Binghamton University Math Graduate Student Seminar
The Math Graduate Student Seminar intends to strengthen the communication among grad students by fostering a friendly environment in which to present attractive and stimulating mathematics to other grads and have discussion around various topics.  Presentations should be accessible to any mathematics grad student; everyone is encouraged to contribute a talk!

If you are a graduate student interested in giving a talk, please email Chris Eppolito or Matt Evans (department emails eppolito and evans resp.).

For a list of talks from previous semesters, see the archive.

Fall 2018
Meetings: Tuesdays at Noon in WH 309
Organizers: Chris Eppolito and Matt Evans

DATE SPEAKER TITLE AND ABSTRACT


4 September


Matt Evans
Binghamton University

A Weird Categorical Equivalence

Recently, I came across a pretty weird categorical equivalence, so I want to talk about. We'll look at a specific unary algebra and the quasi-variety it generates. This is a category, and somehow, magically, this category is equivalent to a particular category of directed graphs! (All relevant terms will be defined, and this is a first-year friendly talk.)



11 September



No Seminar (Rosh Hashanah)



18 September


Chris Eppolito
Binghamton University


Geometry of Matroids


Matroids are combinatorial models of linear independence; such objects are related to vector arrangements, convex polytopes, graphs, tropical varieties, and more.  Assuming only some basic linear algebra, we will explore some facets of the deep interplay between matroids and geometry.



25 September


Kunle Abawonse
Binghamton University

Partition Identities, Young diagram and Young Tableaux

In this talk, we will discuss q-analogues, some partition
identities, and give some introductory talk to Young Tableaux.



2 October


Ted Ofner
Binghamton University

Geodesic Metrics and Warped Products


We discuss metric geometry, path spaces and length functions; we will focus on the particular example of a warped product metric and how it can be used to correct Baumslag-Solitar obstructions to non-positively curved geometry.


9 October




No Seminar


16 October


Garrett Proffitt
Binghamton University

An exposition on mapping class groups, Teichmüller spaces, and hyperbolic surfaces


In anticipation of the upcoming topics class in topology class next semester, we take a look at the link between mapping class groups, Teichmüller spaces, and hyperbolic surfaces using the torus as our main example. Depending on time, we may get around to showing that the action of the Mobius transformation on the complex plane is compatible with the action of SL_2(Z) on the lattice.



23 October


Chris Chia
Binghamton University

Brouwer fixed-point theorem and a proof using board games


The Brouwer fixed-point theorem is a well-known result about continuous functions on a closed disk. However, in this talk we'll prove the theorem by making a discrete argument; in particular, we will examine the relationship between the theorem and a seemingly simple board game called Hex. No background required!



30 October


Uly Alvarez
Binghamton University

Hyperbolic Groups


Manifolds with negative curvature enjoy many geometric features, such as geodesics which diverge exponentially fast. I will present a discrete counterpart which attempts to capture the geometry of such objects. 



6 November


Josh Carey
Binghamton University

Monstrous Moonshine and the Monster Lie Algebra


In 1978 John McKay noticed that 196884 = 196883+1, giving way to the Monstrous Moonshine Conjecture, which in part claims a relationship between the elliptic modular function J and graded dimension of representations of the Monster Group. From 1978-1990 many chipped away at a proof of Moonshine, with the final piece completed by Richard Borcherds in 1990. In this talk, I will discuss a brief history of this conjecture as well as how Borcherds abstracted the notion of semisimple Lie algebras to construct the Monster Lie Algebra and solve Moonshine once and for all. This talk will be first year friendly.



13 November


Kyle Bayes
Binghamton University

The Universal Approximation Theorem


A nice result about feedforward neural networks is that they can approximate any continuous function.  We will prove this result in this talk.  No prior knowledge about neural networks is necessary.



20 November


Zach Costanzo
Binghamton University

An Introduction to Frobenius Groups

We will introduce Frobenius groups and some nice facts about them. We will use these to prove a special case of the Structure Theorem for Finite Frobenius Groups.


29 November
(Thursday)


Mike Gottstein
Binghamton University

Introduction to De Rahm Theory


In this talk we’ll introduce DeRahm theory through the fundamental theorem of calculus. The talk will be aimed towards any person that has taken a full sequence of calculus courses and wants to see how the story can continue.



6 December


David Cervantes Nava
Binghamton University

Sobolev Spaces: A Weak Approximation to a Partial Talk on Diff. Eq's


Solutions to PDE’s are required to possess a certain degree of differentiability. When looking for solutions, it’s natural to start your search in the space of all functions with the necessary level of “niceness.” Unfortunately, this is not always feasible. It’s often simpler to find a weak solution in a larger space. We’ll provide a basic introduction to these spaces and state some nifty theorems.



11 December


Sayak Sengupta
Binghamton University

An overview on Jacobian Conjecture with positive characteristic


I will start with the statement of the Jacobian conjecture. Then talk a little bit about my problem (mathematical problem) which is a variant of the Jacobian conjecture concluding the talk with some fine examples and some basic tricks that might be used to get an answer to the problem.


Subpages (1): Archive