# Talks

A lightning talk is a short presentation meant to quickly introduce a topic or concept to an audience.

These talks are held monthly and are entirely student-run. Attendance is open to any and all students, with any level of mathematical background.

We also hold raffles for math-related books and provide light refreshments.

This quarter’s talks will be held on the following dates:

- Thursday, March 1st

If you’d like to give a talk, just fill out the form below.

# Past Talks

Here are some of the talks that have been given in the past:

## Haskell for Mathematicians

(Zack Garza)

Basic of Haskell syntax and semantics, using examples from Mathematics. Topics: types, functions, lazy evaluation, partial application/currying, custom datatypes/records, common paradigms in functional programming (map/filter/reduce), overview of Prelude & Hackage

## The Next Greatest Number

(Matt Chan)

Basics of point-free style programming (i.e. programming by function composition) and equational reasoning. How to derive a solution to a typical CS interview brain teaser by equational reasoning in Haskell, and how to transform the derived algorithm into an efficient one by calculation.

## Introduction to Category Theory, Part 1

(Zack Garza)

Topics: Motivation and history, basic definitions, examples of categories, overview of big ideas (commuting diagrams, universal properties, functors, naturality, duality, limits/colimits, Yoneda)

## Introduction to Category Theory, Part 2

(Zack Garza)

Topics: Initial and terminal objects, products and coproducts, use of universal property in quotient and polynomial ring constructions, pullbacks/pushforwards, adjunction, monoids, monads

## Math Jokes by Physicists: fractal dimension, random walks, the Ising model, and the continuum limit

(David Moore)

Efforts in statistical field theory - a physics subject similar to quantum field theory - are plagued with infinities. In this talk I will outline the path from fractals and self-avoiding random walks, to the Ising model and its ilk. This involves hilarities like the scrubbing away of infinities, limits as integers approach zero, and the path integral.

## Matroids and Greedy Algorithms

(Abel Mariam)

There are a class of algorithms referred to as Greedy algorithms which are broadly characterized by the strategy of “picking what looks best at the moment”. It turns out that the theory of matroids provides the appropriate framework to partially characterize problems that have a greedy solution. A matroid, first introduced in 1935 by Hassler Whitney, is a combinatorial structures that generalizes the notion of independence common in many different areas of mathematics.

In this talk, I will introduce some basic definitions and results and discuss Matroid formulations of some classic problems in Graph Theory (Minimum Spanning Tree, Vertex Matching, and Interval Scheduling).

## Category Theory as an Organization Tool

(Zack Garza)

This talk will continue some of the ideas introduced in last quarter’s talks on Category Theory. (We’ll also review some of the basics for people that didn’t make the first one.) The focus this time will be to see a number of examples of how Category Theory ties together various branches of branches of Mathematics.

We’ll cover many of the structures seen in undergraduate classes like Analysis, Algebra, Combinatorics, and Topology, and how they are related to each other. I’ll also be explaining what the term “isomorphism” means in all of these contexts.

## The Galilean Group and Mechanics, both Classical and Quantum

(David Moore)

This talk will discuss the mathematical formulation of nonrelativistic classical and quantum mechanics. Both boil down to ordinary and partial differential equations, and both possess the galilean group as their symmetry group.

We will start at the group and its corresponding Lie algebra, introduce the Poisson bracket (classical) and commutator (quantum), and derive some implications of the bracket + symmetry group laws. Throughout, we will stick as close as possible to differential equations, and ignore or tread around any functional analysis issues that crop up.

## Brownian Motion

(Kim Udomprapasup)

This talk will discuss the mathematical theory of Brownian motion. We will begin with the description of Brownian motion, then move on to some of its interesting properties. Its connections to other areas in mathematics will also be mentioned, for example, harmonic analysis and PDE.

If time permits, we will get a glimpse of stochastic calculus as well.

## Vibrations on a Drumhead

(Simon Hu)

In this talk, we will discuss the problem of vibrations on a drum-head. Specifically, we find an analytical solution to the wave equation in two dimensions by using Bessel’s functions.

We first derive the Bessel’s function, which is a solution to a Second-Order, Linear, Ordinary Differential Equation. Then we discuss, shortly, the wave equation and the fundamental solution. Finally, we will discuss the problem of vibrations on a drum-head. If time permits, we will discuss applications of this problem.

## Boolean Fourier Analysis

(Peter Amidon)

Boolean Fourier Analysis has proven to be a remarkably versatile tool in various fields in theoretical computer science. In this talk I will introduce the basics of the technique and show how the simple change-of-basis that is Fourier analysis can solve many problems. In addition I will show a Fourier-analysis based proof of the famous Arrow’s Theorem which shows an approximate version of it: if a ranked-choice voting system has a high probably of choosing a Condorcet winner, then in some way it is “close” to being a dictatorship.

## Algebraic Geometry: A Historical Primer

(Zack Garza)

Algebraic Geometry is often touted as an abstruse, difficult to penetrate subject - however, these two branches of Mathematics have been intertwined since the time of the Greeks! In this talks, we will discuss Algebraic Geometry from a historical perspective, leading up to a brief, high-level modern overview of “the Nullstellensatz”, a theorem which provides a dictionary between the worlds of algebra and geometry.

## Homology and the Snake Lemma

(Zack Garza)

Homology is an algebraic tool that has proved to be useful in many areas of Mathematics, and in recent years has even been used in applied settings such as large scale data analysis.

This talk is motivated by the movie “It’s My Turn” from 1980, which features an infamous scene involving a result known as “The Snake Lemma.” Surprisingly, this scene is mathematically precise, and is even referenced as a proof in a text by Weibel’s “Introduction to Homological Algebra”!

The goal of this talk will be to provide a brief overview of some of the mathematics used in this scene, and ultimately to formulate what the Snake Lemma is and an example of how it can be used. In the process, we will also cover some of the basics of homology and its generalization in homological algebra.