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
UCLA
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
TBA
TBA
March 14 Spring Break
March 21 Wenliang Zhang
University of Illinois at Chicago
TBA
TBA
March 28 Roi Docampo
University of Oklahoma
TBA
TBA
April 4 David H. Yang
Massachusetts Institute of Technology
TBA
TBA
April 11 Tyler Kelly
University of Cambridge
TBA
TBA
April 18
April 25

Archive of previous seminars.


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