Geometry and Topology Seminar 2019-2020: Difference between revisions

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The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.
<br>
<br>  
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].
For more information, contact Shaosai Huang.


[[Image:Hawk.jpg|thumb|300px]]
[[Image:Hawk.jpg|thumb|300px]]




== Fall 2013==
== Fall 2018 ==
 
 


{| cellpadding="8"
{| cellpadding="8"
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!align="left" | host(s)
!align="left" | host(s)
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|September 6
|TBA
|  
|TBA
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|TBA
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|TBA
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|September 13, <b>10:00 AM in 901!</b>
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]
| [http://www.math.wisc.edu/~rkent/ Kent]
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|September 20
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|September 27
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|October 4
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|October 11
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|October 18
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]
| [http://www.math.wisc.edu/~rkent/ Kent]
|-
|October 25
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]
| local
|-
|November 1
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
 
|-
|November 8
| Neil Hoffman (Melbourne)
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]
|[http://www.math.wisc.edu/~rkent/ Kent]
|-
|November 15
| Khalid Bou-Rabee (Minnesota)
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]
|[http://www.math.wisc.edu/~rkent/ Kent]
|-
|November 22
| Morris Hirsch (Wisconsin)
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of  vector fields on real and complex
2-manifolds.'']]
| local
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|Thanksgiving Recess
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|December 6
| Sean Paul (Wisconsin)
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]
| local
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|December 13
| Sean Paul (Wisconsin)
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]
| local
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== Fall Abstracts ==
== Fall Abstracts ==


===Alex Zupan (Texas)===
=== TBA ===
''Totally geodesic subgraphs of the pants graph''


Abstract:
For a compact surface S, the associated pants graph P(S) consists of vertices corresponding to pants decompositions of S and edges corresponding to elementary moves between pants decompositions.  Motivated by the Weil-Petersson geometry of Teichmüller space, Aramayona, Parlier, and Shackleton conjecture that the full subgraph G of P(S) determined by fixing a multicurve is totally geodesic in P(S).  We resolve this conjecture in the case that G is a product of Farey graphs.  This is joint work with Sam Taylor.


===Jayadev Athreya (Illinois)===
== Archive of past Geometry seminars ==
''Gap Distributions and Homogeneous Dynamics''
2017-2018 [[Geometry_and_Topology_Seminar_2017-2018]]
 
<br><br>
Abstract:
2016-2017  [[Geometry_and_Topology_Seminar_2016-2017]]
We discuss the notion of gap distributions of various lists of numbers in [0, 1], in particular focusing on those which are associated to certain low-dimensional dynamical systems. We show how to explicitly compute some examples using techniques of homogeneous dynamics, generalizing earlier work on gaps between Farey Fractions. This works gives some possible notions of `randomness' of special trajectories of billiards in polygons, and is based partly on joint works with J. Chaika, J. Chaika and S. Lelievre, and with Y.Cheung. This talk may also be of interest to number theorists.
 
===Joel Robbin (Wisconsin)===
GIT and  <math>\mu</math>-GIT
 
Many problems in differential geometry can be reduced to solving a PDE of form
<br><br>
<br><br>
<math>
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]
    \mu(x)=0
</math>
<br><br>
<br><br>
where <math>x</math> ranges over some function space and <math>\mu</math> is an infinite dimensional analog of the moment map in symplectic geometry. 
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE.
It was soon discovered that the moment map could be applied to Geometric Invariant Theory:  
if a  compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>,
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds
<br><br>
<br><br>
<math>
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]
    X^s/G^c=X//G:=\mu^{-1}(0)/G
</math>
<br><br>
<br><br>
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient.
In September of 2013 Dietmar Salamon, his student Valentina Georgoulas, and I wrote an exposition of (finite dimensional) GIT from the point of view of symplectic geometry.
The theory works for compact Kaehler manifolds, not just projective varieties.
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.
===Anton Lukyanenko (Illinois)===
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''
Abstract:
A quasi-regular (QR) mapping between metric manifolds is a branched cover with bounded dilatation, e.g. f(z)=z^2. In a joint work with K. Fassler and K. Peltonen, we define QR mappings of sub-Riemannian manifolds and show that:
1) Every lens space admits a uniformly QR (UQR) mapping f.
2) Every UQR mapping leaves invariant a measurable conformal structure.
The first result uses an explicit "conformal trap" construction, while the second builds on similar results by Sullivan-Tukia and a connection to higher-rank symmetric spaces.
===Neil Hoffman (Melbourne)===
''Verified computations for hyperbolic 3-manifolds''
Abstract:
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?
While this question can be answered in the negative if M is known to
be reducible or toroidal, it is often difficult to establish a
certificate of hyperbolicity, and so computer methods have developed
for this purpose. In this talk, I will describe a new method to
establish such a certificate via verified computation and compare the
method to existing techniques.
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.
===Khalid Bou-Rabee (Minnesota)===
''On generalizing a theorem of A. Borel''
The proof of the Hausdorff-Banach-Tarski paradox relies on the existence of a nonabelian free group in the group of rotations of <math>\mathbb{R}^3</math>. To help generalize this paradox, Borel proved the following result on free groups.
Borel’s Theorem (1983): Let <math>F</math> be a free group of rank two. Let <math>G</math> be an arbitrary connected semisimple linear algebraic group (i.e., <math>G = \mathrm{SL}_n</math> where <math>n \geq 2</math>). If <math>\gamma</math> is any  nontrivial element in <math>F</math> and <math>V</math> is any proper subvariety of <math>G(\mathbb{C})</math>, then there exists a homomorphism <math>\phi: F \to G(\mathbb{C})</math> such that <math>\phi(\gamma) \notin V</math>.
What is the class, <math>\mathcal{L}</math>, of groups that may play the role of <math>F</math> in Borel’s Theorem? Since the free group of rank two is in <math>\mathcal{L}</math>, it follows that all residually free groups are in <math>\mathcal{L}</math>. In this talk, we present some methods for determining whether a finitely generated group is in <math>\mathcal{L}</math>. Using these methods, we give a concrete example of a finitely generated group in <math>\mathcal{L}</math> that is *not* residually free. After working out a few other examples, we end with a discussion on how this new theory provides an answer to a question of Brueillard, Green, Guralnick, and Tao concerning double word maps. This talk covers joint work with Michael Larsen.
===Morris Hirsch (Wisconsin)===
''Common zeros for Lie algebras of  vector fields on real and complex 2-manifolds.''
===Sean Paul (Wisconsin)===
''(Semi)stable Pairs I''
===Sean Paul (Wisconsin)===
''(Semi)stable Pairs II''
== Spring 2014 ==
{| cellpadding="8"
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|January 24
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|January 31
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|February 7
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|February 14
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|February 21
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|February 28
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|March 7
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|March 14
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|Spring Break
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|March 28
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| April 4
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]
| [[#Matthew Kahle (Ohio)| ''TBA'']]
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
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|April 11
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|April 18
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|April 25
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|May 2
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|May 9
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== Spring Abstracts ==
===Matthew Kahle (Ohio)===
''TBA''
== Archive of past Geometry seminars ==
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]
<br><br>
<br><br>

Revision as of 15:51, 4 May 2018

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

Hawk.jpg


Fall 2018

date speaker title host(s)
TBA TBA TBA TBA

Fall Abstracts

TBA

Archive of past Geometry seminars

2017-2018 Geometry_and_Topology_Seminar_2017-2018

2016-2017 Geometry_and_Topology_Seminar_2016-2017

2015-2016: Geometry_and_Topology_Seminar_2015-2016

2014-2015: Geometry_and_Topology_Seminar_2014-2015

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