Binghamton University Math Graduate Student Seminar

Fall 2025

Usual meetings: Fridays at 5pm and for 45 minutes , WH 100E.

The Mathematics Graduate Student Seminar seeks to strengthen communication among grad students at Binghamton University and also with other grad students outside 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!

Organizer : Marwa Mosallam, email her (mmosallam@binghamton.edu) to schedule your talk!

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

Schedule of Talks

Aug. 22: Welcome Party

Aug. 29 : Juan Mendoza 

Affiliation: Binghamton University 

Title: The Spectrum of an Abelian Category 

Abstract: -

In 1962, P. Gabriel proved that if $X$ and $Y$ are noetherian schemes and their categories of quasi-coherent sheaves $\textup{Qcoh}(X)$ and $\textup{Qcoh}(Y)$ are equivalent, then X and Y are isomorphic. Then, in 1998 A. Rosenberg generalized this result to arbitrary schemes, and finally in 2004 he extended it to the quasi-separated case. This statement is now known as the Gabriel-Rosenberg Reconstruction Theorem.

The central construction underlying this theorem is the spectrum of an abelian category, which provides a way to recover a scheme from its category of quasi-coherent sheaves. In this talk, we will present this construction, compare it with the spectrum of a ring and give a brief outline of the proof of the theorem. We will also present a partial result related to this Reconstruction Theorem.  

Sept. 5:  Eric Yin 

Affiliation: Binghamton University

Title: Abelian Extensions, Elliptic Curves, and Complex multiplication

Abstract:- 

The Kronecker-Weber theorem provides a complete description of the behavior of abelian extensions of the rationals, as well as a description of the generators of the maximal abelian extension - the primitive roots of unity.  For the case of general algebraic number fields, the problem is much more difficult.

In this talk we discuss some arithmetic on elliptic curves, how they relate to number theory, and complex multiplication on elliptic curves. In particular, we find generators for both the maximal unramified abelian extensions and maximal abelian extensions of an imaginary quadratic field and describe their relationship to the associated elliptic curves.

Sept. 12:  Zhaoshen Zhai  

Affiliation: McGill University, CA.

Title :- Curves Intersecting at-most Once

Abstract:-

Given a closed orientable surface S with genus $g$, how many simple closed curves can we draw on $S$ so that, up to homotopy, they pairwise intersect at most once? The maximum number $N_g$ of such curves is related to the dimension of the $1$-curve complex of $S$, a sister of the now classical, and fundamental, curve complex on $S$. As such, determining $N_g$ is of interest to geometric topologists. We give a survey of the asymptotics of $N_g$ and then focus on the case when $g=3$, where conjecturally $N_3=33$ (it is known that $N_1=3$ and $N_2=12$). In particular, we show that $N_3 \geq 33$ via an explicit construction of a system of curves, which is moreover maximal with respect to inclusion.

Notes: 

Zoom Recording:

Sept. 19:  Thu Quan  

Affiliation: Binghamton University

Title: Some Generalizations of Camina Pairs

Abstract:-

 Let $G$ be a finite group with a nontrivial proper subgroup $H$. If $H$ is normal in $G$ and for every element $x\in G\setminus H$, $x$ is conjugate to $xh$ for all $h\in H$, then the pair $(G,H)$ is called a Camina pair. In 1992, Kuisch and van der Waall proved that $(G,H)$ is a Camina pair if and only if every nontrivial irreducible character of $H$ induces homogeneously to $G$. In this talk, we discuss the equivalence of these two conditions on the pair $(G,H)$ without assuming that $H$ is normal in $G$.  Furthermore, we determine the structure of $H$ under the hypothesis that, for every element $x\in G\setminus H$ of odd order, all elements in the coset $xH$ also have odd order. 

Sept. 26: Julie Rasmusen 

Affiliation: University of Warwick, UK.

Title:- THR of Poincaré ∞-categories

Abstract: In recent years, work by Calmés–Dotto–Harpaz–Hebestreit–Land–Moi–Nardin–Nikolaus–Steimle has moved the theory of Hermitian K-theory into the framework of stable ∞-categories. I will introduce the basic ideas and notions of this theory, but as it is often the case when working with K-theory in any form, this can be very hard to describe. I will therefore introduce a tool which might make our life a bit easier: Real Topological Hochschild Homology. I will explain the ingredients that go into constructing in particular the geometric fixed points of this as a functor, generalizing the formula for ring spectra with anti-involution of Dotto–Moi–Patchkoria–Reeh.

Oct. 3: Trent Lucas 

Affiliation: University of California, Irvine.

Title:-  Why should I care about the mapping class group? 

Abstract:- I’ll discuss the “mapping class group” of a closed surface S; this is the group of homotopy classes of homeomorphisms of S.  What makes this group so interesting is that it lies at the intersection of many different areas of math, including low dimensional topology, group theory, algebraic geometry, complex analysis, number theory, dynamics, and more.  My goal in this talk is to explain some of these connections and try to give a sense of why so many people are interested in this group. 

Oct. 10: Aditya Sarma Phukon

Affiliation: Temple University

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Oct. 17: Samuel Richter 

Affiliation: Binghamton University

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Oct. 24: No Meeting (Rejuvenation Day)

Oct. 31: Dalton Ray Sconce

Affiliation:- Indiana University

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Nov. 7: Chad Nelson

Affiliation: Binghamton University

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Nov. 14: Alexander Waugh 

Affiliation:- University of Washington

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Nov. 21: Han Lim Jang

Affiliation: Binghamton University

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Nov. 28: No Meeting (Happy Thanksgiving!)

Dec. 5: No Meeting for Preparing for Final Exams