### Winter 2018

The Winter 2018 SASMS will be held on Friday, February 9 at 4:00 in MC 5417. If you would like to give a talk, you may do so by clicking "Sign Up" above.

### Talks

Time
Speaker
Talk Title
4:00
Anzo Zhao Yang Teh
Trigonometry and Euclidean Geometry
4:30
Harry Sivasubramaniam
Applications of Entropy
5:00
Shouzhen Gu
Banach Algebras, $H^\infty$, and the Corona Theorem
5:30
Letian Chen
Real Harmonic Analysis
6:00
Pure Math Club
Dinner
6:30
Sean Harrap
Regular Languages & Boolean Matrix Automata
7:00
Felix Bauckholt
Stochastic Processes and why they're Actually Awful
7:30
Sally Dong
Probabilistic Method Quickies
8:00
Xinrui Jia
8:30
Zishen Qu
Every graph has a cycle or path of length the number of vertices of G or two times the minimum degre

### Abstracts

#### Trigonometry and Euclidean Geometry

The plan is to show how can one use tricks and identities in trigonometry to solve difficult contest problems in Euclidean Geometry, by transforming a geometry problem (fully or partially) into an algebra problem that's easier to see the trick. The content of the talk will be based on this: https://anzoteh96.github.io/trigonometry.html

#### Applications of Entropy

We will use entropy to get a cute bound on the number of triangles in a graph given the number of edges. Also, Letian is a cutie.

#### Banach Algebras, $H^\infty$, and the Corona Theorem

I will talk about commutative Banach algebras and their basic properties. The Hardy space $H^\infty$ of bounded analytic functions on the open disk is an example of such a Banach algebra, and its maximal ideal ideal space has many interesting topological properties. Time permitting, I will discuss the Corona Theorem, which states that the open disk in the maximal ideal space is dense.

#### Real Harmonic Analysis

Test functions, distributions, Schwartz space, Fourier transforms. NO LOCALLY COMPACT GROUPS.

#### Dinner

Hey bois, what's good?

#### Regular Languages & Boolean Matrix Automata

The SASMS termly CS infiltration talk. I'm going to introduce core formal language concepts including DFAs and some problems involving them, hopefully leading to some tricks applying basic ideas from linear algebra and graph theory to show that unusual languages are in fact regular.

#### Stochastic Processes and why they're Actually Awful

A while ago, I came up with a counterexample about stochastic processes to make people angry. Unfortunately, the few people I beta-tested my talk on were too stunned by Letian's beauty to get very angry. I'll give the talk anyways and explain some basic concepts in probability theory in the process. Depending on how the talk goes, you can also look forward to an exciting marital arts choreography in collaboration with Rana!

#### Probabilistic Method Quickies

I'll present some cute examples using the probabilistic method.

#### Colouring Theorems in Additive Combinatorics

Ramsey theory asks questions about how large structures must be to guarantee certain properties. We will present and prove a few key results in Ramsey theory involving colouring, by using combinatorial arguments.

#### Every graph has a cycle or path of length the number of vertices of G or two times the minimum degre

I will prove the above easy theorem.