https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Rkent&feedformat=atomUW-Math Wiki - User contributions [en]2021-02-25T03:35:44ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=12738Colloquia/Fall182016-11-19T21:55:16Z<p>Rkent: </p>
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<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|September 16<br />
|[http://www.math.cmu.edu/~ploh/ Po-Shen Loh] (CMU)<br />
|Directed paths: from Ramsey to Pseudorandomness<br />
|Ellenberg<br />
|<br />
|-<br />
|September 23<br />
| [http://www.math.wisc.edu/~craciun/ Gheorghe Craciun] (UW-Madison)<br />
|Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
| Street<br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|September 30<br />
|[http://math.uga.edu/~magyar/ Akos Magyar] (University of Georgia)<br />
|Geometric Ramsey theory<br />
| Cook<br />
|<br />
|-<br />
|October 7<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|October 14<br />
| [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)<br />
|Hypergeometric functions over finite fields<br />
| Yang<br />
|<br />
|-<br />
|October 21<br />
|'''No colloquium this week'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Tuesday, October 25, 9th floor'''<br />
|[http://users.math.yale.edu/users/steinerberger/ Stefan Steinerberger] (Yale)<br />
|Three Miracles in Analysis<br />
|Seeger<br />
|<br />
|-<br />
|October 28, 9th floor<br />
| [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)<br />
|Microscopic hydrodynamic modes in a binary mixture<br />
|Minh-Binh Tran<br />
|<br />
|-<br />
|'''Monday, October 31, B239'''<br />
| [https://math.berkeley.edu/~kpmann/ Kathryn Mann] (Berkeley)<br />
|Groups acting on the circle<br />
|Smith<br />
|<br />
|-<br />
|November 4<br />
|<br />
|<br />
| <br />
|<br />
|-<br />
|'''Monday, November 7 at 4:30, 9th floor''' ([http://www.ams.org/meetings/lectures/maclaurin-lectures AMS Maclaurin lecture])<br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (New Zealand Institute for Advanced Study)<br />
|Siegel's problem on small volume lattices<br />
| Marshall<br />
|<br />
|-<br />
|November 11<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, November 16, 9th floor'''<br />
| [http://math.uchicago.edu/~klindsey/ Kathryn Lindsey] (U Chicago)<br />
|Shapes of Julia Sets<br />
|Michell<br />
|<br />
|-<br />
|November 18, B239<br />
|[http://www-personal.umich.edu/~asnowden/ Andrew Snowden] (University of Michigan)<br />
|Recent progress in representation stability<br />
|Ellenberg<br />
|<br />
|-<br />
|'''Monday, November 21, 9th floor'''<br />
|[https://www.fmi.uni-sofia.bg/fmi/logic/msoskova/index.html Mariya Soskova] (University of Wisconsin-Madison)<br />
|Definability in degree structures<br />
|Smith<br />
|<br />
|-<br />
|November 25<br />
| '''Thanksgiving break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 2, 9th floor<br />
| [http://math.columbia.edu/~hshen/ Hao Shen] (Columbia)<br />
|TBA<br />
|Roch<br />
|<br />
|-<br />
|'''Monday, December 5, B239'''<br />
| [https://www.math.wisc.edu/~wang/ Botong Wang] (UW Madison)<br />
|TBA<br />
|Maxim<br />
|<br />
|-<br />
|December 9<br />
| [http://math.uchicago.edu/~awbrown/ Aaron Brown] (U Chicago)<br />
| [[#Friday, December 9: Aaron Brown (U Chicago) | ''Lattice actions and recent progress in the Zimmer program'']]<br />
|Kent<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 20<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3<br />
|<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|February 6 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[# TBA| TBA ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture)<br />
| Alina Chertock (NC State Univ.)<br />
|[[# | ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
|[[# | ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|February 24<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|March 3<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[# | ]]<br />
|Dymarz<br />
|<br />
|-<br />
|Tuesday, March 7, 4PM (Distinguished Lecture)<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|Wednesday, March 8, 2:25PM <br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|March 17<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
| TBA<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|Wednesday, March 29 (Wasow)<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# TBA| TBA]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|TBA<br />
| Maxim <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang). <br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=12737Geometry and Topology Seminar 2019-20202016-11-19T21:54:00Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "TBA"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "TBA"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "TBA"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 24<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| <br />
| <br />
| <br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| <br />
| <br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Gaven Marin ===<br />
''TBA''<br />
<br />
=== Peyman Morteza ===<br />
''TBA''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=12688Geometry and Topology Seminar 2019-20202016-11-10T02:46:10Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "TBA"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "TBA"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| <br />
| <br />
| <br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 24<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| <br />
| <br />
| <br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| <br />
| <br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Gaven Marin ===<br />
''TBA''<br />
<br />
=== Peyman Morteza ===<br />
''TBA''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=12687Geometry and Topology Seminar 2019-20202016-11-10T00:12:46Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "TBA"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "TBA"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "TBA"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| <br />
| <br />
| <br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 24<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| <br />
| <br />
| <br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| <br />
| <br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Gaven Marin ===<br />
''TBA''<br />
<br />
=== Peyman Morteza ===<br />
''TBA''<br />
<br />
=== Caglar Uyanik ===<br />
''TBA''<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=12686Geometry and Topology Seminar 2019-20202016-11-10T00:11:38Z<p>Rkent: /* Richard Kent */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| [http://www.math.wisc.edu/~rkent Richard Kent] (Wisconsin)<br />
| [[#Richard Kent| ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "TBA"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "TBA"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "TBA"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| <br />
| <br />
| <br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 24<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| <br />
| <br />
| <br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| <br />
| <br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Gaven Marin ===<br />
''TBA''<br />
<br />
=== Peyman Morteza ===<br />
''TBA''<br />
<br />
=== Caglar Uyanik ===<br />
''TBA''<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=12564Geometry and Topology Seminar 2019-20202016-10-19T14:55:03Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon<br />
| [[#Ronan Conlon| "TBA"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|'''November 7''' <br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (University of New Zealand) <br />
| [[#Gaven Martin| "TBA"]]<br />
| Simon Marshall <br />
|-<br />
|November 11<br />
| [http://www.math.wisc.edu/~rkent Richard Kent] (Wisconsin)<br />
| [[#Richard Kent| ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "TBA"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "TBA"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| <br />
| <br />
| <br />
|-<br />
|December 16<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''TBA''<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Gaven Marin ===<br />
''TBA''<br />
<br />
=== Peyman Morteza ===<br />
''TBA''<br />
<br />
=== Richard Kent ===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
Thurston's Geometrization Conjecture, now a celebrated theorem of Perelman, tells us that most 3-manifolds are naturally geometric in nature. In fact, most 3-manifolds admit hyperbolic metrics. In the 1970s, Thurston proved the Geometrization conjecture in the case of Haken manifolds, and the proof revolutionized 3-dimensional topology, hyperbolic geometry, Teichm&uuml;ller theory, and dynamics. Thurston's proof is by induction, constructing a hyperbolic structure from simpler pieces. At the heart of the proof is an analytic function called the ''skinning map'' that one must understand in order to glue hyperbolic structures together. A better understanding of this map would more brightly illuminate the interaction between topology and geometry in dimension three. I will discuss what is currently known about this map.<br />
<br />
=== Caglar Uyanik ===<br />
''TBA''<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=12218Geometry and Topology Seminar 2019-20202016-09-06T21:08:33Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''B223 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "TBA"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "TBA"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "TBA"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| <br />
| <br />
| <br />
|-<br />
|October 28<br />
| Ronan Conlon<br />
| [[#Ronan Conlon| "TBA"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "TBA"]]<br />
| Lu Wang<br />
|-<br />
|'''November 7''' <br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (University of New Zealand) <br />
| [[#Gaven Martin| "TBA"]]<br />
| Simon Marshall <br />
|-<br />
|November 11<br />
| <br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "TBA"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "TBA"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| <br />
| <br />
| <br />
|-<br />
|December 16<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''TBA''<br />
<br />
=== Jiyuan Han ===<br />
''TBA''<br />
<br />
=== Sean Howe ===<br />
''TBA''<br />
<br />
===Yu Li ===<br />
''TBA''<br />
<br />
===Gaven Marin ===<br />
''TBA''<br />
<br />
=== Caglar Uyanik ===<br />
''TBA''<br />
<br />
===Peyman Morteza ===<br />
''TBA''<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''TBA''<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=9736Geometry and Topology Seminar 2019-20202015-05-19T17:38:49Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| [http://www.math.wisc.edu/~strenner/ Balazs Strenner] (Wisconsin)<br />
| [[#Balazs Strenner (Wisconsin) |''Penner’s conjecture on pseudo-Anosov mapping classes.'']]<br />
| local<br />
|-<br />
|<b>Thursday, February 12, at 11AM in VV 901</b><br />
| [http://rybu.org/ Ryan Budney] (Victoria)<br />
| [[#Ryan Budney (Victoria)|''Operads and spaces of knots.'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|February 20<br />
| [http://www.math.illinois.edu/~jsapir2/ Jenya Sapir] (UIUC)<br />
|[[#Jenya Sapir (UIUC) |''Counting non-simple closed curves on surfaces.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
|[http://www3.nd.edu/~bwang3/ Botong Wang] (Notre Dame)<br />
|[[#Botong Wang (Notre Dame) |''Deformation theory with cohomology constraints.'']]<br />
|Max<br />
|<br />
|-<br />
|March 13<br />
| [http://www.math.vanderbilt.edu/~saleaw/ Andrew Sale] (Vanderbilt)<br />
|[[#Andrew Sale (Vanderbilt) | ''A geometric version of the conjugacy problem.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
|| [http://homepages.math.uic.edu/~mbhull/ Michael Hull] (UIC)<br />
|[[#Michael Hull (UIC)|''Acylindrically hyperbolic groups'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
| April 17<br />
|| [https://sites.google.com/site/seanlimath/ Sean Li] (UChicago)<br />
|[[#Sean Li (UChicago)|''Coarse differentiation of Lipschitz functions.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
|| [http://www.math.sunysb.edu/~ssun/ Song Sun] (Stony Brook)<br />
|[[#Song Sun (Stony Brook) | ''Algebraic structure on Gromov-Hausdorff limits'']]<br />
|[http://www.math.wisc.edu/~bwang/ Wang]<br />
|-<br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Balazs Strenner (Wisconsin)===<br />
''Penner’s conjecture on pseudo-Anosov mapping classes.''<br />
<br />
There are many constructions of pseudo-Anosov elements of mapping class groups of surfaces. Some of them are known to generate all pseudo-Anosov mapping classes, others are known not to. In 1988, Penner gave a very general construction of pseudo-Anosov mapping classes, and he conjectured that all pseudo-Anosov mapping classes arise this way up to finite power. This conjecture was known to be true on some simple surfaces, including the torus, but has otherwise remained open. In this talk I prove that the conjecture is false for most surfaces. (This is joint work with Hyunshik Shin.)<br />
<br />
===Ryan Budney (Victoria)===<br />
''Operads and spaces of knots.''<br />
<br />
I will describe a connection between the geometrization of 3-manifolds and a subject called operads. It manifests itself as a structure theorem for the space of smooth embeddings of the circle in the 3-sphere and points to a homotopy-theoretic approach to old questions about finite-type invariants.<br />
<br />
===Jenya Sapir (UIUC)===<br />
''Counting non-simple closed curves on surfaces.''<br />
<br />
We show how to get coarse bounds on the number of (non-simple) closed geodesics on a surface, given upper bounds on both length and self-intersection number. Recent work by Mirzakhani has produced asymptotics for the growth of the number of simple closed curves, and this work has been extended to curves with at most 3 self-intersections with respect to length. However, no asymptotics, or even bounds, were previously known for other bounds on self-intersection number. Time permitting, we will discuss some applications of this result.<br />
<br />
===Botong Wang (Notre Dame)===<br />
''Deformation theory with cohomology constraints.''<br />
<br />
Deformation theory is a powerful tool to study the local structure of moduli spaces. I will first give an introduction to the theory of Deligne-Goldman-Millson, which translates deformation theory problems to problems of differential graded Lie algebras. I will also talk about a generalization to deformation theory problems with cohomology constraints. This is used to study the local structure of cohomology jump loci in various moduli spaces. <br />
<br />
===Andrew Sale (Vanderbilt)===<br />
''A geometric version of the conjugacy problem.''<br />
<br />
The classic conjugacy problem of Max Dehn asks whether, for a given group, there is an algorithm that decides whether pairs of elements are conjugate. Related to this is the following question: given two conjugate elements u,v, what is the shortest length element w such that uw=wv? The conjugacy length function (CLF) formalises this question. I will survey what is known for CLFs of groups, giving a sketch proof for a result in semisimple Lie groups. I will also discuss a new, closely related function, the permutation conjugacy length function (PCL). I will outline its potential application to studying the computational complexity of the conjugacy problem, and describe a result, joint with Y. Antolin, for the PCL of relatively hyperbolic groups.<br />
<br />
===Michael Hull (UIC)===<br />
''Acylindrically hyperbolic groups''<br />
<br />
Hyperbolic and relatively hyperbolic groups have played an important role in the development of geometric group theory. However, there are many other groups which admit interesting and useful actions on hyperbolic metric spaces, including mapping class groups, Out(F_n), directly indecomposable RAAGs, and many 3-manifold groups. The class of acylindrically hyperbolic groups provides a framework for studying all of these groups (and many more) using many of the same techniques developed for hyperbolic and relatively hyperbolic groups. We will give a brief survey of examples and properties of acylindrically hyperbolic groups and show how the study of this class has yielded new results in a number of particular cases.<br />
<br />
===Sean Li (UChicago)===<br />
''Coarse differentiation of Lipschitz functions.''<br />
<br />
Bates, Johnson, Lindenstrauss, Preiss, and Schechtman introduced a notion of large scale differentiation for Lipschitz functions between normed linear spaces. We discuss an extension of this result to the nonabelian setting of Carnot groups and use it to derive quantitative estimates for nonembeddability of such groups into certain classes of metric spaces.<br />
<br />
===Song Sun (Stony Brook)===<br />
''Algebraic structure on Gromov-Hausdorff limits''<br />
<br />
Given a sequence of compact Riemannian manifolds of fixed dimension, under fairly general assumptions we can obtain ``Gromov-Hausdorf limits" that are complete metric spaces. When the manifolds have bounded Ricci curvature and non-collapsing volume, the Anderson-Cheeger-Colding theory provides a regular-singular decomposition of a limit space. It is a central question in Riemannian geometry to understand these singularities. In the case when the manifolds are projective and the metrics are Kahler, we will discuss some recent progress towards an algebro-geometric understanding of the singularities of Gromov-Hausdorff limits. This talk is based on joint work with Simon Donaldson.<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''Rational homology of configuration spaces via factorization homology'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| [http://homepages.math.uic.edu/~kwhyte/ Kevin Whyte] (UIC)<br />
|[[#Kevin Whyte (UIC)|''Quasi-isometric embeddings of symmetric spaces'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 10<br />
|[http://math.uchicago.edu/~akwalker/ Alden Walker] (UChicago)<br />
|[[#Alden Walker (UChicago)|''Roots, Schottky Semigroups, and a proof of Bandt's Conjecture'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''Growth Tight Actions'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 1<br />
| [http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
|-<br />
|November 7<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelm&eacute;] (Penn State)<br />
| [[#Thomas Barthelm&eacute; (Penn State)|''Counting orbits of Anosov flows in free homotopy classes'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 14<br />
| [http://www.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (University of Pennsylvania)<br />
