Difference between revisions of "Algebraic Geometry Seminar Spring 2018"

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(Spring 2018 Schedule)
(Spring 2018 Schedule)
 
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The seminar meets on Fridays at 2:25 pm in room TBD
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The seminar meets on Fridays at 2:25 pm in room B113.
  
 
Here is the schedule for [[Algebraic Geometry Seminar Spring 2017 | the previous semester]].
 
Here is the schedule for [[Algebraic Geometry Seminar Spring 2017 | the previous semester]].
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|January 26
 
|January 26
 
|[http://homepages.math.uic.edu/~tmoulinos/ Tasos Moulinos (UIC)]  
 
|[http://homepages.math.uic.edu/~tmoulinos/ Tasos Moulinos (UIC)]  
|[[#Tasos Moulinos|TBA]]
+
|[[#Tasos Moulinos|Derived Azumaya Algebras and Twisted K-theory]]
 
|Michael
 
|Michael
 
+
|-
 +
|February 2
 +
|Daniel Erman (Wisconsin)
 +
|[[#Daniel Erman|TBA]]
 +
|Local
 
|-
 
|-
 
|February 9
 
|February 9
 +
|Juliette Bruce (Wisconsin)
 +
|[[#Juliette Bruce|TBA]]
 +
|Local
 +
|-
 +
|February 23
 +
|Aron Heleodoro (Northwestern)
 +
|[[#Aron Heleodoro|TBA]]
 +
|Dima
 +
|-
 +
|April 6
 +
|[http://www-personal.umich.edu/~ptoste/ Phil Tosteson (Michigan)]
 +
|[[#Phil Tosteson|TBA]]
 +
|Steven
 +
|-
 +
|-
 +
|April 13
 +
|Reserved
 +
|
 +
|Daniel
 +
|-
 +
|April 20
 +
|Alena Pirutka (NYU)
 +
|[[#Alena Pirutka|TBA]]
 +
|Jordan
 +
|-
 +
|April 27
 
|Alexander Yom Din (Caltech)  
 
|Alexander Yom Din (Caltech)  
 
|[[#Alexander Yom Din|TBA]]
 
|[[#Alexander Yom Din|TBA]]
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== Abstracts ==
 
== Abstracts ==
 +
 +
===Tasos Moulinos===
 +
 +
'''Derived Azumaya Algebras and Twisted K-theory'''
 +
 +
Topological K-theory of dg-categories is a localizing invariant of dg-categories over <math> \mathbb{C} </math>
 +
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
 +
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
 +
spaces over <math> X </math>, of <math> KU(P) </math> in terms of the twisted topological K-theory of <math> X </math> ; 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===
 
===Alexander Yom Din===
  
 
'''TBA'''
 
'''TBA'''

Latest revision as of 14:14, 18 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) Derived Azumaya Algebras and Twisted K-theory Michael
February 2 Daniel Erman (Wisconsin) TBA Local
February 9 Juliette Bruce (Wisconsin) TBA Local
February 23 Aron Heleodoro (Northwestern) TBA Dima
April 6 Phil Tosteson (Michigan) TBA Steven
April 13 Reserved Daniel
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