1/9 
No Seminar 
1/16 
No Seminar (Colloquium) 
1/23 
No Seminar 
1/30 
David ZureickBrown 
Emory University 
Canonical rings of stacky curves 

Abstract: We give a generalization to stacks of the classical (1920's) theorem of Petri  we give a presentation for the canonical ring of a stacky curve. This is motivated by the following application: we give an explicit presentation for the ring of modular forms for a Fuchsian group with cofinite area, which depends on the signature of the group. This is joint work with John Voight.

2/6 
Tom Sutherland 
University of Mainz 
Stability conditions and rational elliptic surfaces 

Abstract: I will describe the space of Bridgeland stability conditions of the derived category of some CY3 algebras of quivers coming from dimer models on the Riemann sphere. We give a biholomorphic map from the upperhalf plane to the space of stability conditions lifting the period map of a meromorphic differential on a 1dimensional family of elliptic curves, the complement of certain singular fibres in a rational elliptic surface. The map is equivariant with respect to the actions of a congruence subgroup of PSL(2, Z), on the left by monodromy of the rational elliptic surface and on the right by autoequivalences of the derived category.

2/13 
Benjamin Antieau 
University of Illinois at Chicago 
The topological periodindex conjecture 

Abstract: I will survey recent progress on the topological periodindex problem for Brauer groups and its connection to the algebraic periodindex problem.

2/20 
Dan Erman 
University of Wisconsin  Madison 
Big polynomial rings and Stillman's Conjecture 

Abstract: AnanyanHochster's recent proof of Stillman's conjecture is based on a key principle: if $f_1, \ldots, f_r$ are sufficiently general forms in a polynomial ring, then as the number of variables tends to infinity, they will behave increasingly like independent variables. We show that this principle becomes a theorem if ones passes to a limit of polynomial rings, using either the inverse limit or the ultraproduct. This yields the surprising fact that these limiting rings are themselves polynomial rings (in uncountably many variables). It also yields two new proofs of Stillman's conjecture. This is joint work with Steven Sam and Andrew Snowden.

2/27 
Ronen Mukamel 
Rice University 

3/6 
Gordon Heier 
University of Houston 
A generalized Schmidt subspace theorem for closed subschemes 

Abstract: I will discuss our recent generalized version of Schmidt's subspace theorem for closed subschemes in general position in terms of suitably defined Seshadri constants with respect to a fixed ample divisor. I will also explain how our theorem allows to recover a higherdimensional Diophantine approximation theorem of K.F. Rothtype due to D. McKinnon and M. Roth with a significantly shortened proof. This is joint work with A. Levin.

3/13 
Spring Break 
3/20 
Anastassia Etropolski 
Rice University 
Explicit rational point calculations for certain hyperelliptic curves 

Abstract: Given a curve of genus at least 2, it was proven in 1983 by Faltings that it has only finitely many rational points. Unfortunately, this result is ineffective, in that it gives no bound on the number of rational points. 40 years earlier, Chabauty proved the same result under the condition that the rank of the Jacobian of the curve is strictly smaller than the genus. While this is obviously a weaker result, the methods behind that proof could be made effective, and this was done by Coleman in 1985. Coleman's work led to a procedure known as the ChabautyColeman method, which has shown to be extremely effective at determining the set of rational points exactly, particularly in the case of hyperelliptic curves. In this talk I will discuss how we implement this method using Magma and Sage to provably determine the set of rational points on a large set of genus 3, rank 1 hyperelliptic curves, and how these calculations fit into the context of the state of the art conjectures in the field. The subject of this talk is joint work with Jennifer Balakrishnan, Francesca Bianchi, Victoria CantoralFarfan, and Mirela Ciperiani.

3/27 
No Seminar 
4/3 
No Seminar 
4/10 
No Seminar 
4/17 
Jen Berg 
Rice University 
