Schedule and Abstracts

The pre-talks are intended to provide some extra background for graduate students and postdocs so they can more easily follow the talks.

Zoom Link: https://rutgers.zoom.us/j/92913598195?pwd=SElqL05Tc21GRFdwMDZPRjcvcCtyZz09

Friday

1:00 pm - 2:00 pm Registration/Coffee

2:00 pm - 2:30 pm Pre-talk

2:30 pm - 3:30 pm Nadia Ott

3:30 pm - 4:00 pm Break

4:00 pm - 4:30 pm Pre-talk

4:30 pm - 5:30 pm Hannah Larson

Saturday

8:00 am - 9:00 am Registration

9:00 am - 9:30 am Pre-talk

9:30 am - 10:30 am Ziquan Zhuang

10:30 am - 11:00 am coffee

11:00 am - 11:30 am Pre-talk

11:30 am - 12:30 pm Renee Bell

12:30 pm - 1:30 pm Lunch Break

1:30 pm - 2:15 pm Poster Session 1

2:15 pm - 2:45 pm Coffee

2:45 pm - 3:15 pm Pre-talk

3:15 pm - 4:15 pm Marco Castronovo

4:15 pm - 5:00 pm Poster Session 2

Renee Bell

Title: Monodromy of Tamely Ramified Covers of Curves

Abstract: Galois theory describes the rich connection between field theory and group theory. Similarly, the fundamental group in topology connects group theory to the study of topological spaces. In this talk, we formalize this analogy with the étale fundamental group $\pi_1(X)$. Over fields of characteristic 0 $\pi_1(X)$ closely resembles its topological analogue, but in characteristic $p$, dramatic differences and new phenomena have inspired many conjectures, including analogues of the inverse Galois problem. Let k be an algebraically closed field of characteristic p and let X be the projective line over k with three points removed. In joint work with Booher, Chen, and Liu, we show that for each prime $p \geq 5$, there are families of tamely ramified covers with monodromy the symmetric group $S_n$ or alternating group $A_n$ for infinitely many $n$, producing these covers from moduli spaces of elliptic curves.

Marco Castronovo

Title: Symplectic cohomology and toric singularities

Abstract: I will start with a quick introduction to symplectic cohomology, mentioning some recent applications to algebraic geometry. I will then focus on two results, one complete and one in progress, roughly saying that toric projective varieties have an associated symplectic cohomology ring, which is functorial under equivariant resolution of singularities.

Hannah Larson

Title: Chow rings of low-degree Hurwitz spaces

Abstract: The Chow ring of a variety packages information about its subvarieties and how they intersect (a sort of "algebraic version" of the cohomology ring). When studying Chow rings of moduli spaces, there are often certain "tautological" classes that arise naturally from the moduli problem. While determining the full Chow ring of a moduli space may be difficult, the subring generated by tautological classes may have a nicer structure. This motivates two questions: (1) What is the structure of the tautological ring? (2) To what extent are all classes tautological? I'll start by giving some background about these questions for the moduli space of curves M_g, and explain how they also motivated us to study Hurwitz spaces H_{k,g}, parametrizing degree k, genus g covers of P^1. Then, I'll give some results addressing (1) and (2) for the Hurwitz spaces H_{k,g} for k \leq 5. This is joint work with Samir Canning.

Nadia Ott

Title: Artin's theorems in supergeometry

Abstract: Artin's theorems on approximation and algebraization of formal deformations and stacks give general criteria for functors to be, in various senses, described by algebraic objects. It has long been expected that analogous results hold in supergeometry, however proofs of the full suite of Artin theorems have remained absent from the supergeometry literature. One reason for this may be the sense that establishing the Artin theorems in supergeometry would require the tedious repetition of various difficult arguments in commutative algebra, deformation theory, and algebraic geometry. I have recently proved the Artin theorems in the super case. Moreover, at several key points I was able to reduce to the (known) bosonic case by an argument which is significantly simpler than the original bosonic argument.

Ziquan Zhuang

Title: Finite generation and Kähler-Ricci soliton degenerations of Fano varieties

Abstract: By the Hamilton-Tian conjecture on the limit behavior of Kähler-Ricci flows, every complex Fano manifold degenerates to a Fano variety that has a Kähler-Ricci soliton. In this talk, I'll discuss the algebro-geometric analogue of this statement and explain its connection to certain finite generation results in birational geometry. Based on joint work with Harold Blum, Yuchen Liu and Chenyang Xu.