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# Binghamton University Math Graduate Student Seminar

## Fall 2022

Usual meetings: Wednesday 3:30-4:30 PM, WH 329

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

**Sep. 1: Seminar and BUGCAT Organizational Meeting**

**Abstract:** We will begin by talking about the Graduate Student Seminar. Interested students can sign up for talks!

After that, we will talk about the BUGCAT Conference (Binghamton University Graduate Combinatorics, Algebra, and Topology Conference) that will be held on November 5th - 6th, this year. As the name suggests, the conference is largely organized by graduate students in our department.

This meeting, we will discuss a few different things that will be involved in planning the 2022 Conference. In particular we will be talking about the possibility of online talks and participant funding. Members of 2022 BUGCAT Conference Organizing committee and new graduate students are encouraged to attend. If you are interested but can't come, feel free to email me at mjyothi1@binghamton.edu

**Sep. 8: ****Grad Gathering- Welcome first years!**

**Abstract:** For this week's grad seminar, we would like to invite all of the grad students to help us 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. 15: Sarah Lamoureux, ***Zermelo-Fraenkel Set Theory*** **

**Abstract: **ZF is the most common underlying set theory used in math. We will discuss its axioms and their basic consequences. Our goal is to demonstrate that the fundamental constructions of set theory- unions, products, quotients by equivalence relations, etc.- are indeed valid in ZF.

**Sep. 22: Sayak Sengupta, ***Locally Nilpotent polynomials over Z (Part III)*

**Abstract: **This is the continuation of two talks on the subject which were given in the Spring semester of 2022. So far, we have defined locally nilpotent polynomials at r, seen few examples and also stated and proved a complete classification of locally nilpotent polynomials at 1 and -1. We only needed tools from elementary number theory to prove this. In this talk we will see how such iteration works for locally nilpotent polynomials at r when r\in Z without \pm 1 and also how the difficulty in classifying these polynomials escalates when r is different from \pm 1. In this case we had to resort to a very deep result from algebraic number theory and even then, only the linear polynomials could be covered.

I will start with a brief recollection of the major definitions and results covered in the previous two talks and build our way up to the "general r" case.

**Sep. 29: ****Sayak Sengupta, ***Locally Nilpotent polynomials over Z (Part I**V**)*

**Abstract: **This is the continuation of three talks on the subject which were given in the Spring and Fall semester of 2022. So far, we have defined locally nilpotent polynomials at r, seen few examples and also stated and proved a complete classification of locally nilpotent polynomials at 1 and -1. We only needed tools from elementary number theory to prove this. In this talk we will see how such iteration works for locally nilpotent polynomials at r when r\in Z without \pm 1 and also how the difficulty in classifying these polynomials escalates when r is different from \pm 1. In this case we had to resort to a very deep result from algebraic number theory and even then, only the linear polynomials could be covered.

I will start with a brief recollection of the major definitions and results covered in the previous talks and build our way up to the "general r" case.

**Oct. 6**

**Oct. 12: Hari Asokan, ***Geometric Invariant Theory*

**Abstract: **We will discuss affine group actions on varieties and their quotients with some examples.

**Oct. 19:** no seminar (fall break)

**Oct. 26**

**Nov. 2**

**Nov. 9**

**Nov. 16**

**Nov. 30**

**Dec. 7: Shuchen Mu**