Binghamton University Math Graduate Student Seminar

Fall 2021

Usual meetings: Thursday 4-5 PM, Whitney 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 mathematics research. We provide a venue for grad student talks on interesting math; we also hope to stimulate discussion around various topics--mathematical and otherwise--relevant to math grad students.

Presentations should be accessible to mathematics grad students, and all are encouraged to contribute a talk!

Email Uly Alvarez or Andrew Lamoureux (math emails alvarez and lamoureux respectively) to schedule your talk!

For a list of talks from previous semesters, see the link in the top right corner.

Schedule of Talks

Sep. 2: Organizational Meeting and BUGCAT Meeting

Abstract: We will begin by discussing the grad seminar and setting times for interested students to give talks. After that, we will talk about BUGCAT. This BUGCAT (Binghamton University Graduate Combinatorics, Algebra, and Topology) Conference meeting will introduce BUGCAT to first year graduate students. We will go through all the updates that have happened since this summer. We will also talk about the possibility of in-person conferences with current university covid protocol.

Sep. 9: Grad Gathering- Welcome first years!

Abstract: For this week's grad seminar, we would like to invite all of the grad students to tune in to fulfill the following task:

Welcome the first years, answer questions about the grad life and show them that the pictures the math department uses don't catch our good side.

It will also give us the opportunity to see old faces, get a chance to catch up, complain, remind ourselves that certain people exist, share some survival tips, etc.

Sep. 16: no seminar- Yom Kippur

Sep. 23: Anthony Ercolano, Cellular Automata, The Garden of Eden Theorem and Surjunctive Groups

Abstract: In this talk we will introduce the theory of cellular automata, beginning with a simple explanation of the most famous cellular automaton, John Conway's Game of Life. We will then generalize the Game of Life, putting the theory on more rigorous mathematical footing so we can discuss important classes of groups related to the theory, namely surjunctive groups, residually finite groups, and Hopfian groups. Our talk will conclude with a discussion of some of the open problems related to them.

Sep. 30: Uly Alvarez, Mirrored topological posets and the tropical phase hyperfield

Abstract: Topological posets are Hausdorff spaces with a partial ordering where the relation is closed in the product space. We will dicuss how the tropical phase hyperfield gives rise to several interesting and well-behaved topological posets.

Oct. 7: Andrew Lamoureux, Points: Schemes -> Varieties

Abstract: The concept of an algebraic variety (let's say over a field K) is easier to understand than that of a scheme over K (a scheme X with a morphism X -> Spec K), even if we restrict to the affine case. The notion of a K-point, which is a section Spec K -> X of the morphism X -> Spec K, helps us obtain a variety from a scheme X of finite type over K, namely the set X(K) of all K-points of X. We will see why X(K) should be a variety, at least in the affine case.

Oct. 14: no seminar- fall break

Oct. 21: Meenakshy Jyothis, Generalized intersection number using geodesic currents

Abstract: Roughly speaking, a geodesic current on a closed surface S is a measure defined on the space of geodesics of the surface. Using geodesic currents we can define intersection form, a concept that generalizes the geometric intersection number between two curves. In this talk I will introduce geodesic currents and intersection form, and we will talk about maps on geodesic currents that preserve the intersection form.

Oct. 28: Chris Chia, Traces and fixed points in a category theory setting

Abstract: I'll talk about the classical definitions of traces and fixed point theory (linear algebra and algebraic topology 1) and then make it much more complicated by thinking about it category theoretically. The talk will have plenty of pictures and examples to make it digestible!

Nov. 4: no seminar

Nov. 11: no seminar

Nov. 18: Lucas Williams, The Pontryagin-Thom Theorem: Connections between geometric and algebraic topology

Abstract: In this talk we will explore the celebrated Pontryagin-Thom theorem which builds a connection between cobordism groups of manifolds and homotopy groups of Thom spaces. We will begin with Pontryagin's construction linking framed cobordism of manifolds with the homotopy groups of spheres. We will then discuss Thom's construction of cobordism of manifolds with additional structure and the ensuing connection with stable homotopy theory.

Nov. 25: no seminar- Thanksgiving break

Dec. 2: Merrick Chang, Universality and the Riemann Zeta Function

Abstract: The Riemman Zeta Function possesses a remarkable property called universality: some translate of the zeta function is able to approximate any holomorphic function of compact subsets of the upper half critical strip up to arbitrary precision. In this talk I briefly discuss the history of "universality" properties, followed by a discussion of the discovery of Voronin's Universality Theorem. I will then discuss developments thereafter which extended the results of the theorem to other functions related to the zeta function, including other L-functions.