Binghamton University Math Graduate Student Seminar

Fall 2023

Usual meetings: Wednesdays at 4:40pm, 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 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 Meenakshy Jyothis or Tara Koskulitz (math emails jyothis and koskulitz, respectively) to schedule your talk!

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

Schedule of Talks

Aug. 31 (4PM) : Welcome Meeting for First Year Students

Abstract: We will meet to welcome all the first year students (and welcome back all returning students). We'll discuss any questions the new students have about grad school in general, Binghamton, the seminar, etc. Our first meeting each year is always a nice time for returning students to get caught up and for new students to get to know the other people in the department!

We will also be choosing a more permanent time for the seminar for the rest of the semester.

Sept.  6 (4:40PM) : BUGCAT Organizational Meeting

Abstract: We will meet to discuss the status of plans for BUGCAT 2023, including volunteering to help organize the conference.

Conferences organized entirely by graduate students are a rarity in mathematics. It is especially rare for a conference organized by graduate students to be as large as BUGACT and to cover such a broad range of topics and to attract participants from all over the country. We would really like to encourage everyone to get involved in organizing this very special conference--- especially the current first year students. If enough people help out just a little bit, we'll be able to make it a great conference together.

Sept.  13 : No Meeting

Sept.  20 (4:40PM) : Ezekiel Lemann, Hilbert's third problem and its generalizations

Abstract: When can a given polyhedron be decomposed into pieces and then reassembled into a different polyhedron? This is the basic question of scissors congruence. The aim is to construct invariants which give necessary and sufficient conditions for two polyhedra to be scissors congruent. We will discuss classical results in this area, focusing on the Dehn invariant. Time permitting, we will mention generalizations and higher relations in scissors congruence.

Sept. 27: No Meeting

Oct. 4 (4:40PM): Sarah Lamoureux,  Maximal Ideals and the Axiom of Choice

Abstract: In this talk, we will prove that the existence of maximal ideals in nonzero commutative rings is equivalent over ZF set theory to the Axiom of Choice.

Oct. 11 (4:40PM): Andrew Velasquez-Berroteran, Category Theory in Cognitive Psychology

Abstract: In cognitive psychology, systemacity is the idea that one ought to have the ability of being able to understand and relate two cognitive abilities if they have the same thought structure. This is a concept of how we may be able to perform certain actions or relate two ideas if they share a certain structure or process, and the aspects of systemacity have been studied by psychologists for decades. In recent years, category theory has been put to use to provide some explanation or perspective of how we may look at systemacity and what are things that psychologists may still need to find answers to. In this talk, I will first begin introducing the basic notions of category theory, then talk about systematicity and how category theory has been applied to this area of cognitive psychology.

Oct. 18: No Meeting (Fall Break)

Oct. 25 (4:40PM): Career Panel

Abstract: We will have five former math graduate students working in both academia and industry in the panel. Most of the panelists are Binghamton math department alumni.

If you have any questions for the panelists you can submit them using the following link: https://forms.gle/E6XJWhBhZ7QdX7vU8. You can submit more than one question. Please submit your questions by October 11th. We will also leave a box in the common room to collect more questions. The questions will be emailed to the panelists ahead of time.

Nov. 1 (4:40PM): Paul Barber, From the heat equation to Ricci flow: An introduction to geometric analysis

Abstract: In the 19th and 20th centuries, a vast analytical theory of partial differential equations (PDEs) was developed, in no small part

to study some PDEs arising in differential geometry, for example the minimal surface equation. Geometric analysis is the modern

continuation of this tradition, using PDE theory to attack otherwise intractable problems in geometry and topology. One striking example of

a geometric analysis success story was Grigori Perelman's solution to the 3-dimensional Poincaré conjecture in the early 2000's using Ricci

flow.

In this talk, we introduce the Ricci flow and study its relation to a much simpler linear PDE, the heat equation. No familiarity with

Riemannian geometry or partial differential equations will be assumed. Other elements of geometric analysis besides Ricci flow, such as mean curvature flow and minimal surfaces, will also be introduced.

We hope for this talk to be the first in a series discussing geometric flows, eventually culminating in a presentation of Perelman's 2003

proof of the 3-dimensional Poincaré conjecture.

Nov. 8 (4:40PM): Shuchen Mu, Cyclic homology and derivation

Abstract: The connection between cyclic homology and theory of differential forms and its application

Nov. 15 (4:40PM): Bruce Phillips, An Introduction to Support Vector Machines

Abstract: Support vector machines (SVM) are a powerful tool for binary classification. We will introduce the background and machinery of SVMs with some examples.

Nov. 22: No Meeting (Thanksgiving)

Nov. 29 (4:40PM): Yiyi Cao, An Overview of Machine Learning & Artificial Neural Network

Abstract: To discover how machines mimic intelligent human behaviors to analyze data for insightful decisions, we will first introduce the machine learning framework and methods in a nutshell, with many examples of relevant techniques and algorithms, such as Logistic regression, K-Means clustering, Random Forests and so on. We will then have a brief overview of deep learning, which has many powerful applications particularly with the method of Artificial Neural Network (ANN) in image recognition, computer vision, natural language processing, and speech recognition. 

Mathematics serves AI algorithms and models as the fundamental tool, which could be very useful to better understand modern techniques and help solve real-world problems. Relevant theoretical topics and practical challenges based on mathematics will be shared for future research interests, such as machine learning for causal inference in biological networks.

Dec. 6: No Meeting 

Have a wonderful break, everyone!