Back-To-School seminar
Fall 2024
Back-To-School seminar
Fall 2024
Over the summer the graduate students at UW have learned many new and interesting topics, whether it be at a conference, at a summer school, through a reading course, or just on your own. This seminar is a place where we can share what we have learned to our fellow graduate students. Not only does this serve as a way to reengage with our existing student body after summer break, but it also welcomes the incoming cohort of students and introduces topics that we are interested in.
The seminar is aimed at all of the graduate students, and the talks should be accessible to a wide selection. For example, roughly half of each talk should be accessible to incoming first year students. Talks are of 50 minute length, with 10 minutes for questions afterwards.
If you are interested in participating, fill out this form.
Schedule
Time: Friday 2:30-3:30
Location: PDL C-401
October 4
Speaker: Tracy Chin
Title: Real Algebraic Geometry
Abstract: This talk will be a survey of a hierarchy of classes of real polynomials. Along the way, we'll investigate the underlying geometry and see some surprising connections to combinatorial objects. We'll start from real-rooted univariate polynomials, then make our way through real stable polynomials to Lorentzian and log-concave polynomials, building more evidence along the way that all math is secretly linear algebra.
October 11
Speaker: Linhang Huang
Title: Mating of Continuum Random Trees
Abstract: In this talk, I will introduce a probabilistic object called the continuum random tree (CRT). We will talk about how gluing two such trees together can help us model the quantum gravity in 2D. We will go through the definition of these random trees as well as their associated random process—Brownian excursion. Using the techniques from probability and topology, we will show why the gluing process of two CRTs produces a topological 2-sphere.
October 18
Speaker: Isaiah Siegl
Title: Non-Intersecting Paths and Real-Rooted Polynomials
Abstract: A matrix is totally non-negative (TNN) if all of the determinants of square submatrices are non-negative. Lindstrom's lemma gives a correspondence between TNN matrices and graphs that can be drawn in a disc, with minors of the matrix corresponding to collections of non-intersecting paths in the graph. I will show how Lindstrom's lemma can be used to give inequalities on the coefficients of polynomials with negative real roots. These inequalities then give Schur-positivity results for symmetric functions obtained from polynomials with negative real roots.
October 25
Speaker: Alex Wang
Title: The Brauer-Manin obstruction on del Pezzo surfaces of degree 2
Abstract: When looking for rational points on varieties, we can often disprove the existence of solutions by checking various positivity or modular arithmetic conditions. However, even if we pass all of these checks, we could still fail to have rational points! In this talk, we'll explore the Brauer-Manin obstruction as a way to explain the absence of rational points. We'll also discuss my ongoing project to prove the local-to-global principle of certain special del Pezzo surfaces of degree 2.
November 1
Speaker: Mal Dolorfino
Title: Galois groups, fundamental groups, and the étale fundamental group
Abstract: The fundamental correspondence for Galois extensions in algebra and Galois covers in topology are nearly identical, and the similarities between these two theories run deep. In this talk, we explore the deeper connections between Galois extensions and Galois covers, and we use this to motivate the definition of the étale fundamental group for algebraic curves.
November 8
Speaker: Jackson Morris
Title: Interactions between algebraic geometry and homotopy theory
Abstract: There is a rich two-way connection between algebraic geometry and homotopy theory. In this talk, we will highlight how each of these fields can help the other. We will start by investigating complex-oriented cohomology theories and motivic homotopy theory, before moving into two key examples: A^1 enumerative geometry and algebraic K-theory.
November 15
Speaker: Jay Reiter
Title: Computing bordism rings with homotopy theory
Abstract: Structured bordism classes of manifolds form a ring—but which ring? In this talk, we will see how answering this question is actually a homotopical problem. The process of translation from geometric topology to homotopy theory is as exciting as the final result: our M.O. will be a tour of classifying spaces, Thom spectra, and many, many pairs of pants.
November 22
Speaker: Charlie Magland
Title: Affine Group Schemes of Multiplicative Type
Abstract: What is an affine group scheme? An example heavy introduction to the topic from someone who is afraid of the word scheme. In particular we will learn about affine group schemes of multiplicative type, the first half of the decomposition classification of abelian affine group schemes.
December 6
Speaker: Andrew Aguilar
Title: Etale Group Schemes
Abstract: Affine group schemes come in many shapes, as we’ve seen with those of multiplicative type. But what other conditions can we impose on the coordinate algebra to get something interesting? In this talk a e’ll introduce what it means for an affine group scheme to be Etale, and give some examples. Then we will outline a connection to group schemes of multiplicative type. Finally, we’ll classify Etale group schemes using Galois theory.