If you’d like to give a talk this quarter, just fill out the form below!
This quarter’s talks will be in AP&M 7421, and will be at the following dates and times:
Friday, April 28th, 5-6:30pm
Friday, May 26th, 5-6:30pm
Here are some of the talks that have been given in the past:
Haskell for Mathematicians
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
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
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
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
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
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
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
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.
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.