Difference between revisions of "Algebraic Geometry Seminar Fall 2017"

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!align="left" | title
 
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!align="left" | host(s)  
 
!align="left" | host(s)  
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|-
 
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|October 6
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|[http://www.math.wisc.edu/~mkbrown5// Michael Brown (UW-Madison)]
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|[[#Michael Brown|Topological K-theory of equivariant singularity categories]]
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|local
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|-
 
|-
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|October 9 (Monday!!, 3:30-4:30, B119)
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|[http://www.math.utah.edu/~bertram/ Aaron Bertram (Utah)]
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|[[#Aaron Bertram|LePotier's Strange Duality and Quot Schemes]]
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|Andrei
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|-
 
|-
|-
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|December 1st
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|[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce (UW-Madison)]
 
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|[[#Juliette Bruce |tba]]
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|local
  
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|-
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|December 8
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|[https://www.math.brown.edu/~mtchan/ Melody Chan (Brown))]
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|[[#Melody Chan|tba]]
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|Jordan
 
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|}
  
 
== Abstracts ==
 
== Abstracts ==
  
<!-- ===Sam Raskin===
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===Michael Brown===
  
'''W-algebras and Whittaker categories'''
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'''Topological K-theory of equivariant singularity categories'''
  
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of attention because of Feigin-Frenkel's duality theorem for them, which identifies W-algebras for a Lie algebra and for its Langlands dual through a subtle construction.
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This is joint work with Tobias Dyckerhoff. Topological K-theory of complex-linear dg categories is a notion introduced by Blanc in his recent article "Topological K-theory of complex noncommutative spaces". In this talk, I will discuss a calculation of the topological K-theory of the dg category of graded matrix factorizations associated to a quasi-homogeneous polynomial with complex coefficients in terms of a classical topological invariant of a complex hypersurface singularity: the Milnor fiber and its monodromy.
  
The purpose of this talk is threefold: 1) to introduce a ``stratification" of the category of modules for the affine W-algebra, 2) to prove an analogue of Skryabin's equivalence in this setting, realizing the categoryof (discrete) modules over the W-algebra in a more natural way, and 3) to explain how these constructions help understand Whittaker categories in the more general setting of local geometric Langlands. These three points all rest on the same geometric observation, which provides a family of affine analogues of Bezrukavnikov-Braverman-Mirkovic. These results lead to a new understanding of the exactness properties of the quantum Drinfeld-Sokolov functor.
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===Aaron Bertram===
  
--->
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'''LePotier's Strange Duality and Quot Schemes'''
 +
Finite schemes of quotients over a smooth curve are a vehicle
 +
for proving strange duality for determinant line bundles on
 +
moduli spaces of vector bundles on Riemann surfaces. This was observed
 +
by Marian and Oprea. In work with Drew Johnson and Thomas Goller,
 +
we extend this idea to del Pezzo surfaces, where we are able to use it to prove cases of Le Potier's strange duality conjecture.

Revision as of 21:13, 2 October 2017

The seminar meets on Fridays at 2:25 pm in Van Vleck B321.

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).

Fall 2017 Schedule

date speaker title host(s)
October 6 Michael Brown (UW-Madison) Topological K-theory of equivariant singularity categories local
October 9 (Monday!!, 3:30-4:30, B119) Aaron Bertram (Utah) LePotier's Strange Duality and Quot Schemes Andrei
December 1st Juliette Bruce (UW-Madison) tba local
December 8 Melody Chan (Brown)) tba Jordan

Abstracts

Michael Brown

Topological K-theory of equivariant singularity categories

This is joint work with Tobias Dyckerhoff. Topological K-theory of complex-linear dg categories is a notion introduced by Blanc in his recent article "Topological K-theory of complex noncommutative spaces". In this talk, I will discuss a calculation of the topological K-theory of the dg category of graded matrix factorizations associated to a quasi-homogeneous polynomial with complex coefficients in terms of a classical topological invariant of a complex hypersurface singularity: the Milnor fiber and its monodromy.

Aaron Bertram

LePotier's Strange Duality and Quot Schemes Finite schemes of quotients over a smooth curve are a vehicle for proving strange duality for determinant line bundles on moduli spaces of vector bundles on Riemann surfaces. This was observed by Marian and Oprea. In work with Drew Johnson and Thomas Goller, we extend this idea to del Pezzo surfaces, where we are able to use it to prove cases of Le Potier's strange duality conjecture.