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 GromovWitten theory and tropical curves
GromovWitten (GW) theory is concerned with virtual counts of
algebraic curves which satisfy various conditions. I will motivate the log
GW theory of GrossSiebert and AbramovichChen by explaining how log
structures result in a theory which is better behaved than ordinary GW
theory (e.g., less superabundance, betterbehaved psiclasses, easily
imposed tangency conditons, and invariance in logsmooth families). I will
then explain a correspondence between certain descendant log GW invariants
and certain counts of tropical curves (from the perspective of
NishinousSiebert, but allowing for psiclasses 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 nonclosed fields
Toric varieties over nonclosed fields can be viewed as "noncommutative"
algebraic varieties. More precisely, in MerkurjevPanin 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
nonclosed 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 


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