About 

This is a one day algebraic geometry event, happening on Saturday, November 18, 2023 at Michigan State University. 

Schedule 

All talks will be held in Wells Hall C304. Refreshments and lunch will be available in the atrium,  Wells D101.  (The C and D wings of Wells Hall are the parts of the building closest to N. Shaw Ln.)

9:30-10:00 Refreshments

10:00-10:50 Abhishek Oswal

11:10-12:00 David Stapleton

12:00-1:30 Lunch

1:30-2:30 Jarod Alper

2:50-3:40 Kelly Jabbusch

3:40-4:10 Refreshments

4:10-4:40 Shitan Xu

5:00-5:30 Sridhar Venkatesh

6:30-- Conference Dinner

Parking 

The two cloest parking lots are Parking Lot 79 (at the stadium) and Parking Lot 39 (at the fork of N. Shaw Ln and S. Shaw Ln).  

Speaker and Abstracts 

• Jarod Alper (University of Washington) 

Evolution of Moduli: From Deligne and Mumford to Now

Deligne and Mumford's 1969 article "The irreducibility of the space of curves of given genus" laid the foundations of modern moduli theory in algebraic geometry.  In addition to stable curves and the stable reduction theorem, this paper also first introduced algebraic stacks and provided two irreducibility proofs of M_g in positive characteristic.  After summarizing the contributions from this remarkable paper, I will explain how Deligne and Mumford's ideas have evolved over the last 60 years.

• Kelly Jabbusch (University of Michigan–Dearborn)

The minimal projective bundle dimension and toric 2-Fano manifolds

In this talk we will discuss higher Fano manifolds, which are Fano manifolds with positive higher Chern characters.  In particular we will focus on toric 2-Fano manifolds.  Motivated by the problem of classifying toric 2-Fano manifolds, we will introduce a new invariant for smooth projective toric varieties, the minimal projective bundle dimension, m(X). This invariant m(X) captures the minimal degree of a dominating family of rational curves on X or, equivalently, the minimal length of a centrally symmetric primitive relation for the fan of X.  We'll present a classification of smooth projective toric varieties with m(X) ≥ dim(X)-2, and show that projective spaces are the only 2-Fano manifolds among smooth projective toric varieties with m(X) equal to 1, 2, dim(X)-2, dim(X)-1, or dim(X).  This is joint work with Carolina Araujo, Roya Beheshti, Ana-Maria Castravet, Svetlana Makarova, Enrica Mazzon, and Nivedita Viswanathan.

• Abhishek Oswal (Michigan State University)

p-adic Borel hyperbolicity of Shimura varieties of abelian type

Let S be a Shimura variety such that every connected component of the space of complex points of S arises as the quotient of a Hermitian symmetric domain by a torsion-free arithmetic group. In the 1970s, Borel proved that any holomorphic map from a complex algebraic variety V into such a Shimura variety S is algebraic. In this talk, I'll discuss joint work with Anand Patel, Ananth Shankar, and Xinwen Zhu on a p-adic version of this result.

• David Stapleton (University of Michigan) 

Complexes of stable birational invariants

Degenerating algebraic varieties has been an important tool to study birational geometry in the past 10 years. There are many ways to understand the geometric fiber of a degeneration using the special fiber: e.g. (1) the dual complex, (2) the decomposition of the diagonal, and (3) the motivic volume. In this talk we introduce a chain complex that we attach to such a degeneration that is (A) functorial, and (B) a stable birational invariant of the geometric fiber. This invariant lives somewhere between (1), (2), and (3). As an application, we show that A1-connectedness specializes in smooth projective families. This is joint work with James Hotchkiss.

• Sridhar Venkatesh (University of Michigan)

Higher Du Bois and Higher Rational Singularities

k-Du Bois and k-rational singularities are recently introduced refinements of the classical notions of Du Bois and rational singularities, and they have been extensively studied in the local complete intersection (lci) case. Building on a well known result of Kovács that rational singularities are Du Bois, we prove that k-rational singularities are k-Du Bois. This extends previous work of Mustaţă-Popa and Friedman-Laza in the lci and the isolated singularities cases. Additionally, since Kähler differentials are typically not reflexive outside the lci case, we propose new definitions of these singularities that depend only on the cohomologies of the Du Bois complex and not on the behaviour of Kähler differentials. This is based on joint work with Wanchun Shen and Anh Duc Vo.

• Shitan Xu (Michigan State University)

Rationality of Brauer-Severi surface bundle over rational 3-folds

Rationality problems for conic bundles have been well studied over surfaces. In this talk, we generalize an etale cohomology diagram from the case of conic bundles to Brauer-Severi surface bundles. We use this generalization to prove a sufficient condition for a Brauer-Severi surface bundle to be not stably Rational. We also give an example satisfying these sufficient conditions.

Registration 

If you would like to attend, please fill out the registration form, where you can indicate whether you would like to attend the conference dinner or be considered for travel funding. 

The registration deadline is October 28, 2023 for those who wish to attend the conference dinner, and November 10, 2023 otherwise. 

Contact

Please send any questions to flapanla@msu.edu, greerfra@msu.edu, or waldro51@msu.edu.