| [[#Alexandra Kjuchukova (University of Pennsylvania)|''On the classification of irregular branched covers of four-manifolds'']]<br />
| [http://www.math.wisc.edu/~Maxim/ Maxim]<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4, <b>Thursday at 4pm in VV 901</b><br />
| Oyku Yurttas (Georgia Tech) <br />
|[[#Oyku Yurttas (Georgia Tech)|''Dynnikov and train track transition matrices of pseudo-Anosov braids'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Thiffeault]<br />
|-<br />
|December 5<br />
| No seminar. <br />
|<br />
|<br />
|-<br />
|December 12<br />
| No seminar.<br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
<br />
''Rational homology of configuration spaces via factorization homology''<br />
<br />
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.<br />
<br />
===Kevin Whyte (UIC)===<br />
The rigidity theorems of Mostow and Margulis for lattices in semi simple Lie groups are some of the most celebrated in their field, and are motivation for much of geometric group theory. Mostow's result, which states that every isomorphism between lattices extends to an equivariant isometry between symmetric spaces, has been generalized by Kleiner and Leeb to say that any map between higher rank symmetric spaces which is quasi-isometric (a large scale version of bilipschitz) is actually a perturbation of an isometry. Margulis' superrigidity theorem, which says every homomorphism between lattices which has infinite image extends to an equivariant isometric embedding of symmetric spaces, has resisted a generalization of this sort. We will discuss one such result, which considers when quasi-isometric embeddings of symmetric spaces are near isometric embeddings. Our results show that the situation is complicated - in some cases one does have rigidity while in others there are exotic quasi-isometric embeddings. What geometric properties distinguish the two cases is only starting to be understood. This is joint work with David Fisher (Indiana).<br />
<br />
===Alden Walker (UChicago)===<br />
In 1985, Barnsley and Harrington defined a "Mandlebrot set" M for pairs of complex dilations. This is the set of complex numbers<br />
c such that the limit set generated by the pair of dilations x-> cx+1 and x-> cx-1 is connected. The set M is also the closure of the set of roots of polynomials with coefficients in {-1,0,1}. As with the usual Mandlebrot set, M has strong connections to dynamics and algebra, and it has been studied by Bousch, Bandt, Solomyak, Xu, Thurston, and Tiozzo. For a geometric group theorist, the study of M is qualitatively similar to the study of Kleinian groups acting on their limit sets or on universal circles.<br />
<br />
Barnsley and Harrington noted the (numerically apparent) existence of infinitely many "holes" in M, which correspond to exotic components of the space of Schottky semigroups. Bandt rigorously confirmed a single hole in 2002 and conjectured that the interior of M is dense in M away from the real axis. We give the new technique of "traps" to certify an interior point of M, and we use these traps to prove Bandt's conjecture and certify the existence of infinitely many holes in M.<br />
<br />
The only prerequisite for this talk is point-set topology. Fun pictures will be provided. This is joint work with Danny Calegari and Sarah Koch.<br />
<br />
===Jing Tao (Oklahoma)===<br />
''Growth Tight Actions''<br />
<br />
Let G be a group equipped with a finite generating set S. G is called growth tight if its exponential growth rate relative to S is strictly greater than that of every quotient G/N with N infinite. This notion was first introduced by Grigorchuk and de la Harpe. Examples of groups that are growth tight include free groups relative to bases and, more generally, hyperbolic groups relative to any generating set. In this talk, I will provide some sufficient conditions for growth tightness which encompass all previous known examples.<br />
<br />
===Thomas Barthelm&eacute; (Penn State)===<br />
''Counting orbits of Anosov flows in free homotopy classes''<br />
<br />
In 1972, Plante and Thurston asked the following question: If M is a manifold supporting an Anosov flow, does the number of conjugacy classes in the fundamental group grows exponentially fast with the length of the shortest orbit representative?<br />
This question can be solved by answering the following: Can one give an upper bound on the growth rate of the length of orbits inside a free homotopy class?<br />
<br />
In this talk, I will explain how one can use the geometry and topology of Anosov flows to answer both questions in the 3-manifold case. This is joint work with Sergio Fenley.<br />
<br />
===Alexandra Kjuchukova (University of Pennsylvania)===<br />
''On the classification of irregular branched covers of four-manifolds''<br />
<br />
It is a famous result of Hilden and Montesinos that every closed orientable three-manifold can be realized as an irregular three-fold cover of S^3 branched over a knot. In contrast, a smooth four-manifold which can be realized as a cover of S^4 branched over a smooth surface must have signature equal to zero. Given two simply-connected, closed, oriented four-manifolds X and Y and a surface B embedded in X with an isolated singularity, I will prove a necessary condition for the existence of an irregular dihedral branched covering map f: Y -> X with branching set B. Conversely, given a simply-connected oriented closed four-manifold X, I will outline a construction realizing as irregular dihedral covers of X infinitely many (and conjecturally all) of the manifolds Y afforded by the necessary condition.<br />
<br />
===Oyku Yurttas (Georgia Tech)===<br />
''Dynnikov and train track transition matrices of pseudo-Anosov braids''<br />
<br />
In this talk we will compare a <i>Dynnikov matrix</i> with the train track transition matrix of a given pseudo-Anosov braid on the finitely punctured disk. Our main result is that these matrices are isospectral up to roots of unity and some zeros under particular conditions.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=9729Geometry and Topology Seminar 2019-20202015-05-06T17:46:48Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Machine Learning and Topology.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Machine Learning and Topology.''<br />
<br />
Suppose we do lots of experiments on various gases, measuring their pressure P, volume V, absolute temperature T and quantity Q (in moles). This gives lot of points in 4 dimensions, with experimental error in observing them. The question is: how can we recover (an approximation to) the 3d-submanifold P.V=const.T.Q? (This is the Ideal Gas Law.) In general, given a point cloud in n-space, clustered round a manifold, how can one recover the manifold? A main tool is splines. <br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| [http://www.math.wisc.edu/~strenner/ Balazs Strenner] (Wisconsin)<br />
| [[#Balazs Strenner (Wisconsin) |''Penner’s conjecture on pseudo-Anosov mapping classes.'']]<br />
| local<br />
|-<br />
|<b>Thursday, February 12, at 11AM in VV 901</b><br />
| [http://rybu.org/ Ryan Budney] (Victoria)<br />
| [[#Ryan Budney (Victoria)|''Operads and spaces of knots.'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|February 20<br />
| [http://www.math.illinois.edu/~jsapir2/ Jenya Sapir] (UIUC)<br />
|[[#Jenya Sapir (UIUC) |''Counting non-simple closed curves on surfaces.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
|[http://www3.nd.edu/~bwang3/ Botong Wang] (Notre Dame)<br />
|[[#Botong Wang (Notre Dame) |''Deformation theory with cohomology constraints.'']]<br />
|Max<br />
|<br />
|-<br />
|March 13<br />
| [http://www.math.vanderbilt.edu/~saleaw/ Andrew Sale] (Vanderbilt)<br />
|[[#Andrew Sale (Vanderbilt) | ''A geometric version of the conjugacy problem.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
|| [http://homepages.math.uic.edu/~mbhull/ Michael Hull] (UIC)<br />
|[[#Michael Hull (UIC)|''Acylindrically hyperbolic groups'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
| April 17<br />
|| [https://sites.google.com/site/seanlimath/ Sean Li] (UChicago)<br />
|[[#Sean Li (UChicago)|''Coarse differentiation of Lipschitz functions.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
|| [http://www.math.sunysb.edu/~ssun/ Song Sun] (Stony Brook)<br />
|[[#Song Sun (Stony Brook) | ''Algebraic structure on Gromov-Hausdorff limits'']]<br />
|[http://www.math.wisc.edu/~bwang/ Wang]<br />
|-<br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Balazs Strenner (Wisconsin)===<br />
''Penner’s conjecture on pseudo-Anosov mapping classes.''<br />
<br />
There are many constructions of pseudo-Anosov elements of mapping class groups of surfaces. Some of them are known to generate all pseudo-Anosov mapping classes, others are known not to. In 1988, Penner gave a very general construction of pseudo-Anosov mapping classes, and he conjectured that all pseudo-Anosov mapping classes arise this way up to finite power. This conjecture was known to be true on some simple surfaces, including the torus, but has otherwise remained open. In this talk I prove that the conjecture is false for most surfaces. (This is joint work with Hyunshik Shin.)<br />
<br />
===Ryan Budney (Victoria)===<br />
''Operads and spaces of knots.''<br />
<br />
I will describe a connection between the geometrization of 3-manifolds and a subject called operads. It manifests itself as a structure theorem for the space of smooth embeddings of the circle in the 3-sphere and points to a homotopy-theoretic approach to old questions about finite-type invariants.<br />
<br />
===Jenya Sapir (UIUC)===<br />
''Counting non-simple closed curves on surfaces.''<br />
<br />
We show how to get coarse bounds on the number of (non-simple) closed geodesics on a surface, given upper bounds on both length and self-intersection number. Recent work by Mirzakhani has produced asymptotics for the growth of the number of simple closed curves, and this work has been extended to curves with at most 3 self-intersections with respect to length. However, no asymptotics, or even bounds, were previously known for other bounds on self-intersection number. Time permitting, we will discuss some applications of this result.<br />
<br />
===Botong Wang (Notre Dame)===<br />
''Deformation theory with cohomology constraints.''<br />
<br />
Deformation theory is a powerful tool to study the local structure of moduli spaces. I will first give an introduction to the theory of Deligne-Goldman-Millson, which translates deformation theory problems to problems of differential graded Lie algebras. I will also talk about a generalization to deformation theory problems with cohomology constraints. This is used to study the local structure of cohomology jump loci in various moduli spaces. <br />
<br />
===Andrew Sale (Vanderbilt)===<br />
''A geometric version of the conjugacy problem.''<br />
<br />
The classic conjugacy problem of Max Dehn asks whether, for a given group, there is an algorithm that decides whether pairs of elements are conjugate. Related to this is the following question: given two conjugate elements u,v, what is the shortest length element w such that uw=wv? The conjugacy length function (CLF) formalises this question. I will survey what is known for CLFs of groups, giving a sketch proof for a result in semisimple Lie groups. I will also discuss a new, closely related function, the permutation conjugacy length function (PCL). I will outline its potential application to studying the computational complexity of the conjugacy problem, and describe a result, joint with Y. Antolin, for the PCL of relatively hyperbolic groups.<br />
<br />
===Michael Hull (UIC)===<br />
''Acylindrically hyperbolic groups''<br />
<br />
Hyperbolic and relatively hyperbolic groups have played an important role in the development of geometric group theory. However, there are many other groups which admit interesting and useful actions on hyperbolic metric spaces, including mapping class groups, Out(F_n), directly indecomposable RAAGs, and many 3-manifold groups. The class of acylindrically hyperbolic groups provides a framework for studying all of these groups (and many more) using many of the same techniques developed for hyperbolic and relatively hyperbolic groups. We will give a brief survey of examples and properties of acylindrically hyperbolic groups and show how the study of this class has yielded new results in a number of particular cases.<br />
<br />
===Sean Li (UChicago)===<br />
''Coarse differentiation of Lipschitz functions.''<br />
<br />
Bates, Johnson, Lindenstrauss, Preiss, and Schechtman introduced a notion of large scale differentiation for Lipschitz functions between normed linear spaces. We discuss an extension of this result to the nonabelian setting of Carnot groups and use it to derive quantitative estimates for nonembeddability of such groups into certain classes of metric spaces.<br />
<br />
===Song Sun (Stony Brook)===<br />
''Algebraic structure on Gromov-Hausdorff limits''<br />
<br />
Given a sequence of compact Riemannian manifolds of fixed dimension, under fairly general assumptions we can obtain ``Gromov-Hausdorf limits" that are complete metric spaces. When the manifolds have bounded Ricci curvature and non-collapsing volume, the Anderson-Cheeger-Colding theory provides a regular-singular decomposition of a limit space. It is a central question in Riemannian geometry to understand these singularities. In the case when the manifolds are projective and the metrics are Kahler, we will discuss some recent progress towards an algebro-geometric understanding of the singularities of Gromov-Hausdorff limits. This talk is based on joint work with Simon Donaldson.<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''Rational homology of configuration spaces via factorization homology'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| [http://homepages.math.uic.edu/~kwhyte/ Kevin Whyte] (UIC)<br />
|[[#Kevin Whyte (UIC)|''Quasi-isometric embeddings of symmetric spaces'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 10<br />
|[http://math.uchicago.edu/~akwalker/ Alden Walker] (UChicago)<br />
|[[#Alden Walker (UChicago)|''Roots, Schottky Semigroups, and a proof of Bandt's Conjecture'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''Growth Tight Actions'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 1<br />
| [http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
|-<br />
|November 7<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelm&eacute;] (Penn State)<br />
| [[#Thomas Barthelm&eacute; (Penn State)|''Counting orbits of Anosov flows in free homotopy classes'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 14<br />
| [http://www.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (University of Pennsylvania)<br />
| [[#Alexandra Kjuchukova (University of Pennsylvania)|''On the classification of irregular branched covers of four-manifolds'']]<br />
| [http://www.math.wisc.edu/~Maxim/ Maxim]<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4, <b>Thursday at 4pm in VV 901</b><br />
| Oyku Yurttas (Georgia Tech) <br />
|[[#Oyku Yurttas (Georgia Tech)|''Dynnikov and train track transition matrices of pseudo-Anosov braids'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Thiffeault]<br />
|-<br />
|December 5<br />
| No seminar. <br />
|<br />
|<br />
|-<br />
|December 12<br />
| No seminar.<br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
<br />
''Rational homology of configuration spaces via factorization homology''<br />
<br />
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.<br />
<br />
===Kevin Whyte (UIC)===<br />
The rigidity theorems of Mostow and Margulis for lattices in semi simple Lie groups are some of the most celebrated in their field, and are motivation for much of geometric group theory. Mostow's result, which states that every isomorphism between lattices extends to an equivariant isometry between symmetric spaces, has been generalized by Kleiner and Leeb to say that any map between higher rank symmetric spaces which is quasi-isometric (a large scale version of bilipschitz) is actually a perturbation of an isometry. Margulis' superrigidity theorem, which says every homomorphism between lattices which has infinite image extends to an equivariant isometric embedding of symmetric spaces, has resisted a generalization of this sort. We will discuss one such result, which considers when quasi-isometric embeddings of symmetric spaces are near isometric embeddings. Our results show that the situation is complicated - in some cases one does have rigidity while in others there are exotic quasi-isometric embeddings. What geometric properties distinguish the two cases is only starting to be understood. This is joint work with David Fisher (Indiana).<br />
<br />
===Alden Walker (UChicago)===<br />
In 1985, Barnsley and Harrington defined a "Mandlebrot set" M for pairs of complex dilations. This is the set of complex numbers<br />
c such that the limit set generated by the pair of dilations x-> cx+1 and x-> cx-1 is connected. The set M is also the closure of the set of roots of polynomials with coefficients in {-1,0,1}. As with the usual Mandlebrot set, M has strong connections to dynamics and algebra, and it has been studied by Bousch, Bandt, Solomyak, Xu, Thurston, and Tiozzo. For a geometric group theorist, the study of M is qualitatively similar to the study of Kleinian groups acting on their limit sets or on universal circles.<br />
<br />
Barnsley and Harrington noted the (numerically apparent) existence of infinitely many "holes" in M, which correspond to exotic components of the space of Schottky semigroups. Bandt rigorously confirmed a single hole in 2002 and conjectured that the interior of M is dense in M away from the real axis. We give the new technique of "traps" to certify an interior point of M, and we use these traps to prove Bandt's conjecture and certify the existence of infinitely many holes in M.<br />
<br />
The only prerequisite for this talk is point-set topology. Fun pictures will be provided. This is joint work with Danny Calegari and Sarah Koch.<br />
<br />
===Jing Tao (Oklahoma)===<br />
''Growth Tight Actions''<br />
<br />
Let G be a group equipped with a finite generating set S. G is called growth tight if its exponential growth rate relative to S is strictly greater than that of every quotient G/N with N infinite. This notion was first introduced by Grigorchuk and de la Harpe. Examples of groups that are growth tight include free groups relative to bases and, more generally, hyperbolic groups relative to any generating set. In this talk, I will provide some sufficient conditions for growth tightness which encompass all previous known examples.<br />
<br />
===Thomas Barthelm&eacute; (Penn State)===<br />
''Counting orbits of Anosov flows in free homotopy classes''<br />
<br />
