Difference between revisions of "Algebraic Geometry Seminar Spring 2018"

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|Dima
 
|Dima
 
|-
 
|-
|March 9
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|April 6
 
|[http://www-personal.umich.edu/~ptoste/ Phil Tosteson (Michigan)]
 
|[http://www-personal.umich.edu/~ptoste/ Phil Tosteson (Michigan)]
 
|[[#Phil Tosteson|TBA]]
 
|[[#Phil Tosteson|TBA]]
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== Abstracts ==
 
== Abstracts ==
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 +
===Tasos Moulinos===
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 +
'''Derived Azumaya Algebras and Twisted K-theory'''
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Topological K-theory of dg-categories is a localizing invariant of dg-categories over <math> \mathbb{C} </math>
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taking values in the <math> \infty </math>-category of  <math> KU </math>-modules. In this talk I describe a relative version
 +
of this construction; namely for <math>X</math> a quasi-compact, quasi-separated <math> \mathbb{C} </math>-scheme I construct a
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functor valued in the <math> \infty </math>-category of sheaves of spectra on <math> X(\mathbb{C}) </math>, the complex points of <math>X</math>. For inputs
 +
of the form <math>\operatorname{Perf}(X, A)</math> where <math>A</math> is an Azumaya algebra over <math>X</math>, I characterize the values
 +
of this functor in terms of the twisted topological K-theory of <math> X(\mathbb{C}) </math>. From this I deduce
 +
a certain decomposition, for <math> X </math> a finite CW-complex equipped with a bundle <math> P </math> of projective
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spaces over <math> X </math>, of <math> KU(P) </math> in terms of the twisted topological K-theory of <math> X </math> ; this is
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a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer
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schemes.
  
 
===Aron Heleodoro===
 
===Aron Heleodoro===

Revision as of 11:27, 17 January 2018

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

Here is the schedule for the previous semester.

Algebraic Geometry Mailing List

  • Please join the AGS Mailing List to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).

Spring 2018 Schedule

date speaker title host(s)
January 26 Tasos Moulinos (UIC) TBA Michael
February 23 Aron Heleodoro (Northwestern) TBA Dima
April 6 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 Algebras and Twisted K-theory

Topological K-theory of dg-categories is a localizing invariant of dg-categories over  \mathbb{C} taking values in the  \infty -category of  KU -modules. In this talk I describe a relative version of this construction; namely for X a quasi-compact, quasi-separated  \mathbb{C} -scheme I construct a functor valued in the  \infty -category of sheaves of spectra on  X(\mathbb{C}) , the complex points of X. For inputs of the form \operatorname{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(\mathbb{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