic geometry.

2/15/2022: No colloquium

2/22/2022: Andrew Suk
Title: Sums versus product: number theory, graph theory, and geometry
Abstract: In this talk, I will sketch a surprising proof due to Gyorgy Elekes on a non-trivial lower bound for the sums-versus-product problem in combinatorial number theory.

3/1/2022: Rayan Saab
Title: TBA
Abstract: TBA

3/8/2022: Freddie Manners
Title: TBA
Abstract: TBA