In 1972, Plante and Thurston asked the following question: If M is a manifold supporting an Anosov flow, does the number of conjugacy classes in the fundamental group grows exponentially fast with the length of the shortest orbit representative?<br />
This question can be solved by answering the following: Can one give an upper bound on the growth rate of the length of orbits inside a free homotopy class?<br />
<br />
In this talk, I will explain how one can use the geometry and topology of Anosov flows to answer both questions in the 3-manifold case. This is joint work with Sergio Fenley.<br />
<br />
===Alexandra Kjuchukova (University of Pennsylvania)===<br />
''On the classification of irregular branched covers of four-manifolds''<br />
<br />
It is a famous result of Hilden and Montesinos that every closed orientable three-manifold can be realized as an irregular three-fold cover of S^3 branched over a knot. In contrast, a smooth four-manifold which can be realized as a cover of S^4 branched over a smooth surface must have signature equal to zero. Given two simply-connected, closed, oriented four-manifolds X and Y and a surface B embedded in X with an isolated singularity, I will prove a necessary condition for the existence of an irregular dihedral branched covering map f: Y -> X with branching set B. Conversely, given a simply-connected oriented closed four-manifold X, I will outline a construction realizing as irregular dihedral covers of X infinitely many (and conjecturally all) of the manifolds Y afforded by the necessary condition.<br />
<br />
===Oyku Yurttas (Georgia Tech)===<br />
''Dynnikov and train track transition matrices of pseudo-Anosov braids''<br />
<br />
In this talk we will compare a <i>Dynnikov matrix</i> with the train track transition matrix of a given pseudo-Anosov braid on the finitely punctured disk. Our main result is that these matrices are isospectral up to roots of unity and some zeros under particular conditions.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=9728Geometry and Topology Seminar 2019-20202015-05-06T16:14:55Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|June 23 or 24, Time and Location TBA<br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Machine Learning and Topology.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Machine Learning and Topology.''<br />
<br />
Suppose we do lots of experiments on various gases, measuring their pressure P, volume V, absolute temperature T and quantity Q (in moles). This gives lot of points in 4 dimensions, with experimental error in observing them. The question is: how can we recover (an approximation to) the 3d-submanifold P.V=const.T.Q? (This is the Ideal Gas Law.) In general, given a point cloud in n-space, clustered round a manifold, how can one recover the manifold? A main tool is splines. <br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| [http://www.math.wisc.edu/~strenner/ Balazs Strenner] (Wisconsin)<br />
| [[#Balazs Strenner (Wisconsin) |''Penner’s conjecture on pseudo-Anosov mapping classes.'']]<br />
| local<br />
|-<br />
|<b>Thursday, February 12, at 11AM in VV 901</b><br />
| [http://rybu.org/ Ryan Budney] (Victoria)<br />
| [[#Ryan Budney (Victoria)|''Operads and spaces of knots.'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|February 20<br />
| [http://www.math.illinois.edu/~jsapir2/ Jenya Sapir] (UIUC)<br />
|[[#Jenya Sapir (UIUC) |''Counting non-simple closed curves on surfaces.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
|[http://www3.nd.edu/~bwang3/ Botong Wang] (Notre Dame)<br />
|[[#Botong Wang (Notre Dame) |''Deformation theory with cohomology constraints.'']]<br />
|Max<br />
|<br />
|-<br />
|March 13<br />
| [http://www.math.vanderbilt.edu/~saleaw/ Andrew Sale] (Vanderbilt)<br />
|[[#Andrew Sale (Vanderbilt) | ''A geometric version of the conjugacy problem.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
|| [http://homepages.math.uic.edu/~mbhull/ Michael Hull] (UIC)<br />
|[[#Michael Hull (UIC)|''Acylindrically hyperbolic groups'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
| April 17<br />
|| [https://sites.google.com/site/seanlimath/ Sean Li] (UChicago)<br />
|[[#Sean Li (UChicago)|''Coarse differentiation of Lipschitz functions.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
|| [http://www.math.sunysb.edu/~ssun/ Song Sun] (Stony Brook)<br />
|[[#Song Sun (Stony Brook) | ''Algebraic structure on Gromov-Hausdorff limits'']]<br />
|[http://www.math.wisc.edu/~bwang/ Wang]<br />
|-<br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Balazs Strenner (Wisconsin)===<br />
''Penner’s conjecture on pseudo-Anosov mapping classes.''<br />
<br />
There are many constructions of pseudo-Anosov elements of mapping class groups of surfaces. Some of them are known to generate all pseudo-Anosov mapping classes, others are known not to. In 1988, Penner gave a very general construction of pseudo-Anosov mapping classes, and he conjectured that all pseudo-Anosov mapping classes arise this way up to finite power. This conjecture was known to be true on some simple surfaces, including the torus, but has otherwise remained open. In this talk I prove that the conjecture is false for most surfaces. (This is joint work with Hyunshik Shin.)<br />
<br />
===Ryan Budney (Victoria)===<br />
''Operads and spaces of knots.''<br />
<br />
I will describe a connection between the geometrization of 3-manifolds and a subject called operads. It manifests itself as a structure theorem for the space of smooth embeddings of the circle in the 3-sphere and points to a homotopy-theoretic approach to old questions about finite-type invariants.<br />
<br />
===Jenya Sapir (UIUC)===<br />
''Counting non-simple closed curves on surfaces.''<br />
<br />
We show how to get coarse bounds on the number of (non-simple) closed geodesics on a surface, given upper bounds on both length and self-intersection number. Recent work by Mirzakhani has produced asymptotics for the growth of the number of simple closed curves, and this work has been extended to curves with at most 3 self-intersections with respect to length. However, no asymptotics, or even bounds, were previously known for other bounds on self-intersection number. Time permitting, we will discuss some applications of this result.<br />
<br />
===Botong Wang (Notre Dame)===<br />
''Deformation theory with cohomology constraints.''<br />
<br />
Deformation theory is a powerful tool to study the local structure of moduli spaces. I will first give an introduction to the theory of Deligne-Goldman-Millson, which translates deformation theory problems to problems of differential graded Lie algebras. I will also talk about a generalization to deformation theory problems with cohomology constraints. This is used to study the local structure of cohomology jump loci in various moduli spaces. <br />
<br />
===Andrew Sale (Vanderbilt)===<br />
''A geometric version of the conjugacy problem.''<br />
<br />
The classic conjugacy problem of Max Dehn asks whether, for a given group, there is an algorithm that decides whether pairs of elements are conjugate. Related to this is the following question: given two conjugate elements u,v, what is the shortest length element w such that uw=wv? The conjugacy length function (CLF) formalises this question. I will survey what is known for CLFs of groups, giving a sketch proof for a result in semisimple Lie groups. I will also discuss a new, closely related function, the permutation conjugacy length function (PCL). I will outline its potential application to studying the computational complexity of the conjugacy problem, and describe a result, joint with Y. Antolin, for the PCL of relatively hyperbolic groups.<br />
<br />
===Michael Hull (UIC)===<br />
''Acylindrically hyperbolic groups''<br />
<br />
Hyperbolic and relatively hyperbolic groups have played an important role in the development of geometric group theory. However, there are many other groups which admit interesting and useful actions on hyperbolic metric spaces, including mapping class groups, Out(F_n), directly indecomposable RAAGs, and many 3-manifold groups. The class of acylindrically hyperbolic groups provides a framework for studying all of these groups (and many more) using many of the same techniques developed for hyperbolic and relatively hyperbolic groups. We will give a brief survey of examples and properties of acylindrically hyperbolic groups and show how the study of this class has yielded new results in a number of particular cases.<br />
<br />
===Sean Li (UChicago)===<br />
''Coarse differentiation of Lipschitz functions.''<br />
<br />
Bates, Johnson, Lindenstrauss, Preiss, and Schechtman introduced a notion of large scale differentiation for Lipschitz functions between normed linear spaces. We discuss an extension of this result to the nonabelian setting of Carnot groups and use it to derive quantitative estimates for nonembeddability of such groups into certain classes of metric spaces.<br />
<br />
===Song Sun (Stony Brook)===<br />
''Algebraic structure on Gromov-Hausdorff limits''<br />
<br />
Given a sequence of compact Riemannian manifolds of fixed dimension, under fairly general assumptions we can obtain ``Gromov-Hausdorf limits" that are complete metric spaces. When the manifolds have bounded Ricci curvature and non-collapsing volume, the Anderson-Cheeger-Colding theory provides a regular-singular decomposition of a limit space. It is a central question in Riemannian geometry to understand these singularities. In the case when the manifolds are projective and the metrics are Kahler, we will discuss some recent progress towards an algebro-geometric understanding of the singularities of Gromov-Hausdorff limits. This talk is based on joint work with Simon Donaldson.<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''Rational homology of configuration spaces via factorization homology'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| [http://homepages.math.uic.edu/~kwhyte/ Kevin Whyte] (UIC)<br />
|[[#Kevin Whyte (UIC)|''Quasi-isometric embeddings of symmetric spaces'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 10<br />
|[http://math.uchicago.edu/~akwalker/ Alden Walker] (UChicago)<br />
|[[#Alden Walker (UChicago)|''Roots, Schottky Semigroups, and a proof of Bandt's Conjecture'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''Growth Tight Actions'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 1<br />
| [http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
|-<br />
|November 7<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelm&eacute;] (Penn State)<br />
| [[#Thomas Barthelm&eacute; (Penn State)|''Counting orbits of Anosov flows in free homotopy classes'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 14<br />
| [http://www.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (University of Pennsylvania)<br />
| [[#Alexandra Kjuchukova (University of Pennsylvania)|''On the classification of irregular branched covers of four-manifolds'']]<br />
| [http://www.math.wisc.edu/~Maxim/ Maxim]<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4, <b>Thursday at 4pm in VV 901</b><br />
| Oyku Yurttas (Georgia Tech) <br />
|[[#Oyku Yurttas (Georgia Tech)|''Dynnikov and train track transition matrices of pseudo-Anosov braids'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Thiffeault]<br />
|-<br />
|December 5<br />
| No seminar. <br />
|<br />
|<br />
|-<br />
|December 12<br />
| No seminar.<br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
<br />
''Rational homology of configuration spaces via factorization homology''<br />
<br />
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.<br />
<br />
===Kevin Whyte (UIC)===<br />
The rigidity theorems of Mostow and Margulis for lattices in semi simple Lie groups are some of the most celebrated in their field, and are motivation for much of geometric group theory. Mostow's result, which states that every isomorphism between lattices extends to an equivariant isometry between symmetric spaces, has been generalized by Kleiner and Leeb to say that any map between higher rank symmetric spaces which is quasi-isometric (a large scale version of bilipschitz) is actually a perturbation of an isometry. Margulis' superrigidity theorem, which says every homomorphism between lattices which has infinite image extends to an equivariant isometric embedding of symmetric spaces, has resisted a generalization of this sort. We will discuss one such result, which considers when quasi-isometric embeddings of symmetric spaces are near isometric embeddings. Our results show that the situation is complicated - in some cases one does have rigidity while in others there are exotic quasi-isometric embeddings. What geometric properties distinguish the two cases is only starting to be understood. This is joint work with David Fisher (Indiana).<br />
<br />
===Alden Walker (UChicago)===<br />
In 1985, Barnsley and Harrington defined a "Mandlebrot set" M for pairs of complex dilations. This is the set of complex numbers<br />
c such that the limit set generated by the pair of dilations x-> cx+1 and x-> cx-1 is connected. The set M is also the closure of the set of roots of polynomials with coefficients in {-1,0,1}. As with the usual Mandlebrot set, M has strong connections to dynamics and algebra, and it has been studied by Bousch, Bandt, Solomyak, Xu, Thurston, and Tiozzo. For a geometric group theorist, the study of M is qualitatively similar to the study of Kleinian groups acting on their limit sets or on universal circles.<br />
<br />
Barnsley and Harrington noted the (numerically apparent) existence of infinitely many "holes" in M, which correspond to exotic components of the space of Schottky semigroups. Bandt rigorously confirmed a single hole in 2002 and conjectured that the interior of M is dense in M away from the real axis. We give the new technique of "traps" to certify an interior point of M, and we use these traps to prove Bandt's conjecture and certify the existence of infinitely many holes in M.<br />
<br />
The only prerequisite for this talk is point-set topology. Fun pictures will be provided. This is joint work with Danny Calegari and Sarah Koch.<br />
<br />
===Jing Tao (Oklahoma)===<br />
''Growth Tight Actions''<br />
<br />
Let G be a group equipped with a finite generating set S. G is called growth tight if its exponential growth rate relative to S is strictly greater than that of every quotient G/N with N infinite. This notion was first introduced by Grigorchuk and de la Harpe. Examples of groups that are growth tight include free groups relative to bases and, more generally, hyperbolic groups relative to any generating set. In this talk, I will provide some sufficient conditions for growth tightness which encompass all previous known examples.<br />
<br />
===Thomas Barthelm&eacute; (Penn State)===<br />
''Counting orbits of Anosov flows in free homotopy classes''<br />
<br />
In 1972, Plante and Thurston asked the following question: If M is a manifold supporting an Anosov flow, does the number of conjugacy classes in the fundamental group grows exponentially fast with the length of the shortest orbit representative?<br />
This question can be solved by answering the following: Can one give an upper bound on the growth rate of the length of orbits inside a free homotopy class?<br />
<br />
In this talk, I will explain how one can use the geometry and topology of Anosov flows to answer both questions in the 3-manifold case. This is joint work with Sergio Fenley.<br />
<br />
===Alexandra Kjuchukova (University of Pennsylvania)===<br />
''On the classification of irregular branched covers of four-manifolds''<br />
<br />
It is a famous result of Hilden and Montesinos that every closed orientable three-manifold can be realized as an irregular three-fold cover of S^3 branched over a knot. In contrast, a smooth four-manifold which can be realized as a cover of S^4 branched over a smooth surface must have signature equal to zero. Given two simply-connected, closed, oriented four-manifolds X and Y and a surface B embedded in X with an isolated singularity, I will prove a necessary condition for the existence of an irregular dihedral branched covering map f: Y -> X with branching set B. Conversely, given a simply-connected oriented closed four-manifold X, I will outline a construction realizing as irregular dihedral covers of X infinitely many (and conjecturally all) of the manifolds Y afforded by the necessary condition.<br />
<br />
===Oyku Yurttas (Georgia Tech)===<br />
''Dynnikov and train track transition matrices of pseudo-Anosov braids''<br />
<br />
In this talk we will compare a <i>Dynnikov matrix</i> with the train track transition matrix of a given pseudo-Anosov braid on the finitely punctured disk. Our main result is that these matrices are isospectral up to roots of unity and some zeros under particular conditions.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=9379Geometry and Topology Seminar 2019-20202015-02-13T17:02:58Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| [http://www.math.wisc.edu/~strenner/ Balazs Strenner] (Wisconsin)<br />
| [[#Balazs Strenner (Wisconsin) |''Penner’s conjecture on pseudo-Anosov mapping classes.'']]<br />
| local<br />
|-<br />
|<b>Thursday, February 12, at 11AM in VV 901</b><br />
| [http://rybu.org/ Ryan Budney] (Victoria)<br />
| [[#Ryan Budney (Victoria)|''Operads and spaces of knots.'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|February 20<br />
| [http://www.math.illinois.edu/~jsapir2/ Jenya Sapir] (UIUC)<br />
|[[#Jenya Sapir (UIUC) |''Counting non-simple closed curves on surfaces.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| [http://www.math.vanderbilt.edu/~saleaw/ Andrew Sale] (Vanderbilt)<br />
|[[#Andrew Sale (Vanderbilt) | "TBA"]]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
|| [http://homepages.math.uic.edu/~mbhull/ Michael Hull] (UIC)<br />
|[[#Michael Hull (UIC)|''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
| April 17<br />
|| [https://sites.google.com/site/seanlimath/ Sean Li] (UChicago)<br />
|[[#Sean Li (UChicago)|''Coarse differentiation of Lipschitz functions.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Balazs Strenner (Wisconsin)===<br />
''Penner’s conjecture on pseudo-Anosov mapping classes.''<br />
<br />
There are many constructions of pseudo-Anosov elements of mapping class groups of surfaces. Some of them are known to generate all pseudo-Anosov mapping classes, others are known not to. In 1988, Penner gave a very general construction of pseudo-Anosov mapping classes, and he conjectured that all pseudo-Anosov mapping classes arise this way up to finite power. This conjecture was known to be true on some simple surfaces, including the torus, but has otherwise remained open. In this talk I prove that the conjecture is false for most surfaces. (This is joint work with Hyunshik Shin.)<br />
<br />
===Ryan Budney (Victoria)===<br />
