Algebraic Geometry Seminar - Spring 2017

Descendant log Gromov-Witten theory and tropical curves
2017-02-07 15:30 - 16:30 (America/Denver) | LCB 219
Speaker: Travis Mandel, University of Utah

Gromov-Witten (GW) theory is concerned with virtual counts of algebraic curves which satisfy various conditions. I will motivate the log GW theory of Gross-Siebert and Abramovich-Chen by explaining how log structures result in a theory which is better behaved than ordinary GW theory (e.g., less …

Galois cyclic covers of the projective line and pencils of Fermat hypersurfaces
2017-02-21 15:30 - 16:30
Speaker: Donghai Pan, Stanford University

Classically, there are two objects that are particularly interesting to algebraic geometers: hyperelliptic curves and quadrics. The connection between these two seemingly unrelated objects was first revealed by M. Reid, which roughly says that there's a correspondence between hyperelliptic curves …

Toric varieties over non-closed fields
2017-02-28 15:30 - 16:30
Speaker: Fei Xie, UCLA

Toric varieties over non-closed fields can be viewed as "noncommutative" algebraic varieties. More precisely, in Merkurjev-Panin category of motives (a full subcategory of Tabuada's category of noncommutative motives), a smooth projective toric variety subject to certain conditions is an "affine …

Images of toric varieties and liftability of the Frobenius morphism
2017-03-07 15:30 - 16:30
Speaker: Jakub Witaszek, Imperial College London

The celebrated proof of the Hartshorne conjecture by Shigefumi Mori allowed for the study of the geometry of higher dimensional varieties through the analysis of deformations of rational curves. One of the many applications of Mori's results was Lazarsfeld's positive answer to the conjecture of …

Spring Break
2017-03-14 15:30 - 16:30
Speaker: speaker

A duality theorem for de Rham cohomology of graded D-modules
2017-03-21 15:30 - 16:30
Speaker: Wenliang Zhang, University of Illinois at Chicago

I will discuss a duality result for de Rham cohomology of graded D-modules and its applications to understanding local cohomology modules associated with embedding of complex smooth projective varieties into projective spaces. (No background on de Rham cohomology or D-modules will be assumed.) This …

Differentials on the arc space
2017-03-28 15:30 - 16:30
Speaker: Roi Docampo, University of Oklahoma

We study the sheaf of K?hler differentials on the arc space of an algebraic variety. We obtain explicit formulas that can be used effectively to understand the local structure of the arc space. The approach leads to new results as well as simpler and more direct proofs of some of the fundamental …

Curves on Fano Varieties and Manin's Conjecture
2017-04-04 15:30 - 16:30
Speaker: David H. Yang, Massachusetts Institute of Technology

Following work of Lehmann-Tanimoto, we will discuss what structure can be expected in the moduli space of rational curves of fixed degree in an arbitrary Fano variety X . Among other things, we propose a heuristic that should recover the classical Batyrev-Manin conjecture. Then we will discuss …

A Toric Orlov Theorem via Landau-Ginzburg Models
2017-04-11 15:30 - 16:30
Speaker: Tyler Kelly, University of Cambridge

Orlov's theorem defines and proves that any smooth Fano (resp. general type) hypersurface in projective n-space has a subcategory (resp. supercategory) in its bounded derived category of coherent sheaves that is a Fractional Calabi-Yau category. We prove this is the case for a certain class of toric …

Prime congruences and Krull dimension for additively idempotent semirings
2017-04-18 15:30 - 16:30
Speaker: Kalina Mincheva, Yale University

We propose a definition for prime congruences which allows us to define Krull dimension of a semiring as the length of the longest chain of prime congruences. We give a complete description of prime congruences in the polynomial and Laurent polynomial semirings over the tropical semifield …

Generalizing the Satake-Baily-Borel compactification
2017-04-25 15:30 - 16:30
Speaker: Colleen Robles, Duke University

The SBB compactification realizes a locally Hermitian symmetric space as an open, dense subset of a projective algebraic variety. I will discuss a generalization of this construction to obtain a "horizontal completion" (not a compactification) of an arithmetic quotient of a Mumford-Tate domain. The …
