Algebraic Geometry Seminar Spring 2018

The seminar meets on Fridays at 2:25 pm in room B113.

Here is the schedule for the previous semester.

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Spring 2018 Schedule

date	speaker	title	host(s)
January 26	Tasos Moulinos (UIC)	TBA	Michael
February 23	Aron Heleodoro (Northwestern)	TBA	Dima
March 9	Phil Tosteson (Michigan)	TBA	Steven
April 20	Alena Pirutka (NYU)	TBA	Jordan
April 27	Alexander Yom Din (Caltech)	TBA	Dima

Abstracts

Tasos Moulinos

Derived Azumaya Algebrais and Twisted K-theory

Topological K-theory of dg-categories is a localizing invariant of dg-categories over [math]\displaystyle{ \mathbb{C} }[/math] taking values in the infinity category of KU-modules. In this talk I describe a relative version of this construction; namely for X a quasi-compact, quasi-separated C-scheme I construct a functor valued in the infinity category of sheaves of spectra on X(C), the complex points of X. For inputs of the form Perf(X, A) where A is an Azumaya algebra over X, I characterize the values of this functor in terms of the twisted topological K-theory of X(C). From this I deduce a certain decomposition, for X a finite CW-complex equipped with a bundle P of projective spaces over X, of KU(P) in terms of the twisted topological K-theory of X ; this is a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer schemes.

Aron Heleodoro

TBA

Alexander Yom Din

TBA