''Operads and spaces of knots.''<br />
<br />
I will describe a connection between the geometrization of 3-manifolds and a subject called operads. It manifests itself as a structure theorem for the space of smooth embeddings of the circle in the 3-sphere and points to a homotopy-theoretic approach to old questions about finite-type invariants.<br />
<br />
===Jenya Sapir (UIUC)===<br />
''Counting non-simple closed curves on surfaces.''<br />
<br />
We show how to get coarse bounds on the number of (non-simple) closed geodesics on a surface, given upper bounds on both length and self-intersection number. Recent work by Mirzakhani has produced asymptotics for the growth of the number of simple closed curves, and this work has been extended to curves with at most 3 self-intersections with respect to length. However, no asymptotics, or even bounds, were previously known for other bounds on self-intersection number. Time permitting, we will discuss some applications of this result.<br />
<br />
===Andrew Sale (Vanderbilt)===<br />
"TBA"<br />
<br />
===Michael Hull (UIC)===<br />
"TBA"<br />
<br />
===Sean Li (UChicago)===<br />
''Coarse differentiation of Lipschitz functions.''<br />
<br />
Bates, Johnson, Lindenstrauss, Preiss, and Schechtman introduced a notion of large scale differentiation for Lipschitz functions between normed linear spaces. We discuss an extension of this result to the nonabelian setting of Carnot groups and use it to derive quantitative estimates for nonembeddability of such groups into certain classes of metric spaces.<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''Rational homology of configuration spaces via factorization homology'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| [http://homepages.math.uic.edu/~kwhyte/ Kevin Whyte] (UIC)<br />
|[[#Kevin Whyte (UIC)|''Quasi-isometric embeddings of symmetric spaces'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 10<br />
|[http://math.uchicago.edu/~akwalker/ Alden Walker] (UChicago)<br />
|[[#Alden Walker (UChicago)|''Roots, Schottky Semigroups, and a proof of Bandt's Conjecture'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''Growth Tight Actions'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 1<br />
| [http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
|-<br />
|November 7<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelm&eacute;] (Penn State)<br />
| [[#Thomas Barthelm&eacute; (Penn State)|''Counting orbits of Anosov flows in free homotopy classes'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 14<br />
| [http://www.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (University of Pennsylvania)<br />
| [[#Alexandra Kjuchukova (University of Pennsylvania)|''On the classification of irregular branched covers of four-manifolds'']]<br />
| [http://www.math.wisc.edu/~Maxim/ Maxim]<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4, <b>Thursday at 4pm in VV 901</b><br />
| Oyku Yurttas (Georgia Tech) <br />
|[[#Oyku Yurttas (Georgia Tech)|''Dynnikov and train track transition matrices of pseudo-Anosov braids'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Thiffeault]<br />
|-<br />
|December 5<br />
| No seminar. <br />
|<br />
|<br />
|-<br />
|December 12<br />
| No seminar.<br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
<br />
''Rational homology of configuration spaces via factorization homology''<br />
<br />
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.<br />
<br />
===Kevin Whyte (UIC)===<br />
The rigidity theorems of Mostow and Margulis for lattices in semi simple Lie groups are some of the most celebrated in their field, and are motivation for much of geometric group theory. Mostow's result, which states that every isomorphism between lattices extends to an equivariant isometry between symmetric spaces, has been generalized by Kleiner and Leeb to say that any map between higher rank symmetric spaces which is quasi-isometric (a large scale version of bilipschitz) is actually a perturbation of an isometry. Margulis' superrigidity theorem, which says every homomorphism between lattices which has infinite image extends to an equivariant isometric embedding of symmetric spaces, has resisted a generalization of this sort. We will discuss one such result, which considers when quasi-isometric embeddings of symmetric spaces are near isometric embeddings. Our results show that the situation is complicated - in some cases one does have rigidity while in others there are exotic quasi-isometric embeddings. What geometric properties distinguish the two cases is only starting to be understood. This is joint work with David Fisher (Indiana).<br />
<br />
===Alden Walker (UChicago)===<br />
In 1985, Barnsley and Harrington defined a "Mandlebrot set" M for pairs of complex dilations. This is the set of complex numbers<br />
c such that the limit set generated by the pair of dilations x-> cx+1 and x-> cx-1 is connected. The set M is also the closure of the set of roots of polynomials with coefficients in {-1,0,1}. As with the usual Mandlebrot set, M has strong connections to dynamics and algebra, and it has been studied by Bousch, Bandt, Solomyak, Xu, Thurston, and Tiozzo. For a geometric group theorist, the study of M is qualitatively similar to the study of Kleinian groups acting on their limit sets or on universal circles.<br />
<br />
Barnsley and Harrington noted the (numerically apparent) existence of infinitely many "holes" in M, which correspond to exotic components of the space of Schottky semigroups. Bandt rigorously confirmed a single hole in 2002 and conjectured that the interior of M is dense in M away from the real axis. We give the new technique of "traps" to certify an interior point of M, and we use these traps to prove Bandt's conjecture and certify the existence of infinitely many holes in M.<br />
<br />
The only prerequisite for this talk is point-set topology. Fun pictures will be provided. This is joint work with Danny Calegari and Sarah Koch.<br />
<br />
===Jing Tao (Oklahoma)===<br />
''Growth Tight Actions''<br />
<br />
Let G be a group equipped with a finite generating set S. G is called growth tight if its exponential growth rate relative to S is strictly greater than that of every quotient G/N with N infinite. This notion was first introduced by Grigorchuk and de la Harpe. Examples of groups that are growth tight include free groups relative to bases and, more generally, hyperbolic groups relative to any generating set. In this talk, I will provide some sufficient conditions for growth tightness which encompass all previous known examples.<br />
<br />
===Thomas Barthelm&eacute; (Penn State)===<br />
''Counting orbits of Anosov flows in free homotopy classes''<br />
<br />
In 1972, Plante and Thurston asked the following question: If M is a manifold supporting an Anosov flow, does the number of conjugacy classes in the fundamental group grows exponentially fast with the length of the shortest orbit representative?<br />
This question can be solved by answering the following: Can one give an upper bound on the growth rate of the length of orbits inside a free homotopy class?<br />
<br />
In this talk, I will explain how one can use the geometry and topology of Anosov flows to answer both questions in the 3-manifold case. This is joint work with Sergio Fenley.<br />
<br />
===Alexandra Kjuchukova (University of Pennsylvania)===<br />
''On the classification of irregular branched covers of four-manifolds''<br />
<br />
It is a famous result of Hilden and Montesinos that every closed orientable three-manifold can be realized as an irregular three-fold cover of S^3 branched over a knot. In contrast, a smooth four-manifold which can be realized as a cover of S^4 branched over a smooth surface must have signature equal to zero. Given two simply-connected, closed, oriented four-manifolds X and Y and a surface B embedded in X with an isolated singularity, I will prove a necessary condition for the existence of an irregular dihedral branched covering map f: Y -> X with branching set B. Conversely, given a simply-connected oriented closed four-manifold X, I will outline a construction realizing as irregular dihedral covers of X infinitely many (and conjecturally all) of the manifolds Y afforded by the necessary condition.<br />
<br />
===Oyku Yurttas (Georgia Tech)===<br />
''Dynnikov and train track transition matrices of pseudo-Anosov braids''<br />
<br />
In this talk we will compare a <i>Dynnikov matrix</i> with the train track transition matrix of a given pseudo-Anosov braid on the finitely punctured disk. Our main result is that these matrices are isospectral up to roots of unity and some zeros under particular conditions.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=9356Geometry and Topology Seminar 2019-20202015-02-09T22:22:43Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| [http://www.math.wisc.edu/~strenner/ Balazs Strenner] (Wisconsin)<br />
| [[#Balazs Strenner (Wisconsin) |''Penner’s conjecture on pseudo-Anosov mapping classes.'']]<br />
| local<br />
|-<br />
|<b>Thursday, February 13, at 11AM in VV 901</b><br />
| [http://rybu.org/ Ryan Budney] (Victoria)<br />
| [[#Ryan Budney (Victoria)|''Operads and spaces of knots.'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|February 20<br />
| [http://www.math.illinois.edu/~jsapir2/ Jenya Sapir] (UIUC)<br />
|[[#Jenya Sapir (UIUC) |''Counting non-simple closed curves on surfaces.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| [http://www.math.vanderbilt.edu/~saleaw/ Andrew Sale] (Vanderbilt)<br />
|[[#Andrew Sale (Vanderbilt) | "TBA"]]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
|| [https://sites.google.com/site/seanlimath/ Sean Li] (UChicago)<br />
|[[#Sean Li (UChicago)|''Coarse differentiation of Lipschitz functions.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Balazs Strenner (Wisconsin)===<br />
''Penner’s conjecture on pseudo-Anosov mapping classes.''<br />
<br />
There are many constructions of pseudo-Anosov elements of mapping class groups of surfaces. Some of them are known to generate all pseudo-Anosov mapping classes, others are known not to. In 1988, Penner gave a very general construction of pseudo-Anosov mapping classes, and he conjectured that all pseudo-Anosov mapping classes arise this way up to finite power. This conjecture was known to be true on some simple surfaces, including the torus, but has otherwise remained open. In this talk I prove that the conjecture is false for most surfaces. (This is joint work with Hyunshik Shin.)<br />
<br />
===Ryan Budney (Victoria)===<br />
''Operads and spaces of knots.''<br />
<br />
I will describe a connection between the geometrization of 3-manifolds and a subject called operads. It manifests itself as a structure theorem for the space of smooth embeddings of the circle in the 3-sphere and points to a homotopy-theoretic approach to old questions about finite-type invariants.<br />
<br />
===Jenya Sapir (UIUC)===<br />
''Counting non-simple closed curves on surfaces.''<br />
<br />
We show how to get coarse bounds on the number of (non-simple) closed geodesics on a surface, given upper bounds on both length and self-intersection number. Recent work by Mirzakhani has produced asymptotics for the growth of the number of simple closed curves, and this work has been extended to curves with at most 3 self-intersections with respect to length. However, no asymptotics, or even bounds, were previously known for other bounds on self-intersection number. Time permitting, we will discuss some applications of this result.<br />
<br />
===Sean Li (UChicago)===<br />
''Coarse differentiation of Lipschitz functions.''<br />
<br />
Bates, Johnson, Lindenstrauss, Preiss, and Schechtman introduced a notion of large scale differentiation for Lipschitz functions between normed linear spaces. We discuss an extension of this result to the nonabelian setting of Carnot groups and use it to derive quantitative estimates for nonembeddability of such groups into certain classes of metric spaces.<br />
<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''Rational homology of configuration spaces via factorization homology'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| [http://homepages.math.uic.edu/~kwhyte/ Kevin Whyte] (UIC)<br />
|[[#Kevin Whyte (UIC)|''Quasi-isometric embeddings of symmetric spaces'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 10<br />
|[http://math.uchicago.edu/~akwalker/ Alden Walker] (UChicago)<br />
|[[#Alden Walker (UChicago)|''Roots, Schottky Semigroups, and a proof of Bandt's Conjecture'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''Growth Tight Actions'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 1<br />
| [http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
|-<br />
|November 7<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelm&eacute;] (Penn State)<br />
| [[#Thomas Barthelm&eacute; (Penn State)|''Counting orbits of Anosov flows in free homotopy classes'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 14<br />
| [http://www.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (University of Pennsylvania)<br />
| [[#Alexandra Kjuchukova (University of Pennsylvania)|''On the classification of irregular branched covers of four-manifolds'']]<br />
| [http://www.math.wisc.edu/~Maxim/ Maxim]<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4, <b>Thursday at 4pm in VV 901</b><br />
| Oyku Yurttas (Georgia Tech) <br />
|[[#Oyku Yurttas (Georgia Tech)|''Dynnikov and train track transition matrices of pseudo-Anosov braids'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Thiffeault]<br />
|-<br />
|December 5<br />
| No seminar. <br />
|<br />
|<br />
|-<br />
|December 12<br />
| No seminar.<br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
<br />
''Rational homology of configuration spaces via factorization homology''<br />
<br />
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.<br />
<br />
===Kevin Whyte (UIC)===<br />
The rigidity theorems of Mostow and Margulis for lattices in semi simple Lie groups are some of the most celebrated in their field, and are motivation for much of geometric group theory. Mostow's result, which states that every isomorphism between lattices extends to an equivariant isometry between symmetric spaces, has been generalized by Kleiner and Leeb to say that any map between higher rank symmetric spaces which is quasi-isometric (a large scale version of bilipschitz) is actually a perturbation of an isometry. Margulis' superrigidity theorem, which says every homomorphism between lattices which has infinite image extends to an equivariant isometric embedding of symmetric spaces, has resisted a generalization of this sort. We will discuss one such result, which considers when quasi-isometric embeddings of symmetric spaces are near isometric embeddings. Our results show that the situation is complicated - in some cases one does have rigidity while in others there are exotic quasi-isometric embeddings. What geometric properties distinguish the two cases is only starting to be understood. This is joint work with David Fisher (Indiana).<br />
<br />
===Alden Walker (UChicago)===<br />
In 1985, Barnsley and Harrington defined a "Mandlebrot set" M for pairs of complex dilations. This is the set of complex numbers<br />
c such that the limit set generated by the pair of dilations x-> cx+1 and x-> cx-1 is connected. The set M is also the closure of the set of roots of polynomials with coefficients in {-1,0,1}. As with the usual Mandlebrot set, M has strong connections to dynamics and algebra, and it has been studied by Bousch, Bandt, Solomyak, Xu, Thurston, and Tiozzo. For a geometric group theorist, the study of M is qualitatively similar to the study of Kleinian groups acting on their limit sets or on universal circles.<br />
<br />
Barnsley and Harrington noted the (numerically apparent) existence of infinitely many "holes" in M, which correspond to exotic components of the space of Schottky semigroups. Bandt rigorously confirmed a single hole in 2002 and conjectured that the interior of M is dense in M away from the real axis. We give the new technique of "traps" to certify an interior point of M, and we use these traps to prove Bandt's conjecture and certify the existence of infinitely many holes in M.<br />
<br />
The only prerequisite for this talk is point-set topology. Fun pictures will be provided. This is joint work with Danny Calegari and Sarah Koch.<br />
<br />
===Jing Tao (Oklahoma)===<br />
''Growth Tight Actions''<br />
<br />
Let G be a group equipped with a finite generating set S. G is called growth tight if its exponential growth rate relative to S is strictly greater than that of every quotient G/N with N infinite. This notion was first introduced by Grigorchuk and de la Harpe. Examples of groups that are growth tight include free groups relative to bases and, more generally, hyperbolic groups relative to any generating set. In this talk, I will provide some sufficient conditions for growth tightness which encompass all previous known examples.<br />
<br />
===Thomas Barthelm&eacute; (Penn State)===<br />
''Counting orbits of Anosov flows in free homotopy classes''<br />
<br />
In 1972, Plante and Thurston asked the following question: If M is a manifold supporting an Anosov flow, does the number of conjugacy classes in the fundamental group grows exponentially fast with the length of the shortest orbit representative?<br />
This question can be solved by answering the following: Can one give an upper bound on the growth rate of the length of orbits inside a free homotopy class?<br />
<br />
In this talk, I will explain how one can use the geometry and topology of Anosov flows to answer both questions in the 3-manifold case. This is joint work with Sergio Fenley.<br />
<br />
===Alexandra Kjuchukova (University of Pennsylvania)===<br />
''On the classification of irregular branched covers of four-manifolds''<br />
<br />
It is a famous result of Hilden and Montesinos that every closed orientable three-manifold can be realized as an irregular three-fold cover of S^3 branched over a knot. In contrast, a smooth four-manifold which can be realized as a cover of S^4 branched over a smooth surface must have signature equal to zero. Given two simply-connected, closed, oriented four-manifolds X and Y and a surface B embedded in X with an isolated singularity, I will prove a necessary condition for the existence of an irregular dihedral branched covering map f: Y -> X with branching set B. Conversely, given a simply-connected oriented closed four-manifold X, I will outline a construction realizing as irregular dihedral covers of X infinitely many (and conjecturally all) of the manifolds Y afforded by the necessary condition.<br />
<br />
===Oyku Yurttas (Georgia Tech)===<br />
''Dynnikov and train track transition matrices of pseudo-Anosov braids''<br />
<br />
