Binghamton University Math Graduate Student Seminar

The Mathematics Graduate Student Seminar seeks to strengthen communication among grad students at Binghamton University, thereby cultivating our community and fostering a friendly environment in which to do maths research. We provide a venue for grad student talks on interesting maths; we also hope to stimulate discussion around various topics--mathematical and otherwise--relevant to maths grad students.

Presentations should be accessible to mathematics grad students, and all are encouraged to contribute a talk.
 Email Chris Eppolito or Matt Evans (math emails eppolito and evans resp) to schedule your talk!

Spring 2019

Usual Meetings: Wednesdays at 5pm in WH309
Organizers: Chris Eppolito and Matt Evans

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

Schedule of Talks

23 January
Organizational Meeting

30 January
Chris Eppolito (Binghamton University)

Elementary Properties of the Chameleon Group

Thompson's group F is an example of some importance in geometric
group theory. We will construct Thompson's group F combinatorially
and subsequently describe a number of seemingly paradoxical
properties it enjoys.

6 February
Samantha Wyler (Binghamton University)

An introduction to polygonal numbers

Polygonal numbers are number represented as dots or pebbles arranged in
the shape of a regular polygon. We will look at a formula for computing
them and some famous theorems they are involved in.

13 February
BUGCAT General Interest Meeting

20 February
Matt Evans (Binghamton University)

Spectra of Commutative BCK-algebras

BCK-algebras are algebraic structures that come from a non-classical logic. Mimicking
a well-known construction for commutative rings, we can put a topology on the set of
prime ideals; the resulting space is called the spectrum. I will discuss some
results/properties of the spectrum, particularly when the underlying algebra is a
so-called BCK-union. In some special cases, there is a strong connection to ring spectra.

27 February
Uly Alvarez (Binghamton University)

Judging a space by its cover

Given a space X with a "nice enough" cover U, we can get close to
knowing the homotopy type of X. In particular, it can be shown that
the order complex of U is weakly homotopy equivalent to X.

6 March
Changwei Zhou (Binghamton University)

The Markov Chain Monte Carlo Revolution

In 2000s, a psychologist from California state prison dropped in to
consult with legendary statistician Persi Diaconis. They need someone
to decode cryptic messages used by prisoners. The solution used the so
called "MCMC" method from Bayesian statistics. In this talk I will
review basics of Metropolis algorithm and discuss some of the applications
in other fields like machine learning and algebraic geometry.

13 March
John Brown (Binghamton University)

A minor step toward proving a character theory conjecture

In this talk we'll discuss a bit of the work done on a conjecture by Isaacs and
others which states that the degree of any primitive character of a finite group G
divides the size of some conjugacy class of G. We'll focus on the case that G is
symmetric or alternating, with a view to showing that the result holds for every
irreducible character of either group. The talk should be fairly easy to follow.

20 March
NO SEMINAR--Spring Break :/

27 March
Yuan Fang (Binghamton University)

A Review of Bayesian Approach to Model-based Clustering and Some Application

Finite mixture models has been used to model heterogeneous data with a finite number
of unobserved sub-population, hence are widely applied in clustering. Bayesian approach
to parameter estimation for mixture models via Monte Carlo Markov Chain methods has been
proven to possess many advantages over the classical approach. In this talk we will have
a brief review of mixture models and Bayesian approach to model-based clustering. Recent
research project as well as ongoing work related to this area will also be discussed.

3 April
Jon Doane (Binghamton University)

Restriction of Stone Duality to Generalized Cantor Spaces

Stone duality is a correspondence between Boolean algebras (BAs) and Boolean/Stone
topological spaces. Dualizing the free BA F(S) on set S yields a product space 2S,
where 2 = {0,1} is discrete. We call 2S a generalized binary Cantor space (GCS2),
and similarly define the spaces GCSn with n ≥ 2. This talk introduces Stone
duality and then answers the question "what is dual to the class of GCS's?"

10 April
Chris Eppolito (Binghamton University)

Hopf Algebras of Matroids

Hopf algebras are naturally arising algebraic objects, and matroids are interesting
combinatorial objects. This talk is a selective introduction to these topics,
with an eye to constructing and studying Hopf algebras from matroids.

17 April
Zach Moltion (Binghamton University)

Modern Methods of Primality Testing

We will give the background for modern deterministic and probablistic primality
testing for large integers, including Fermat, Lucas, Frobenius, and Baillie-PSW
style tests, as well as some approximate bounds on their testing time. We will
develop some modest field and character theory required to implement these tests.
If time allows, I will present the Lucas-Lehmer algorithm for proving Mersenne
numbers primarily used by GIMPS to find the record breaking large prime numbers.

24 April
Kyle Bayes (Binghamton University) 

The Calculus of Variations

This talk will be an introduction to a powerful tool called the
calculus of variations along with some applications in Riemannian geometry.

1 May
Kunle Abawonse (Binghamton University)

Combinatorial vector bundle

In finding a local combinatorial formula for characteristic classes of smooth
manifolds, comes a theory of combinatorial differential manifold. We will
discuss this and the corresponding bundle theory on oriented matroid and how
it relates to the continuous case.

8 May
Mike Gottstein (Binghamton University)

Introduction to Kummer Theory

A Kummer extension of exponent n is a Galois field extension L|K such that K
contains n distinct roots of unity and the Galois group G is abelian of exponent n.
In particular, every element of G has a finite order and the lcm of all these orders
is n. When G is a finite group, the exponent of G divides |G|. Let K be a field that
contains n distinct roots of unity. Adjoining to K the nth root of any element h of
K creates a (finite) Kummer extension of degree d, where d divides n. Kummer theory
is concerned with classifying all Kummer extensions L of K that have exponent n. To do
this as stated, the machinery needed is more sophisticated than for the finite case.
In this talk we will discuss the problem and the techniques involved so that we can
see some of the first results in the theory.

Subpages (1): Archive