Binghamton University Math Graduate Student Seminar

Fall 2019

Usual meetings: Tuesdays at 12:05pm in WH 309

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 Matt Evans or Andrew Lamoureux (math emails evans and lamoureux resp) to schedule your talk! 

For a list of talks from previous semesters, see the archives (link in the top left corner).

Schedule of Talks

27 August 

Organizational Meeting

3 September

Matt Evans

Generalized spectral spaces and commutative BCK-algebras

There are many methods to obtain algebraic structures from topological spaces: homotopy, co/homology, etc, 

and this is the backbone of algebraic topology. In this field, one uses algebra to answer topological questions. 

But we can also go the other way: given an algebraic structure, we can define a topological space! 

In this talk I will define the spectrum of a commutative BCK-algebra, a topological space, 

and discuss some of its properties. To make the talk a little more first-year-friendly, 

I will begin with the spectrum of a commutative *ring* before going into the more exotic BCK-structures.

10 September

Jon Doane 

Dualizing Kleene Algebras

It is well-known that the class of Boolean algebras is "generated" by the two element chain F<T 

equipped with negation ~F:=T, ~T:=F. When we include an uncertainty element F<U<T, 

along with negation ~U:=U, we generate the class of Kleene algebras.

Of course, there is a famous correspondence between Boolean algebras and Boolean 

topological spaces, named Stone duality; this leads us to wonder if we can 

somehow represent Kleene algebras by topological spaces as well.

In fact, Stone duality is but an application of a more general theory of dual equivalences 

between categories. In this talk, we will utilize this theory to construct 

a dual equivalence between the categories of Kleene algebras

and certain topological spaces.

17 September

Andrew Lamoureux

Kuratowski's Closure-Complement Theorem for Posets

In topology, Kuratowski's Closure-Complement Theorem, also called his Fourteen Set Theorem, states 

that iterating closures and complements on a subset A of a topological space X yields at most 14 

distinct sets. This is true more generally for an element a of a poset P, where the closure is a 

closure map, and an order-reversing involution plays the role of complement. We will also

explore related questions in which interiors and boundaries are generalized, and

we will see that totally ordered sets often satisfy stricter bounds.

24 September

Chris Eppolito

The Category of Matroids is Proto-Exact

Matroids are a combinatorial abstraction of properties of linear independence in a vector space; 

with an appropriate notion of morphism, we obtain a category abstracting that of vector spaces 

with linear maps.  Working from the ground up, this talk sketches a proof that the category

of matroids with strong maps has a proto-exact structure.  Time permitting, we also describe 

some aspects of the K-theory of this category.

This talk is based on joint work with J. Jun and M. Szczesny.

1 October

NO SEMINAR: Rosh Hoshanah

8 October

Josh Carey

AbsolutLIE Terrible

In this talk I will ramble on about some results for my dissertation.

No prior knowledge of Lie Algebras required (if I don't know

anything about it, why should you?!).

15 October

No speaker

22 October

Shuchen Mu

Introduction to Hochschild Homology

How to define homology for an algebra over a commutative ring 

and some basic calculation.

29 October

Zach Costanzo

An Introduction To Character Degree Graphs

Many properties of a group can be obtained by studying its representations over GL(n,F)

for some field F. In particular, we can get a lot of information about the group by studying the

degrees of its irreducible complex representations. I will define group representations and

characters, and discuss their relationship to the structure of groups.

5 November

Seminar cancelled

12 November

Wei Yang

50 Shades of Catalan Number

 Catalan Numbers is ubiquitous in mathematics, the

combinatorist Stanley has an entire book on it.  I came accros this

object on my study of Random Matrices (they are the even moments of

the Semicircle Law).  In this talk, we will observe a few

manifestations and properties of Catalan Numbers.

19 November

Pat McGinty 

L-functions and Primes in Arithmetic Progression

The theory of analytic functions has many applications in number theory.

One particular application was discovered by Dirichlet in 1837 where he

proved there are infinitely many primes in any arithmetic progression 

a, a+b, a+2b,... given gcd(a,b)=1. To do this he introduced L-functions. In

this talk we will define these functions and discuss other tools needed to

prove his theorem.

26 November

No speaker

3 December

Seminar cancelled