In this talk we will compare a <i>Dynnikov matrix</i> with the train track transition matrix of a given pseudo-Anosov braid on the finitely punctured disk. Our main result is that these matrices are isospectral up to roots of unity and some zeros under particular conditions.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology&diff=9338Geometry and Topology2015-02-06T22:35:14Z<p>Rkent: </p>
<hr />
<div>=='''Seminars'''==<br />
<br />
<b><font size="3">[[Geometry and Topology Seminar]]</font></b><br />
<br />
[[PDE Geometric Analysis seminar]]<br />
<br />
[[Symplectic Geometry Seminar]]<br />
<br />
== '''Faculty''' ==<br />
<br />
'''Faculty in Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/ Tullia Dymarz] (U Chicago 2007) Geometric group theory, quasi-isometric rigidity.<br />
<br />
[http://www.math.wisc.edu/~rkent Richard Peabody Kent IV] (UT Austin 2006) <br />
Hyperbolic geometry, mapping class groups, geometric group theory, connections to algebra.<br />
<br />
[http://www.math.wisc.edu/~maribeff/ Gloria Mari-Beffa] (U Minnesota &ndash; Minneapolis 1991) <br />
Differential geometry, invariant theory, completely integrable systems.<br />
<br />
[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim] (U Penn 2005)<br />
Geometry and topology of singularities.<br />
<br />
[http://www.math.wisc.edu/~stpaul/ Sean T. Paul] (Princeton 2000)<br />
Complex differential geometry.<br />
<br />
[http://www.math.wisc.edu/~jeffv/ Jeff Viaclovsky] (Princeton 1999)<br />
Differential geometry, geometric analysis.<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW &ndash; Madison 2008) <br />
Geometric flows.<br />
<br />
<br />
'''Faculty with research tied to Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~angenent/ Sigurd Angenent] (Leiden 1986) Partial differential equations.<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru] (Cornell 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin 1998) Fluid dynamics, mixing, biological swimming and mixing, topological dynamics.<br />
<br />
<br />
'''Postdoctoral faculty in Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~villa/ Manuel Gonz&aacute;lez Villa] (Universidad Complutense de<br />
Madrid 2010)<br />
Geometry and topology of singularities of complex algebraic varieties. <br />
<br />
<br />
'''Honorary Fellow'''<br />
<br />
Morris Hirsch (U Chicago 1958)<br />
<br />
<br />
'''Emeriti'''<br />
<br />
Edward Fadell (Ohio State 1952)<br />
<br />
Sufiàn Husseini (Princeton 1960)<br />
Algebraic topology and applications.<br />
<br />
[http://www.math.wisc.edu/~robbin/ Joel Robbin] (Princeton 1965)<br />
Dynamical systems and symplectic geometry.<br />
<br />
Peter Orlik (U Michigan 1966)<br />
<br />
Mary Ellen Rudin (UT Austin 1949)<br />
<br />
<br />
=='''Conferences'''==<br />
<br />
'''Upcoming conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~rkent/MXRI.html Moduli Crossroads Retreat, I]<br />
<br />
'''Previous conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day]<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/home Mirror Symmetry in the Midwest II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing12.html Singularities in the Midwest, II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest]<br />
<br />
[http://www.math.wisc.edu/~oh/glgc/ 2010 Great Lakes Geometry Conference]<br />
<br />
<br />
<!-- ''Graduate study in Geometry and Topology at UW-Madison''' --></div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=9233Geometry and Topology Seminar 2019-20202015-01-26T21:42:24Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''Rational homology of configuration spaces via factorization homology'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| [http://homepages.math.uic.edu/~kwhyte/ Kevin Whyte] (UIC)<br />
|[[#Kevin Whyte (UIC)|''Quasi-isometric embeddings of symmetric spaces'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 10<br />
|[http://math.uchicago.edu/~akwalker/ Alden Walker] (UChicago)<br />
|[[#Alden Walker (UChicago)|''Roots, Schottky Semigroups, and a proof of Bandt's Conjecture'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''Growth Tight Actions'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 1<br />
| [http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
|-<br />
|November 7<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelm&eacute;] (Penn State)<br />
| [[#Thomas Barthelm&eacute; (Penn State)|''Counting orbits of Anosov flows in free homotopy classes'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 14<br />
| [http://www.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (University of Pennsylvania)<br />
| [[#Alexandra Kjuchukova (University of Pennsylvania)|''On the classification of irregular branched covers of four-manifolds'']]<br />
| [http://www.math.wisc.edu/~Maxim/ Maxim]<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4, <b>Thursday at 4pm in VV 901</b><br />
| Oyku Yurttas (Georgia Tech) <br />
|[[#Oyku Yurttas (Georgia Tech)|''Dynnikov and train track transition matrices of pseudo-Anosov braids'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Thiffeault]<br />
|-<br />
|December 5<br />
| No seminar. <br />
|<br />
|<br />
|-<br />
|December 12<br />
| No seminar.<br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
<br />
''Rational homology of configuration spaces via factorization homology''<br />
<br />
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.<br />
<br />
===Kevin Whyte (UIC)===<br />
The rigidity theorems of Mostow and Margulis for lattices in semi simple Lie groups are some of the most celebrated in their field, and are motivation for much of geometric group theory. Mostow's result, which states that every isomorphism between lattices extends to an equivariant isometry between symmetric spaces, has been generalized by Kleiner and Leeb to say that any map between higher rank symmetric spaces which is quasi-isometric (a large scale version of bilipschitz) is actually a perturbation of an isometry. Margulis' superrigidity theorem, which says every homomorphism between lattices which has infinite image extends to an equivariant isometric embedding of symmetric spaces, has resisted a generalization of this sort. We will discuss one such result, which considers when quasi-isometric embeddings of symmetric spaces are near isometric embeddings. Our results show that the situation is complicated - in some cases one does have rigidity while in others there are exotic quasi-isometric embeddings. What geometric properties distinguish the two cases is only starting to be understood. This is joint work with David Fisher (Indiana).<br />
<br />
===Alden Walker (UChicago)===<br />
In 1985, Barnsley and Harrington defined a "Mandlebrot set" M for pairs of complex dilations. This is the set of complex numbers<br />
c such that the limit set generated by the pair of dilations x-> cx+1 and x-> cx-1 is connected. The set M is also the closure of the set of roots of polynomials with coefficients in {-1,0,1}. As with the usual Mandlebrot set, M has strong connections to dynamics and algebra, and it has been studied by Bousch, Bandt, Solomyak, Xu, Thurston, and Tiozzo. For a geometric group theorist, the study of M is qualitatively similar to the study of Kleinian groups acting on their limit sets or on universal circles.<br />
<br />
Barnsley and Harrington noted the (numerically apparent) existence of infinitely many "holes" in M, which correspond to exotic components of the space of Schottky semigroups. Bandt rigorously confirmed a single hole in 2002 and conjectured that the interior of M is dense in M away from the real axis. We give the new technique of "traps" to certify an interior point of M, and we use these traps to prove Bandt's conjecture and certify the existence of infinitely many holes in M.<br />
<br />
The only prerequisite for this talk is point-set topology. Fun pictures will be provided. This is joint work with Danny Calegari and Sarah Koch.<br />
<br />
===Jing Tao (Oklahoma)===<br />
''Growth Tight Actions''<br />
<br />
Let G be a group equipped with a finite generating set S. G is called growth tight if its exponential growth rate relative to S is strictly greater than that of every quotient G/N with N infinite. This notion was first introduced by Grigorchuk and de la Harpe. Examples of groups that are growth tight include free groups relative to bases and, more generally, hyperbolic groups relative to any generating set. In this talk, I will provide some sufficient conditions for growth tightness which encompass all previous known examples.<br />
<br />
===Thomas Barthelm&eacute; (Penn State)===<br />
''Counting orbits of Anosov flows in free homotopy classes''<br />
<br />
In 1972, Plante and Thurston asked the following question: If M is a manifold supporting an Anosov flow, does the number of conjugacy classes in the fundamental group grows exponentially fast with the length of the shortest orbit representative?<br />
This question can be solved by answering the following: Can one give an upper bound on the growth rate of the length of orbits inside a free homotopy class?<br />
<br />
In this talk, I will explain how one can use the geometry and topology of Anosov flows to answer both questions in the 3-manifold case. This is joint work with Sergio Fenley.<br />
<br />
===Alexandra Kjuchukova (University of Pennsylvania)===<br />
''On the classification of irregular branched covers of four-manifolds''<br />
<br />
It is a famous result of Hilden and Montesinos that every closed orientable three-manifold can be realized as an irregular three-fold cover of S^3 branched over a knot. In contrast, a smooth four-manifold which can be realized as a cover of S^4 branched over a smooth surface must have signature equal to zero. Given two simply-connected, closed, oriented four-manifolds X and Y and a surface B embedded in X with an isolated singularity, I will prove a necessary condition for the existence of an irregular dihedral branched covering map f: Y -> X with branching set B. Conversely, given a simply-connected oriented closed four-manifold X, I will outline a construction realizing as irregular dihedral covers of X infinitely many (and conjecturally all) of the manifolds Y afforded by the necessary condition.<br />
<br />
===Oyku Yurttas (Georgia Tech)===<br />
''Dynnikov and train track transition matrices of pseudo-Anosov braids''<br />
<br />
In this talk we will compare a <i>Dynnikov matrix</i> with the train track transition matrix of a given pseudo-Anosov braid on the finitely punctured disk. Our main result is that these matrices are isospectral up to roots of unity and some zeros under particular conditions.<br />
<br />
<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| [http://www.math.wisc.edu/~strenner/ Balazs Strenner] (Wisconsin)<br />
| [[#Balazs Strenner (Wisconsin) |''Penner’s conjecture on pseudo-Anosov mapping classes.'']]<br />
| local<br />
|-<br />
|February 13<br />
| <br />
|<br />
|<br />
|-<br />
|February 20<br />
| [http://www.math.illinois.edu/~jsapir2/ Jenya Sapir] (UIUC)<br />
|[[#Jenya Sapir (UIUC) |''Counting non-simple closed curves on surfaces.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| <br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
|| [https://sites.google.com/site/seanlimath/ Sean Li] (UChicago)<br />
|[[#Sean Li (UChicago)|''Coarse differentiation of Lipschitz functions.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Balazs Strenner (Wisconsin)===<br />
''Penner’s conjecture on pseudo-Anosov mapping classes.''<br />
<br />
There are many constructions of pseudo-Anosov elements of mapping class groups of surfaces. Some of them are known to generate all pseudo-Anosov mapping classes, others are known not to. In 1988, Penner gave a very general construction of pseudo-Anosov mapping classes, and he conjectured that all pseudo-Anosov mapping classes arise this way up to finite power. This conjecture was known to be true on some simple surfaces, including the torus, but has otherwise remained open. In this talk I prove that the conjecture is false for most surfaces. (This is joint work with Hyunshik Shin.)<br />
<br />
===Jenya Sapir (UIUC)===<br />
''Counting non-simple closed curves on surfaces.''<br />
<br />
We show how to get coarse bounds on the number of (non-simple) closed geodesics on a surface, given upper bounds on both length and self-intersection number. Recent work by Mirzakhani has produced asymptotics for the growth of the number of simple closed curves, and this work has been extended to curves with at most 3 self-intersections with respect to length. However, no asymptotics, or even bounds, were previously known for other bounds on self-intersection number. Time permitting, we will discuss some applications of this result.<br />
<br />
===Sean Li (UChicago)===<br />
''Coarse differentiation of Lipschitz functions.''<br />
<br />
Bates, Johnson, Lindenstrauss, Preiss, and Schechtman introduced a notion of large scale differentiation for Lipschitz functions between normed linear spaces. We discuss an extension of this result to the nonabelian setting of Carnot groups and use it to derive quantitative estimates for nonembeddability of such groups into certain classes of metric spaces.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=8934Geometry and Topology Seminar 2019-20202014-12-04T17:33:27Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''Rational homology of configuration spaces via factorization homology'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| [http://homepages.math.uic.edu/~kwhyte/ Kevin Whyte] (UIC)<br />
|[[#Kevin Whyte (UIC)|''Quasi-isometric embeddings of symmetric spaces'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 10<br />
|[http://math.uchicago.edu/~akwalker/ Alden Walker] (UChicago)<br />
|[[#Alden Walker (UChicago)|''Roots, Schottky Semigroups, and a proof of Bandt's Conjecture'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''Growth Tight Actions'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 1<br />
| [http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
|-<br />
|November 7<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelm&eacute;] (Penn State)<br />
| [[#Thomas Barthelm&eacute; (Penn State)|''Counting orbits of Anosov flows in free homotopy classes'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 14<br />
| [http://www.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (University of Pennsylvania)<br />
| [[#Alexandra Kjuchukova (University of Pennsylvania)|''On the classification of irregular branched covers of four-manifolds'']]<br />
| [http://www.math.wisc.edu/~Maxim/ Maxim]<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4, <b>Thursday at 4pm in VV 901</b><br />
| Oyku Yurttas (Georgia Tech) <br />
|[[#Oyku Yurttas (Georgia Tech)|''Dynnikov and train track transition matrices of pseudo-Anosov braids'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Thiffeault]<br />
|-<br />
|December 5<br />
| No seminar. <br />
|<br />
|<br />
|-<br />
|December 12<br />
| No seminar.<br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
<br />
''Rational homology of configuration spaces via factorization homology''<br />
<br />
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.<br />
<br />
===Kevin Whyte (UIC)===<br />
The rigidity theorems of Mostow and Margulis for lattices in semi simple Lie groups are some of the most celebrated in their field, and are motivation for much of geometric group theory. Mostow's result, which states that every isomorphism between lattices extends to an equivariant isometry between symmetric spaces, has been generalized by Kleiner and Leeb to say that any map between higher rank symmetric spaces which is quasi-isometric (a large scale version of bilipschitz) is actually a perturbation of an isometry. Margulis' superrigidity theorem, which says every homomorphism between lattices which has infinite image extends to an equivariant isometric embedding of symmetric spaces, has resisted a generalization of this sort. We will discuss one such result, which considers when quasi-isometric embeddings of symmetric spaces are near isometric embeddings. Our results show that the situation is complicated - in some cases one does have rigidity while in others there are exotic quasi-isometric embeddings. What geometric properties distinguish the two cases is only starting to be understood. This is joint work with David Fisher (Indiana).<br />
<br />
===Alden Walker (UChicago)===<br />
In 1985, Barnsley and Harrington defined a "Mandlebrot set" M for pairs of complex dilations. This is the set of complex numbers<br />
c such that the limit set generated by the pair of dilations x-> cx+1 and x-> cx-1 is connected. The set M is also the closure of the set of roots of polynomials with coefficients in {-1,0,1}. As with the usual Mandlebrot set, M has strong connections to dynamics and algebra, and it has been studied by Bousch, Bandt, Solomyak, Xu, Thurston, and Tiozzo. For a geometric group theorist, the study of M is qualitatively similar to the study of Kleinian groups acting on their limit sets or on universal circles.<br />
<br />
Barnsley and Harrington noted the (numerically apparent) existence of infinitely many "holes" in M, which correspond to exotic components of the space of Schottky semigroups. Bandt rigorously confirmed a single hole in 2002 and conjectured that the interior of M is dense in M away from the real axis. We give the new technique of "traps" to certify an interior point of M, and we use these traps to prove Bandt's conjecture and certify the existence of infinitely many holes in M.<br />
<br />
The only prerequisite for this talk is point-set topology. Fun pictures will be provided. This is joint work with Danny Calegari and Sarah Koch.<br />
<br />
===Jing Tao (Oklahoma)===<br />
''Growth Tight Actions''<br />
<br />
Let G be a group equipped with a finite generating set S. G is called growth tight if its exponential growth rate relative to S is strictly greater than that of every quotient G/N with N infinite. This notion was first introduced by Grigorchuk and de la Harpe. Examples of groups that are growth tight include free groups relative to bases and, more generally, hyperbolic groups relative to any generating set. In this talk, I will provide some sufficient conditions for growth tightness which encompass all previous known examples.<br />
<br />
===Thomas Barthelm&eacute; (Penn State)===<br />
''Counting orbits of Anosov flows in free homotopy classes''<br />
<br />
In 1972, Plante and Thurston asked the following question: If M is a manifold supporting an Anosov flow, does the number of conjugacy classes in the fundamental group grows exponentially fast with the length of the shortest orbit representative?<br />
This question can be solved by answering the following: Can one give an upper bound on the growth rate of the length of orbits inside a free homotopy class?<br />
