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 archives (link in the top left corner).

**Note: Due to the ongoing COVID-19 pandemic, all talks this semester will be online.**

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__Schedule of Talks__

September 3

Organizational Meeting

**September 10**

*Grad Gathering- Welcome first years!*

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.

**September 17**

Andrew Lamoureux

*Zermelo-Fraenkel Set Theory*

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.

**September 24**

Garrett Proffitt

*Infinite-type surfaces and the mapping class group of the plane minus a Cantor set*

There have been many recent developments in the study of so-called "big" mapping class groups of infinite-type surfaces. Notably, in 2016, J. Bavard showed that the mapping class group of a plane minus a Cantor set acts by isometry on a certain infinite diameter, Gromov hyperbolic graph. We present her results, including her joint work with A. Walker on the graph's Gromov boundary. Both papers offer new strategies in the study of "big" mapping class groups.

**October 1**

Uly Alvarez

*Upsetting the Grassmann Poset and its friends*

In the 90's, a topological poset was defined to be a Hausdorff topological space with a partial ordering which "plays nicely" with the topology. In this talk, I will attempt to motivate why I would go ahead and replace the topology with a coarser, generally not Hausdorff, topology.

**October 8**

*No seminar*

**October 15**

Shuchen Mu

*Cayley-Hamilton as a theorem about torsion*

The title speaks for itself.

**October 22**

*No seminar*

**October 29**

Andrew Lamoureux

*Definition of a Scheme*

A scheme is a locally ringed space with an open cover by affine schemes, which are locally ringed spaces isomorphic to the spectrum of some commutative ring. The goal of this talk is to make sense of this. After briefly motivating schemes through varieties, we'll study the Zariski topology on the spectrum- the set of prime ideals- of a commutative ring. Then we'll introduce sheaves and discuss how this gives the spectrum the structure of a locally ringed space.

**November 5**

Zach Costanzo

*Groups Whose Real-valued Character Degrees Are All Prime Powers*

Let G be a finite group. Dolfi, Pacifi, and Sanus show that if all of the real-valued irreducible characters of G have prime degree, then G is solvable and the real-valued characters are contained in a subset of {1,2,p} for some odd prime p. Here, we attempt to generalize some of these results by assuming instead that all of the real-valued irreducible characters of G have prime power degrees. We classify such groups in the case that G is non-solvable, and show a similar result about set of real-valued character degrees in the case that G is solvable.

**November 12**

*No seminar*

**November 19**

Hari Asokan

*Chow Rings*

We will define Chow rings of a Variety and discuss some applications.

**December 3**

Nick Lacasse

*Negation Sets: Minimality and Packing*

A signed graph is a graph with a function that assigns a label of positive or negative to each edge. The sign of a circle is the product of the signs of its edges; a graph is balanced if all of its circles are positive. A set of edges whose negation yields a balanced graph is a negation set. I will discuss my results on determining if a negation set is minimal (i.e., it does not properly contain a negation set) and on packing negation sets (i.e., determining the largest family of negation sets we can find such that its members are pairwise disjoint). No prior knowledge (about signed graphs) will be assumed and my goal is to give you the idea of proofs by using lots of pictures. The talk is based on arXiv:2020.00276.

**December 10**

**December 17**