Difference between revisions of "Geometry and Topology Seminar"

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(Ben Knudsen (Northwestern))
(Ben Knudsen (Northwestern))
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===Ben Knudsen (Northwestern)===
 
===Ben Knudsen (Northwestern)===
  
Rational homology of configuration spaces via factorization homology
+
''Rational homology of configuration spaces via factorization homology''
  
 
The study of configuration spaces is particularly tractable over a field of characteristic zero, and much effort has gone into producing chain complexes simple enough for explicit computations, formulas for Betti numbers, and homological stability results. I will discuss recent work identifying the homology of the configuration spaces of an arbitrary manifold M with the homology of a certain Lie algebra constructed from the compactly supported cohomology of M. The aforementioned results follow immediately from this identification, albeit with hypotheses removed; in particular, one obtains a new, elementary proof of homological stability for configuration spaces.
 
The study of configuration spaces is particularly tractable over a field of characteristic zero, and much effort has gone into producing chain complexes simple enough for explicit computations, formulas for Betti numbers, and homological stability results. I will discuss recent work identifying the homology of the configuration spaces of an arbitrary manifold M with the homology of a certain Lie algebra constructed from the compactly supported cohomology of M. The aforementioned results follow immediately from this identification, albeit with hypotheses removed; in particular, one obtains a new, elementary proof of homological stability for configuration spaces.

Revision as of 21:36, 17 September 2014

The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
For more information, contact Richard Kent.

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Fall 2014

date speaker title host(s)
August 29 Yuanqi Wang Liouville theorem for complex Monge-Ampere equations with conic singularities. Wang
September 5
September 12 Chris Davis (UW-Eau Claire) L2 signatures and an example of Cochran-Harvey-Leidy Maxim
September 19 Ben Knudsen (Northwestern) TBA Ellenberg
September 26
October 3 Kevin Whyte (UIC) Quasi-isometric embeddings of symmetric spaces Dymarz
October 10 Alden Walker (UChicago) Transfers of quasimorphisms Dymarz
October 17
October 24
October 31 Jing Tao (Oklahoma) TBA Kent
November 1 Young Geometric Group Theory in the Midwest Workshop
November 7 Thomas Barthelmé (Penn State) TBA Kent
November 14
November 21
Thanksgiving Recess
December 5
December 12

Fall Abstracts

Yuanqi Wang

Liouville theorem for complex Monge-Ampere equations with conic singularities.

Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations, we prove the Liouville theorem for conic Kähler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic Kähler geometry.

Chris Davis (UW-Eau Claire)

L2 signatures and an example of Cochran-Harvey-Leidy

Ben Knudsen (Northwestern)

Rational homology of configuration spaces via factorization homology

The study of configuration spaces is particularly tractable over a field of characteristic zero, and much effort has gone into producing chain complexes simple enough for explicit computations, formulas for Betti numbers, and homological stability results. I will discuss recent work identifying the homology of the configuration spaces of an arbitrary manifold M with the homology of a certain Lie algebra constructed from the compactly supported cohomology of M. The aforementioned results follow immediately from this identification, albeit with hypotheses removed; in particular, one obtains a new, elementary proof of homological stability for configuration spaces.

Kevin Whyte (UIC)

TBA

Alden Walker (UChicago)

Rotation quasimorphisms on free groups coming from hyperbolic surface realizations are a particularly nice class of quasimorphisms. I'll describe a transfer construction which lifts rotation quasimorphisms from finite index subgroups, and I'll give an infinite family of examples of group chains for which this construction produces an extremal quasimorphism. Though dynamics and geometry underlie this construction, my talk will be primary combinatorial and should be accessible to anyone at all familiar with geometric group theory. This is joint work with Danny Calegari.

Jing Tao (Oklahoma)

TBA

Thomas Barthelmé (Penn State)

TBA

Spring 2015

date speaker title host(s)
January 23
January 30
February 6
February 13
February 20
February 27
March 6
March 13
March 20
March 27
Spring Break
April 10
April 17
April 24
May 1
May 8

Spring Abstracts

Archive of past Geometry seminars

2013-2014: Geometry_and_Topology_Seminar_2013-2014

2012-2013: Geometry_and_Topology_Seminar_2012-2013

2011-2012: Geometry_and_Topology_Seminar_2011-2012

2010: Fall-2010-Geometry-Topology