<br />
In this talk, I will explain how one can use the geometry and topology of Anosov flows to answer both questions in the 3-manifold case. This is joint work with Sergio Fenley.<br />
<br />
===Alexandra Kjuchukova (University of Pennsylvania)===<br />
''On the classification of irregular branched covers of four-manifolds''<br />
<br />
It is a famous result of Hilden and Montesinos that every closed orientable three-manifold can be realized as an irregular three-fold cover of S^3 branched over a knot. In contrast, a smooth four-manifold which can be realized as a cover of S^4 branched over a smooth surface must have signature equal to zero. Given two simply-connected, closed, oriented four-manifolds X and Y and a surface B embedded in X with an isolated singularity, I will prove a necessary condition for the existence of an irregular dihedral branched covering map f: Y -> X with branching set B. Conversely, given a simply-connected oriented closed four-manifold X, I will outline a construction realizing as irregular dihedral covers of X infinitely many (and conjecturally all) of the manifolds Y afforded by the necessary condition.<br />
<br />
===Oyku Yurttas (Georgia Tech)===<br />
''Dynnikov and train track transition matrices of pseudo-Anosov braids''<br />
<br />
In this talk we will compare a <i>Dynnikov matrix</i> with the train track transition matrix of a given pseudo-Anosov braid on the finitely punctured disk. Our main result is that these matrices are isospectral up to roots of unity and some zeros under particular conditions.<br />
<br />
<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| <br />
|<br />
|<br />
|-<br />
|February 13<br />
| <br />
|<br />
|<br />
|-<br />
|February 20<br />
| <br />
|<br />
|<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| <br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
| <br />
|<br />
|<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=8863Geometry and Topology Seminar 2019-20202014-11-21T21:52:53Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''Rational homology of configuration spaces via factorization homology'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| [http://homepages.math.uic.edu/~kwhyte/ Kevin Whyte] (UIC)<br />
|[[#Kevin Whyte (UIC)|''Quasi-isometric embeddings of symmetric spaces'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 10<br />
|[http://math.uchicago.edu/~akwalker/ Alden Walker] (UChicago)<br />
|[[#Alden Walker (UChicago)|''Roots, Schottky Semigroups, and a proof of Bandt's Conjecture'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''Growth Tight Actions'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 1<br />
| [http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
|-<br />
|November 7<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelm&eacute;] (Penn State)<br />
| [[#Thomas Barthelm&eacute; (Penn State)|''Counting orbits of Anosov flows in free homotopy classes'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 14<br />
| [http://www.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (University of Pennsylvania)<br />
| [[#Alexandra Kjuchukova (University of Pennsylvania)|''On the classification of irregular branched covers of four-manifolds'']]<br />
| [http://www.math.wisc.edu/~Maxim/ Maxim]<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4, <b>Thursday at 4pm in VV 901</b><br />
| Oyku Yurttas (Georgia Tech) <br />
|[[#Oyku Yurttas (Georgia Tech)|''Dynnikov and train track transition matrices of pseudo-Anosov braids'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Thiffeault]<br />
|-<br />
|December 5<br />
| [http://www.math.illinois.edu/~jsapir2/ Jenya Sapir] (UIUC)<br />
|[[#Jenya Sapir (UIUC)|''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|December 12<br />
| [https://sites.google.com/site/seanlimath/ Sean Li] (UChicago)<br />
|[[#Sean Li (UChicago)|''Coarse differentiation of Lipschitz functions'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
<br />
''Rational homology of configuration spaces via factorization homology''<br />
<br />
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.<br />
<br />
===Kevin Whyte (UIC)===<br />
The rigidity theorems of Mostow and Margulis for lattices in semi simple Lie groups are some of the most celebrated in their field, and are motivation for much of geometric group theory. Mostow's result, which states that every isomorphism between lattices extends to an equivariant isometry between symmetric spaces, has been generalized by Kleiner and Leeb to say that any map between higher rank symmetric spaces which is quasi-isometric (a large scale version of bilipschitz) is actually a perturbation of an isometry. Margulis' superrigidity theorem, which says every homomorphism between lattices which has infinite image extends to an equivariant isometric embedding of symmetric spaces, has resisted a generalization of this sort. We will discuss one such result, which considers when quasi-isometric embeddings of symmetric spaces are near isometric embeddings. Our results show that the situation is complicated - in some cases one does have rigidity while in others there are exotic quasi-isometric embeddings. What geometric properties distinguish the two cases is only starting to be understood. This is joint work with David Fisher (Indiana).<br />
<br />
===Alden Walker (UChicago)===<br />
In 1985, Barnsley and Harrington defined a "Mandlebrot set" M for pairs of complex dilations. This is the set of complex numbers<br />
c such that the limit set generated by the pair of dilations x-> cx+1 and x-> cx-1 is connected. The set M is also the closure of the set of roots of polynomials with coefficients in {-1,0,1}. As with the usual Mandlebrot set, M has strong connections to dynamics and algebra, and it has been studied by Bousch, Bandt, Solomyak, Xu, Thurston, and Tiozzo. For a geometric group theorist, the study of M is qualitatively similar to the study of Kleinian groups acting on their limit sets or on universal circles.<br />
<br />
Barnsley and Harrington noted the (numerically apparent) existence of infinitely many "holes" in M, which correspond to exotic components of the space of Schottky semigroups. Bandt rigorously confirmed a single hole in 2002 and conjectured that the interior of M is dense in M away from the real axis. We give the new technique of "traps" to certify an interior point of M, and we use these traps to prove Bandt's conjecture and certify the existence of infinitely many holes in M.<br />
<br />
The only prerequisite for this talk is point-set topology. Fun pictures will be provided. This is joint work with Danny Calegari and Sarah Koch.<br />
<br />
===Jing Tao (Oklahoma)===<br />
''Growth Tight Actions''<br />
<br />
Let G be a group equipped with a finite generating set S. G is called growth tight if its exponential growth rate relative to S is strictly greater than that of every quotient G/N with N infinite. This notion was first introduced by Grigorchuk and de la Harpe. Examples of groups that are growth tight include free groups relative to bases and, more generally, hyperbolic groups relative to any generating set. In this talk, I will provide some sufficient conditions for growth tightness which encompass all previous known examples.<br />
<br />
===Thomas Barthelm&eacute; (Penn State)===<br />
''Counting orbits of Anosov flows in free homotopy classes''<br />
<br />
In 1972, Plante and Thurston asked the following question: If M is a manifold supporting an Anosov flow, does the number of conjugacy classes in the fundamental group grows exponentially fast with the length of the shortest orbit representative?<br />
This question can be solved by answering the following: Can one give an upper bound on the growth rate of the length of orbits inside a free homotopy class?<br />
<br />
In this talk, I will explain how one can use the geometry and topology of Anosov flows to answer both questions in the 3-manifold case. This is joint work with Sergio Fenley.<br />
<br />
===Alexandra Kjuchukova (University of Pennsylvania)===<br />
''On the classification of irregular branched covers of four-manifolds''<br />
<br />
It is a famous result of Hilden and Montesinos that every closed orientable three-manifold can be realized as an irregular three-fold cover of S^3 branched over a knot. In contrast, a smooth four-manifold which can be realized as a cover of S^4 branched over a smooth surface must have signature equal to zero. Given two simply-connected, closed, oriented four-manifolds X and Y and a surface B embedded in X with an isolated singularity, I will prove a necessary condition for the existence of an irregular dihedral branched covering map f: Y -> X with branching set B. Conversely, given a simply-connected oriented closed four-manifold X, I will outline a construction realizing as irregular dihedral covers of X infinitely many (and conjecturally all) of the manifolds Y afforded by the necessary condition.<br />
<br />
===Oyku Yurttas (Georgia Tech)===<br />
''Dynnikov and train track transition matrices of pseudo-Anosov braids''<br />
<br />
In this talk we will compare a <i>Dynnikov matrix</i> with the train track transition matrix of a given pseudo-Anosov braid on the finitely punctured disk. Our main result is that these matrices are isospectral up to roots of unity and some zeros under particular conditions.<br />
<br />
===Jenya Sapir (UIUC)===<br />
''TBA''<br />
<br />
===Sean Li (UChicago)===<br />
''Coarse differentiation of Lipschitz functions''<br />
<br />
Bates, Johnson, Lindenstrauss, Preiss, and Schechtman introduced a notion of large scale differentiation for Lipschitz functions between normed linear spaces. We discuss an extension of this result to the nonabelian setting of Carnot groups and use it to derive quantitative estimates for nonembeddability of such groups into certain classes of metric spaces.<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| <br />
|<br />
|<br />
|-<br />
|February 13<br />
| <br />
|<br />
|<br />
|-<br />
|February 20<br />
| <br />
|<br />
|<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| <br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
| <br />
|<br />
|<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=8862Geometry and Topology Seminar 2019-20202014-11-21T21:49:31Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''Rational homology of configuration spaces via factorization homology'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| [http://homepages.math.uic.edu/~kwhyte/ Kevin Whyte] (UIC)<br />
|[[#Kevin Whyte (UIC)|''Quasi-isometric embeddings of symmetric spaces'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 10<br />
|[http://math.uchicago.edu/~akwalker/ Alden Walker] (UChicago)<br />
|[[#Alden Walker (UChicago)|''Roots, Schottky Semigroups, and a proof of Bandt's Conjecture'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''Growth Tight Actions'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 1<br />
| [http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
|-<br />
|November 7<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelm&eacute;] (Penn State)<br />
| [[#Thomas Barthelm&eacute; (Penn State)|''Counting orbits of Anosov flows in free homotopy classes'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 14<br />
| [http://www.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (University of Pennsylvania)<br />
| [[#Alexandra Kjuchukova (University of Pennsylvania)|''On the classification of irregular branched covers of four-manifolds'']]<br />
| [http://www.math.wisc.edu/~Maxim/ Maxim]<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| Oyku Yurttas (Georgia Tech)<br />
|[[#Oyku Yurttas (Georgia Tech)|''Dynnikov and train track transition matrices of pseudo-Anosov braids'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Thiffeault]<br />
|-<br />
|December 5<br />
| [http://www.math.illinois.edu/~jsapir2/ Jenya Sapir] (UIUC)<br />
|[[#Jenya Sapir (UIUC)|''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|December 12<br />
| [https://sites.google.com/site/seanlimath/ Sean Li] (UChicago)<br />
|[[#Sean Li (UChicago)|''Coarse differentiation of Lipschitz functions'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
<br />
''Rational homology of configuration spaces via factorization homology''<br />
<br />
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.<br />
<br />
===Kevin Whyte (UIC)===<br />
The rigidity theorems of Mostow and Margulis for lattices in semi simple Lie groups are some of the most celebrated in their field, and are motivation for much of geometric group theory. Mostow's result, which states that every isomorphism between lattices extends to an equivariant isometry between symmetric spaces, has been generalized by Kleiner and Leeb to say that any map between higher rank symmetric spaces which is quasi-isometric (a large scale version of bilipschitz) is actually a perturbation of an isometry. Margulis' superrigidity theorem, which says every homomorphism between lattices which has infinite image extends to an equivariant isometric embedding of symmetric spaces, has resisted a generalization of this sort. We will discuss one such result, which considers when quasi-isometric embeddings of symmetric spaces are near isometric embeddings. Our results show that the situation is complicated - in some cases one does have rigidity while in others there are exotic quasi-isometric embeddings. What geometric properties distinguish the two cases is only starting to be understood. This is joint work with David Fisher (Indiana).<br />
<br />
===Alden Walker (UChicago)===<br />
In 1985, Barnsley and Harrington defined a "Mandlebrot set" M for pairs of complex dilations. This is the set of complex numbers<br />
c such that the limit set generated by the pair of dilations x-> cx+1 and x-> cx-1 is connected. The set M is also the closure of the set of roots of polynomials with coefficients in {-1,0,1}. As with the usual Mandlebrot set, M has strong connections to dynamics and algebra, and it has been studied by Bousch, Bandt, Solomyak, Xu, Thurston, and Tiozzo. For a geometric group theorist, the study of M is qualitatively similar to the study of Kleinian groups acting on their limit sets or on universal circles.<br />
<br />
Barnsley and Harrington noted the (numerically apparent) existence of infinitely many "holes" in M, which correspond to exotic components of the space of Schottky semigroups. Bandt rigorously confirmed a single hole in 2002 and conjectured that the interior of M is dense in M away from the real axis. We give the new technique of "traps" to certify an interior point of M, and we use these traps to prove Bandt's conjecture and certify the existence of infinitely many holes in M.<br />
<br />
The only prerequisite for this talk is point-set topology. Fun pictures will be provided. This is joint work with Danny Calegari and Sarah Koch.<br />
<br />
===Jing Tao (Oklahoma)===<br />
''Growth Tight Actions''<br />
<br />
Let G be a group equipped with a finite generating set S. G is called growth tight if its exponential growth rate relative to S is strictly greater than that of every quotient G/N with N infinite. This notion was first introduced by Grigorchuk and de la Harpe. Examples of groups that are growth tight include free groups relative to bases and, more generally, hyperbolic groups relative to any generating set. In this talk, I will provide some sufficient conditions for growth tightness which encompass all previous known examples.<br />
<br />
===Thomas Barthelm&eacute; (Penn State)===<br />
''Counting orbits of Anosov flows in free homotopy classes''<br />
<br />
In 1972, Plante and Thurston asked the following question: If M is a manifold supporting an Anosov flow, does the number of conjugacy classes in the fundamental group grows exponentially fast with the length of the shortest orbit representative?<br />
This question can be solved by answering the following: Can one give an upper bound on the growth rate of the length of orbits inside a free homotopy class?<br />
<br />
In this talk, I will explain how one can use the geometry and topology of Anosov flows to answer both questions in the 3-manifold case. This is joint work with Sergio Fenley.<br />
<br />
===Alexandra Kjuchukova (University of Pennsylvania)===<br />
''On the classification of irregular branched covers of four-manifolds''<br />
<br />
It is a famous result of Hilden and Montesinos that every closed orientable three-manifold can be realized as an irregular three-fold cover of S^3 branched over a knot. In contrast, a smooth four-manifold which can be realized as a cover of S^4 branched over a smooth surface must have signature equal to zero. Given two simply-connected, closed, oriented four-manifolds X and Y and a surface B embedded in X with an isolated singularity, I will prove a necessary condition for the existence of an irregular dihedral branched covering map f: Y -> X with branching set B. Conversely, given a simply-connected oriented closed four-manifold X, I will outline a construction realizing as irregular dihedral covers of X infinitely many (and conjecturally all) of the manifolds Y afforded by the necessary condition.<br />
<br />
===Oyku Yurttas (Georgia Tech)===<br />
''Dynnikov and train track transition matrices of pseudo-Anosov braids''<br />
<br />
In this talk we will compare a Dynnikov matrix with the train track transition matrix of a given pseudo-Anosov braid on the finitely punctured disk. Our main result is that these matrices are isospectral up to roots of unity and some zeros under particular conditions.<br />
<br />
===Jenya Sapir (UIUC)===<br />
''TBA''<br />
<br />
===Sean Li (UChicago)===<br />
''Coarse differentiation of Lipschitz functions''<br />
<br />
Bates, Johnson, Lindenstrauss, Preiss, and Schechtman introduced a notion of large scale differentiation for Lipschitz functions between normed linear spaces. We discuss an extension of this result to the nonabelian setting of Carnot groups and use it to derive quantitative estimates for nonembeddability of such groups into certain classes of metric spaces.<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| <br />
|<br />
|<br />
|-<br />
|February 13<br />
| <br />
|<br />
|<br />
|-<br />
|February 20<br />
| <br />
|<br />
|<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| <br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
| <br />
|<br />
|<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=8766Geometry and Topology Seminar 2019-20202014-11-10T19:41:39Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''Rational homology of configuration spaces via factorization homology'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| [http://homepages.math.uic.edu/~kwhyte/ Kevin Whyte] (UIC)<br />
|[[#Kevin Whyte (UIC)|''Quasi-isometric embeddings of symmetric spaces'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 10<br />
