Algebraic Geometry Seminar

Spring 2017 — Tuesdays 3:30 - 4:30 PM, location JWB 333

Date Speaker Title — click for abstract (if available)
January 17
January 24
January 31
February 7 Travis Mandel
University of Utah
Descendant log Gromov-Witten theory and tropical curves
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 superabundance, better-behaved psi-classes, easily imposed tangency conditons, and invariance in log-smooth families). I will then explain a correspondence between certain descendant log GW invariants and certain counts of tropical curves (from the perspective of Nishinous-Siebert, but allowing for psi-classes and arbitrary genus). This is based on joint work with H. Ruddat.
February 14
February 21
Room Change:
JWB 333
Donghai Pan
Stanford University
Galois cyclic covers of the projective line and pencils of Fermat hypersurfaces
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 and pencil of quadrics. I'll give a brief review of Reid's work and then describe a higher degree generalization of the correspondence.
February 28 Fei Xie
Toric varieties over non-closed fields
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 object", i.e, isomorphic to a single (noncommutative) algebra. In particular, any smooth projective toric surface is an "affine object" in this sense. I will introduce toric varieties over non-closed fields, and study some examples in the motivic category. Time permits, I will briefly discuss the relation between the motivic category and noncommutative motives.
March 7 Jakub Witaszek
Imperial College London
March 14 Spring Break
March 21 Wenliang Zhang
University of Illinois at Chicago
March 28 Roi Docampo
University of Oklahoma
April 4 David H. Yang
Massachusetts Institute of Technology
April 11 Tyler Kelly
University of Cambridge
April 18
April 25

Archive of previous seminars.

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