# Graduate Colloquium

The graduate students of the Mathematics Department coordinate a quarterly colloquium. The talks are generally every Thursday from 4-5 PM, with an informal tea (get-together) beforehand.

**Winter 2021 Grad Colloquium Thursdays**

**talk @ 4pm, "tea" @ ~3:30pm, California Time**

**Schedule ***(click dates for title and abstract)*

1/21 | Andrew Kobin | UCSC |

2/11 | Ryan Pugh |
UCSC |

2/18 | Cheyenne Dowd | UCSC |

2/25 | Sam Miller | UCSC |

3/4 | Ezekiel Lemann | SUNY Binghamton |

**Andrew Kobin, UC Santa Cruz**

*What is a stack? *

Many classification problems in math are made harder by nontrivial automorphisms of the objects one is trying to classify. Groupoids, and ultimately stacks, are the right language to solve these problems in a satisfying way. In this talk, I will gently ease the audience into the waters of algebraic geometry while sprinkling in the motivating principles behind stacks. Then we will look at some important examples of algebraic stacks, including quotient stacks and the moduli stack of elliptic curves.

**Ryan Pugh, UC Santa Cruz**

*An Introduction to Stability and Banach Algebras*

We'll first introduce ourselves to Toeplitz and Hankel matrices and explore a few of their properties. We'll then turn our attention towards the ideas of approximation methods and stability of sequences of operators. As if that weren't enough exciting content, we'll end the talk with a discussion on Banach algebras, a bit of Gelfand theory and C*-Algebras, all venerable additions to our mathematical toolboxes. One goal of this talk is to show how the things we learn in functional analysis can pop up in different contexts, so I'll do my best to point these out along our journey.

**Cheyenne Dowd, UC Santa Cruz**

*An Introductory Look at Chaos in the Sitnikov Problem*

The Sitnikov problem is a well-known problem in n-body dynamics; it explores the behavior of this 3-body problem with a remarkable set of solutions. We will discuss the well-known Kepler problem of two bodies, and then introduce the third body per the Sitnikov problem. We will then discuss both solutions to this system, and examine the chaotic behavior which it exhibits.

**Sam Miller, UC Santa Cruz**

*Checkers, stacks and other fun things: a potpourri of combinatorial puzzles and games*

Combinatorial game theory is the study of sequential games with perfect information. We survey an assortment of combinatorial puzzles and games, including the Knight's Tour and Conway's Checkers, and present the audience with satisfying combinatorial proofs. Included in this presentation will be original results proven by the presenter prior to entering UC Santa Cruz. No background in combinatorics is required.

**Ezekiel Lemann, SUNY Binghamton**

*Introduction to the Waldhausen S-Construction*

We will give an overview of the construction of K-theory due to Friedhelm Waldhausen and mention a few uses of K-groups.