|[http://math.uchicago.edu/~akwalker/ Alden Walker] (UChicago)<br />
|[[#Alden Walker (UChicago)|''Roots, Schottky Semigroups, and a proof of Bandt's Conjecture'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''Growth Tight Actions'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 1<br />
| [http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
|-<br />
|November 7<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelm&eacute;] (Penn State)<br />
| [[#Thomas Barthelm&eacute; (Penn State)|''Counting orbits of Anosov flows in free homotopy classes'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 14<br />
| [http://www.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (University of Pennsylvania)<br />
| [[#Alexandra Kjuchukova (University of Pennsylvania)|''On the classification of irregular branched covers of four-manifolds'']]<br />
| [http://www.math.wisc.edu/~Maxim/ Maxim]<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 5<br />
| [http://www.math.illinois.edu/~jsapir2/ Jenya Sapir] (UIUC)<br />
|[[#Jenya Sapir (UIUC)|''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|December 12<br />
| [https://sites.google.com/site/seanlimath/ Sean Li] (UChicago)<br />
|[[#Sean Li (UChicago)|''Coarse differentiation of Lipschitz functions'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
<br />
''Rational homology of configuration spaces via factorization homology''<br />
<br />
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.<br />
<br />
===Kevin Whyte (UIC)===<br />
The rigidity theorems of Mostow and Margulis for lattices in semi simple Lie groups are some of the most celebrated in their field, and are motivation for much of geometric group theory. Mostow's result, which states that every isomorphism between lattices extends to an equivariant isometry between symmetric spaces, has been generalized by Kleiner and Leeb to say that any map between higher rank symmetric spaces which is quasi-isometric (a large scale version of bilipschitz) is actually a perturbation of an isometry. Margulis' superrigidity theorem, which says every homomorphism between lattices which has infinite image extends to an equivariant isometric embedding of symmetric spaces, has resisted a generalization of this sort. We will discuss one such result, which considers when quasi-isometric embeddings of symmetric spaces are near isometric embeddings. Our results show that the situation is complicated - in some cases one does have rigidity while in others there are exotic quasi-isometric embeddings. What geometric properties distinguish the two cases is only starting to be understood. This is joint work with David Fisher (Indiana).<br />
<br />
===Alden Walker (UChicago)===<br />
In 1985, Barnsley and Harrington defined a "Mandlebrot set" M for pairs of complex dilations. This is the set of complex numbers<br />
c such that the limit set generated by the pair of dilations x-> cx+1 and x-> cx-1 is connected. The set M is also the closure of the set of roots of polynomials with coefficients in {-1,0,1}. As with the usual Mandlebrot set, M has strong connections to dynamics and algebra, and it has been studied by Bousch, Bandt, Solomyak, Xu, Thurston, and Tiozzo. For a geometric group theorist, the study of M is qualitatively similar to the study of Kleinian groups acting on their limit sets or on universal circles.<br />
<br />
Barnsley and Harrington noted the (numerically apparent) existence of infinitely many "holes" in M, which correspond to exotic components of the space of Schottky semigroups. Bandt rigorously confirmed a single hole in 2002 and conjectured that the interior of M is dense in M away from the real axis. We give the new technique of "traps" to certify an interior point of M, and we use these traps to prove Bandt's conjecture and certify the existence of infinitely many holes in M.<br />
<br />
The only prerequisite for this talk is point-set topology. Fun pictures will be provided. This is joint work with Danny Calegari and Sarah Koch.<br />
<br />
===Jing Tao (Oklahoma)===<br />
''Growth Tight Actions''<br />
<br />
Let G be a group equipped with a finite generating set S. G is called growth tight if its exponential growth rate relative to S is strictly greater than that of every quotient G/N with N infinite. This notion was first introduced by Grigorchuk and de la Harpe. Examples of groups that are growth tight include free groups relative to bases and, more generally, hyperbolic groups relative to any generating set. In this talk, I will provide some sufficient conditions for growth tightness which encompass all previous known examples.<br />
<br />
===Thomas Barthelm&eacute; (Penn State)===<br />
''Counting orbits of Anosov flows in free homotopy classes''<br />
<br />
In 1972, Plante and Thurston asked the following question: If M is a manifold supporting an Anosov flow, does the number of conjugacy classes in the fundamental group grows exponentially fast with the length of the shortest orbit representative?<br />
This question can be solved by answering the following: Can one give an upper bound on the growth rate of the length of orbits inside a free homotopy class?<br />
<br />
In this talk, I will explain how one can use the geometry and topology of Anosov flows to answer both questions in the 3-manifold case. This is joint work with Sergio Fenley.<br />
<br />
===Alexandra Kjuchukova (University of Pennsylvania)===<br />
''On the classification of irregular branched covers of four-manifolds''<br />
<br />
It is a famous result of Hilden and Montesinos that every closed orientable three-manifold can be realized as an irregular three-fold cover of S^3 branched over a knot. In contrast, a smooth four-manifold which can be realized as a cover of S^4 branched over a smooth surface must have signature equal to zero. Given two simply-connected, closed, oriented four-manifolds X and Y and a surface B embedded in X with an isolated singularity, I will prove a necessary condition for the existence of an irregular dihedral branched covering map f: Y -> X with branching set B. Conversely, given a simply-connected oriented closed four-manifold X, I will outline a construction realizing as irregular dihedral covers of X infinitely many (and conjecturally all) of the manifolds Y afforded by the necessary condition.<br />
<br />
<br />
===Jenya Sapir (UIUC)===<br />
"TBA"<br />
<br />
===Sean Li (UChicago)===<br />
''Coarse differentiation of Lipschitz functions''<br />
<br />
Bates, Johnson, Lindenstrauss, Preiss, and Schechtman introduced a notion of large scale differentiation for Lipschitz functions between normed linear spaces. We discuss an extension of this result to the nonabelian setting of Carnot groups and use it to derive quantitative estimates for nonembeddability of such groups into certain classes of metric spaces.<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| <br />
|<br />
|<br />
|-<br />
|February 13<br />
| <br />
|<br />
|<br />
|-<br />
|February 20<br />
| <br />
|<br />
|<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| <br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
| <br />
|<br />
|<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=8765Geometry and Topology Seminar 2019-20202014-11-10T19:36:46Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''Rational homology of configuration spaces via factorization homology'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| [http://homepages.math.uic.edu/~kwhyte/ Kevin Whyte] (UIC)<br />
|[[#Kevin Whyte (UIC)|''Quasi-isometric embeddings of symmetric spaces'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 10<br />
|[http://math.uchicago.edu/~akwalker/ Alden Walker] (UChicago)<br />
|[[#Alden Walker (UChicago)|''Roots, Schottky Semigroups, and a proof of Bandt's Conjecture'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''Growth Tight Actions'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 1<br />
| [http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
|-<br />
|November 7<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelm&eacute;] (Penn State)<br />
| [[#Thomas Barthelm&eacute; (Penn State)|''Counting orbits of Anosov flows in free homotopy classes'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 14<br />
| [http://www.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (University of Pennsylvania)<br />
| [[#Alexandra Kjuchukova (University of Pennsylvania)|''On the classification of irregular branched covers of four-manifolds'']]<br />
| [http://www.math.wisc.edu/~Maxim/ Maxim]<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 5<br />
| [http://www.math.illinois.edu/~jsapir2/ Jenya Sapir] (UIUC)<br />
|[[#Jenya Sapir (UIUC)|''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|December 12<br />
| [https://sites.google.com/site/seanlimath/ Sean Li] (UChicago)<br />
|[[#Sean Li (UChicago)|''Coarse differentiation of Lipschitz functions'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
<br />
''Rational homology of configuration spaces via factorization homology''<br />
<br />
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.<br />
<br />
===Kevin Whyte (UIC)===<br />
The rigidity theorems of Mostow and Margulis for lattices in semi simple Lie groups are some of the most celebrated in their field, and are motivation for much of geometric group theory. Mostow's result, which states that every isomorphism between lattices extends to an equivariant isometry between symmetric spaces, has been generalized by Kleiner and Leeb to say that any map between higher rank symmetric spaces which is quasi-isometric (a large scale version of bilipschitz) is actually a perturbation of an isometry. Margulis' superrigidity theorem, which says every homomorphism between lattices which has infinite image extends to an equivariant isometric embedding of symmetric spaces, has resisted a generalization of this sort. We will discuss one such result, which considers when quasi-isometric embeddings of symmetric spaces are near isometric embeddings. Our results show that the situation is complicated - in some cases one does have rigidity while in others there are exotic quasi-isometric embeddings. What geometric properties distinguish the two cases is only starting to be understood. This is joint work with David Fisher (Indiana).<br />
<br />
===Alden Walker (UChicago)===<br />
In 1985, Barnsley and Harrington defined a "Mandlebrot set" M for pairs of complex dilations. This is the set of complex numbers<br />
c such that the limit set generated by the pair of dilations x-> cx+1 and x-> cx-1 is connected. The set M is also the closure of the set of roots of polynomials with coefficients in {-1,0,1}. As with the usual Mandlebrot set, M has strong connections to dynamics and algebra, and it has been studied by Bousch, Bandt, Solomyak, Xu, Thurston, and Tiozzo. For a geometric group theorist, the study of M is qualitatively similar to the study of Kleinian groups acting on their limit sets or on universal circles.<br />
<br />
Barnsley and Harrington noted the (numerically apparent) existence of infinitely many "holes" in M, which correspond to exotic components of the space of Schottky semigroups. Bandt rigorously confirmed a single hole in 2002 and conjectured that the interior of M is dense in M away from the real axis. We give the new technique of "traps" to certify an interior point of M, and we use these traps to prove Bandt's conjecture and certify the existence of infinitely many holes in M.<br />
<br />
The only prerequisite for this talk is point-set topology. Fun pictures will be provided. This is joint work with Danny Calegari and Sarah Koch.<br />
<br />
===Jing Tao (Oklahoma)===<br />
''Growth Tight Actions''<br />
<br />
Let G be a group equipped with a finite generating set S. G is called growth tight if its exponential growth rate relative to S is strictly greater than that of every quotient G/N with N infinite. This notion was first introduced by Grigorchuk and de la Harpe. Examples of groups that are growth tight include free groups relative to bases and, more generally, hyperbolic groups relative to any generating set. In this talk, I will provide some sufficient conditions for growth tightness which encompass all previous known examples.<br />
<br />
===Thomas Barthelm&eacute; (Penn State)===<br />
''Counting orbits of Anosov flows in free homotopy classes''<br />
<br />
In 1972, Plante and Thurston asked the following question: If M is a manifold supporting an Anosov flow, does the number of conjugacy classes in the fundamental group grows exponentially fast with the length of the shortest orbit representative?<br />
This question can be solved by answering the following: Can one give an upper bound on the growth rate of the length of orbits inside a free homotopy class?<br />
<br />
In this talk, I will explain how one can use the geometry and topology of Anosov flows to answer both questions in the 3-manifold case. This is joint work with Sergio Fenley.<br />
<br />
===Alexandra Kjuchukova (University of Pennsylvania)===<br />
''On the classification of irregular branched covers of four-manifolds''<br />
<br />
It is a famous result of Hilden and Montesinos that every closed orientable three-manifold can be realized as an irregular three-fold cover of S^3 branched over a knot. In contrast, a smooth four-manifold which can be realized as a cover of S^4 branched over a smooth surface must have signature equal to zero. Given two simply-connected, closed, oriented four-manifolds X and Y and a surface B embedded in X with an isolated singularity, I will prove a necessary condition for the existence of an irregular dihedral branched covering map f: Y -> X with branching set B. Conversely, given a simply-connected oriented closed four-manifold X, I will outline a construction realizing as irregular dihedral covers of X infinitely many (and conjecturally all) of the manifolds Y afforded by the necessary condition.<br />
<br />
<br />
===Jenya Sapir (UIUC)===<br />
"TBA"<br />
<br />
===Sean Li (UChicago)===<br />
"Coarse differentiation of Lipschitz functions"<br />
<br />
Bates, Johnson, Lindenstrauss, Preiss, and Schechtman introduced a notion of large scale differentiation for Lipschitz functions between normed linear spaces. We discuss an extension of this result to the nonabelian setting of Carnot groups and use it to derive quantitative estimates for nonembeddability of such groups into certain classes of metric spaces.<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| <br />
|<br />
|<br />
|-<br />
|February 13<br />
| <br />
|<br />
|<br />
|-<br />
|February 20<br />
| <br />
|<br />
|<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| <br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
| <br />
|<br />
|<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=8660Geometry and Topology Seminar 2019-20202014-10-27T18:16:03Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''Rational homology of configuration spaces via factorization homology'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| [http://homepages.math.uic.edu/~kwhyte/ Kevin Whyte] (UIC)<br />
|[[#Kevin Whyte (UIC)|''Quasi-isometric embeddings of symmetric spaces'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 10<br />
|[http://math.uchicago.edu/~akwalker/ Alden Walker] (UChicago)<br />
|[[#Alden Walker (UChicago)|''Roots, Schottky Semigroups, and a proof of Bandt's Conjecture'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''Growth Tight Actions'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 1<br />
| [http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
|-<br />
|November 7<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelm&eacute;] (Penn State)<br />
| [[#Thomas Barthelm&eacute; (Penn State)|''Counting orbits of Anosov flows in free homotopy classes'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 14<br />
| [http://www.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (University of Pennsylvania)<br />
| [[#Alexandra Kjuchukova (UPenn)|''TBA'']]<br />
| [http://www.math.wisc.edu/~Maxim/ Maxim]<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 5<br />
| <br />
|<br />
|<br />
|-<br />
|December 12<br />
| [https://sites.google.com/site/seanlimath/ Sean Li] (UChicago)<br />
|[[#Sean Li (UChicago)|''TBA']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
<br />
''Rational homology of configuration spaces via factorization homology''<br />
<br />
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.<br />
<br />
===Kevin Whyte (UIC)===<br />
The rigidity theorems of Mostow and Margulis for lattices in semi simple Lie groups are some of the most celebrated in their field, and are motivation for much of geometric group theory. Mostow's result, which states that every isomorphism between lattices extends to an equivariant isometry between symmetric spaces, has been generalized by Kleiner and Leeb to say that any map between higher rank symmetric spaces which is quasi-isometric (a large scale version of bilipschitz) is actually a perturbation of an isometry. Margulis' superrigidity theorem, which says every homomorphism between lattices which has infinite image extends to an equivariant isometric embedding of symmetric spaces, has resisted a generalization of this sort. We will discuss one such result, which considers when quasi-isometric embeddings of symmetric spaces are near isometric embeddings. Our results show that the situation is complicated - in some cases one does have rigidity while in others there are exotic quasi-isometric embeddings. What geometric properties distinguish the two cases is only starting to be understood. This is joint work with David Fisher (Indiana).<br />
<br />
===Alden Walker (UChicago)===<br />
In 1985, Barnsley and Harrington defined a "Mandlebrot set" M for pairs of complex dilations. This is the set of complex numbers<br />
c such that the limit set generated by the pair of dilations x-> cx+1 and x-> cx-1 is connected. The set M is also the closure of the set of roots of polynomials with coefficients in {-1,0,1}. As with the usual Mandlebrot set, M has strong connections to dynamics and algebra, and it has been studied by Bousch, Bandt, Solomyak, Xu, Thurston, and Tiozzo. For a geometric group theorist, the study of M is qualitatively similar to the study of Kleinian groups acting on their limit sets or on universal circles.<br />
<br />
Barnsley and Harrington noted the (numerically apparent) existence of infinitely many "holes" in M, which correspond to exotic components of the space of Schottky semigroups. Bandt rigorously confirmed a single hole in 2002 and conjectured that the interior of M is dense in M away from the real axis. We give the new technique of "traps" to certify an interior point of M, and we use these traps to prove Bandt's conjecture and certify the existence of infinitely many holes in M.<br />
<br />
The only prerequisite for this talk is point-set topology. Fun pictures will be provided. This is joint work with Danny Calegari and Sarah Koch.<br />
<br />
===Jing Tao (Oklahoma)===<br />
''Growth Tight Actions''<br />
<br />
Let G be a group equipped with a finite generating set S. G is called growth tight if its exponential growth rate relative to S is strictly greater than that of every quotient G/N with N infinite. This notion was first introduced by Grigorchuk and de la Harpe. Examples of groups that are growth tight include free groups relative to bases and, more generally, hyperbolic groups relative to any generating set. In this talk, I will provide some sufficient conditions for growth tightness which encompass all previous known examples.<br />
<br />
===Thomas Barthelm&eacute; (Penn State)===<br />
''Counting orbits of Anosov flows in free homotopy classes''<br />
<br />
In 1972, Plante and Thurston asked the following question: If M is a manifold supporting an Anosov flow, does the number of conjugacy classes in the fundamental group grows exponentially fast with the length of the shortest orbit representative?<br />
This question can be solved by answering the following: Can one give an upper bound on the growth rate of the length of orbits inside a free homotopy class?<br />
<br />
In this talk, I will explain how one can use the geometry and topology of Anosov flows to answer both questions in the 3-manifold case. This is joint work with Sergio Fenley.<br />
<br />
===Sean Li (UChicago)===<br />
"TBA"<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| <br />
|<br />
|<br />
|-<br />
|February 13<br />
| <br />
|<br />
|<br />
|-<br />
|February 20<br />
| <br />
|<br />
|<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| <br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
| <br />
|<br />
|<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=8619Geometry and Topology Seminar 2019-20202014-10-15T13:12:30Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''Rational homology of configuration spaces via factorization homology'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| [http://homepages.math.uic.edu/~kwhyte/ Kevin Whyte] (UIC)<br />
|[[#Kevin Whyte (UIC)|''Quasi-isometric embeddings of symmetric spaces'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 10<br />
|[http://math.uchicago.edu/~akwalker/ Alden Walker] (UChicago)<br />
|[[#Alden Walker (UChicago)|''Roots, Schottky Semigroups, and a proof of Bandt's Conjecture'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''TBA'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 1<br />
| [http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
|-<br />
|November 7<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelm&eacute;] (Penn State)<br />
| [[#Thomas Barthelm&eacute; (Penn State)|''Counting orbits of Anosov flows in free homotopy classes'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 14<br />
| [http://www.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (University of Pennsylvania)<br />
| [[#Alexandra Kjuchukova (UPenn)|''TBA'']]<br />
| [http://www.math.wisc.edu/~Maxim/ Maxim]<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 5<br />
| <br />
|<br />
|<br />
|-<br />
|December 12<br />
| [https://sites.google.com/site/seanlimath/ Sean Li] (UChicago)<br />
|[[#Sean Li (UChicago)|''TBA']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
<br />
''Rational homology of configuration spaces via factorization homology''<br />
<br />
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.<br />
<br />
===Kevin Whyte (UIC)===<br />
The rigidity theorems of Mostow and Margulis for lattices in semi simple Lie groups are some of the most celebrated in their field, and are motivation for much of geometric group theory. Mostow's result, which states that every isomorphism between lattices extends to an equivariant isometry between symmetric spaces, has been generalized by Kleiner and Leeb to say that any map between higher rank symmetric spaces which is quasi-isometric (a large scale version of bilipschitz) is actually a perturbation of an isometry. Margulis' superrigidity theorem, which says every homomorphism between lattices which has infinite image extends to an equivariant isometric embedding of symmetric spaces, has resisted a generalization of this sort. We will discuss one such result, which considers when quasi-isometric embeddings of symmetric spaces are near isometric embeddings. Our results show that the situation is complicated - in some cases one does have rigidity while in others there are exotic quasi-isometric embeddings. What geometric properties distinguish the two cases is only starting to be understood. This is joint work with David Fisher (Indiana).<br />
<br />
===Alden Walker (UChicago)===<br />
In 1985, Barnsley and Harrington defined a "Mandlebrot set" M for pairs of complex dilations. This is the set of complex numbers<br />
c such that the limit set generated by the pair of dilations x-> cx+1 and x-> cx-1 is connected. The set M is also the closure of the set of roots of polynomials with coefficients in {-1,0,1}. As with the usual Mandlebrot set, M has strong connections to dynamics and algebra, and it has been studied by Bousch, Bandt, Solomyak, Xu, Thurston, and Tiozzo. For a geometric group theorist, the study of M is qualitatively similar to the study of Kleinian groups acting on their limit sets or on universal circles.<br />
<br />
Barnsley and Harrington noted the (numerically apparent) existence of infinitely many "holes" in M, which correspond to exotic components of the space of Schottky semigroups. Bandt rigorously confirmed a single hole in 2002 and conjectured that the interior of M is dense in M away from the real axis. We give the new technique of "traps" to certify an interior point of M, and we use these traps to prove Bandt's conjecture and certify the existence of infinitely many holes in M.<br />
<br />
The only prerequisite for this talk is point-set topology. Fun pictures will be provided. This is joint work with Danny Calegari and Sarah Koch.<br />
<br />
===Jing Tao (Oklahoma)===<br />
''TBA''<br />
<br />
===Thomas Barthelm&eacute; (Penn State)===<br />
''Counting orbits of Anosov flows in free homotopy classes''<br />
<br />
In 1972, Plante and Thurston asked the following question: If M is a manifold supporting an Anosov flow, does the number of conjugacy classes in the fundamental group grows exponentially fast with the length of the shortest orbit representative?<br />
This question can be solved by answering the following: Can one give an upper bound on the growth rate of the length of orbits inside a free homotopy class?<br />
<br />
In this talk, I will explain how one can use the geometry and topology of Anosov flows to answer both questions in the 3-manifold case. This is joint work with Sergio Fenley.<br />
<br />
===Sean Li (UChicago)===<br />
"TBA"<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| <br />
|<br />
|<br />
|-<br />
|February 13<br />
| <br />
|<br />
|<br />
|-<br />
|February 20<br />
| <br />
|<br />
|<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| <br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
| <br />
|<br />
|<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology&diff=8240Geometry and Topology2014-09-10T21:16:42Z<p>Rkent: </p>
<hr />
<div>=='''Seminars'''==<br />
<br />
<b><font size="3">[[Geometry and Topology Seminar]]</font></b><br />
<br />
[[PDE Geometric Analysis seminar]]<br />
<br />
[[Symplectic Geometry Seminar]]<br />
<br />
== '''Faculty''' ==<br />
<br />
'''Faculty in Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/ Tullia Dymarz] (U Chicago 2007) Geometric group theory, quasi-isometric rigidity.<br />
<br />
[http://www.math.wisc.edu/~rkent Richard Peabody Kent IV] (UT Austin 2006) <br />
Hyperbolic geometry, mapping class groups, geometric group theory, connections to algebra.<br />
<br />
[http://www.math.wisc.edu/~maribeff/ Gloria Mari-Beffa] (U Minnesota &ndash; Minneapolis 1991) <br />
Differential geometry, invariant theory, completely integrable systems.<br />
<br />
[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim] (U Penn 2005)<br />
Geometry and topology of singularities.<br />
<br />
[http://www.math.wisc.edu/~stpaul/ Sean T. Paul] (Princeton 2000)<br />
Complex differential geometry.<br />
<br />
[http://www.math.wisc.edu/~jeffv/ Jeff Viaclovsky] (Princeton 1999)<br />
Differential geometry, geometric analysis.<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW &ndash; Madison 2008) <br />
Geometric flows.<br />
<br />
<br />
'''Faculty with research tied to Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~angenent/ Sigurd Angenent] (Leiden 1986) Partial differential equations.<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru] (Cornell 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin 1998) Fluid dynamics, mixing, biological swimming and mixing, topological dynamics.<br />
<br />
<br />
'''Postdoctoral faculty in Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~villa/ Manuel Gonz&aacute;lez Villa] (Universidad Complutense de<br />
Madrid 2010)<br />
Geometry and topology of singularities of complex algebraic varieties. <br />
<br />
<br />
'''Honorary Fellow'''<br />
<br />
Morris Hirsch (U Chicago 1958)<br />
<br />
<br />
'''Emeriti'''<br />
<br />
Edward Fadell (Ohio State 1952)<br />
<br />
Sufiàn Husseini (Princeton 1960)<br />
Algebraic topology and applications.<br />
<br />
[http://www.math.wisc.edu/~robbin/ Joel Robbin] (Princeton 1965)<br />
Dynamical systems and symplectic geometry.<br />
<br />
Peter Orlik (U Michigan 1966)<br />
<br />
Mary Ellen Rudin (UT Austin 1949)<br />
<br />
<br />
=='''Conferences'''==<br />
<br />
'''Upcoming conferences in Geometry and Topology held at UW'''<br />
<br />
<br />
<br />
'''Previous conferences in Geometry and Topology held at UW'''<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day.]<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/home Mirror Symmetry in the Midwest II.]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing12.html Singularities in the Midwest, II.]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest]<br />
<br />
[http://www.math.wisc.edu/~oh/glgc/ 2010 Great Lakes Geometry Conference]<br />
<br />
<br />
<!-- ''Graduate study in Geometry and Topology at UW-Madison''' --></div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=8236Geometry and Topology Seminar 2019-20202014-09-10T19:40:41Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''TBA'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| <br />
|<br />
|<br />
|-<br />
|October 10<br />
|[http://math.uchicago.edu/~akwalker/ Alden Walker] (UChicago)<br />
|[[#Alden Walker (UChicago)|''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''TBA'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 1<br />
| [http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
|-<br />
|November 7<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelm&eacute;] (Penn State)<br />
| [[#Thomas Barthelm&eacute; (Penn State)|''TBA'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 14<br />
| <br />
|<br />
|<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 5<br />
| <br />
|<br />
|<br />
|-<br />
|December 12<br />
| <br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''L<sup>2</sup> signatures and an example of Cochran-Harvey-Leidy''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
''TBA''<br />
<br />
===Alden Walker (UChicago)===<br />
''TBA''<br />
<br />
===Jing Tao (Oklahoma)===<br />
''TBA''<br />
<br />
===Thomas Barthelm&eacute; (Penn State)===<br />
''TBA''<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| <br />
|<br />
|<br />
|-<br />
|February 13<br />
| <br />
|<br />
|<br />
|-<br />
|February 20<br />
| <br />
|<br />
|<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| <br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
| <br />
|<br />
|<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=8079Geometry and Topology Seminar 2019-20202014-08-26T21:55:04Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 29<br />
| Yuanqi Wang<br />
| [[#Yuanqi Wang|''Liouville theorem for complex Monge-Ampere equations with conic singularities.'']]<br />
| [http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| [http://people.uwec.edu/daviscw/ Chris Davis] (UW-Eau Claire)<br />
| [[#Chris Davis (UW-Eau Claire)|''TBA'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''TBA'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| <br />
|<br />
|<br />
|-<br />
|October 10<br />
| <br />
|<br />
|<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''TBA'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 7<br />
| <br />
|<br />
|<br />
|-<br />
|November 14<br />
| <br />
|<br />
|<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 5<br />
| <br />
|<br />
|<br />
|-<br />
|December 12<br />
| <br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Yuanqi Wang===<br />
''Liouville theorem for complex Monge-Ampere equations with conic singularities.''<br />
<br />
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations,<br />
we prove the Liouville theorem for conic K&auml;hler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic K&auml;hler geometry.<br />
<br />
===Chris Davis (UW-Eau Claire)===<br />
''TBA''<br />
<br />
===Ben Knudsen (Northwestern)===<br />
''TBA''<br />
<br />
===Jing Tao (Oklahoma)===<br />
''TBA''<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| <br />
|<br />
|<br />
|-<br />
|February 13<br />
| <br />
|<br />
|<br />
|-<br />
|February 20<br />
| <br />
|<br />
|<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| <br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
| <br />
|<br />
|<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=8038Geometry and Topology Seminar 2019-20202014-08-22T22:57:00Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| <br />
|<br />
|<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''TBA'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| <br />
|<br />
|<br />
|-<br />
|October 10<br />
| <br />
|<br />
|<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| [http://www2.math.ou.edu/~jing/ Jing Tao] (Oklahoma)<br />
| [[#Jing Tao (Oklahoma)|''TBA'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 7<br />
| <br />
|<br />
|<br />
|-<br />
|November 14<br />
| <br />
|<br />
|<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 5<br />
| <br />
|<br />
|<br />
|-<br />
|December 12<br />
| <br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Ben Knudsen (Northwestern)===<br />
''TBA''<br />
<br />
===Jing Tao (Oklahoma)===<br />
''TBA''<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| <br />
|<br />
|<br />
|-<br />
|February 13<br />
| <br />
|<br />
|<br />
|-<br />
|February 20<br />
| <br />
|<br />
|<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| <br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
| <br />
|<br />
|<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=7981Geometry and Topology Seminar 2019-20202014-08-19T17:13:38Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2014==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| <br />
|<br />
|<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''TBA'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| <br />
|<br />
|<br />
|-<br />
|October 10<br />
| <br />
|<br />
|<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| <br />
|<br />
|<br />
|-<br />
|November 7<br />
| <br />
|<br />
|<br />
|-<br />
|November 14<br />
| <br />
|<br />
|<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 5<br />
| <br />
|<br />
|<br />
|-<br />
|December 12<br />
| <br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Ben Knudsen (Northwestern)===<br />
''TBA''<br />
<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| <br />
|<br />
|<br />
|-<br />
|February 13<br />
| <br />
|<br />
|<br />
|-<br />
|February 20<br />
| <br />
|<br />
|<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| <br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
| <br />
|<br />
|<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=7980Geometry and Topology Seminar 2019-20202014-08-19T17:13:13Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| <br />
|<br />
|<br />
|-<br />
|September 19<br />
| [http://www.math.northwestern.edu/~knudsen/ Ben Knudsen] (Northwestern)<br />
| [[#Ben Knudsen (Northwestern)|''TBA'']]<br />
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| <br />
|<br />
|<br />
|-<br />
|October 10<br />
| <br />
|<br />
|<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| <br />
|<br />
|<br />
|-<br />
|November 7<br />
| <br />
|<br />
|<br />
|-<br />
|November 14<br />
| <br />
|<br />
|<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 5<br />
| <br />
|<br />
|<br />
|-<br />
|December 12<br />
| <br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Ben Knudsen (Northwestern)===<br />
''TBA''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| <br />
|<br />
|<br />
|-<br />
|February 13<br />
| <br />
|<br />
|<br />
|-<br />
|February 20<br />
| <br />
|<br />
|<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| <br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
| <br />
|<br />
|<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=7979Geometry and Topology Seminar 2019-20202014-08-19T17:04:21Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 5<br />
| <br />
|<br />
|<br />
|-<br />
|September 12<br />
| <br />
|<br />
|<br />
|-<br />
|September 19<br />
| <br />
|<br />
|<br />
|-<br />
|September 26<br />
| <br />
|<br />
|<br />
|-<br />
|October 3<br />
| <br />
|<br />
|<br />
|-<br />
|October 10<br />
| <br />
|<br />
|<br />
|-<br />
|October 17<br />
| <br />
|<br />
|<br />
|-<br />
|October 24<br />
| <br />
|<br />
|<br />
|-<br />
|October 31<br />
| <br />
|<br />
|<br />
|-<br />
|November 7<br />
| <br />
|<br />
|<br />
|-<br />
|November 14<br />
| <br />
|<br />
|<br />
|-<br />
|November 21<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 5<br />
| <br />
|<br />
|<br />
|-<br />
|December 12<br />
| <br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 23<br />
| <br />
|<br />
|<br />
|-<br />
|January 30<br />
| <br />
|<br />
|<br />
|-<br />
|February 6<br />
| <br />
|<br />
|<br />
|-<br />
|February 13<br />
| <br />
|<br />
|<br />
|-<br />
|February 20<br />
| <br />
|<br />
|<br />
|-<br />
|February 27<br />
| <br />
|<br />
|<br />
|-<br />
|March 6<br />
| <br />
|<br />
|<br />
|-<br />
|March 13<br />
| <br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
| Spring Break<br />
| <br />
|<br />
|<br />
|-<br />
|April 10<br />
| <br />
|<br />
|<br />
|-<br />
| April 17<br />
| <br />
|<br />
|<br />
|-<br />
|April 24<br />
| <br />
|<br />
|<br />
|-<br />
|May 1<br />
| <br />
|<br />
|<br />
|-<br />
|May 8<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2013-2014&diff=7978Geometry and Topology Seminar 2013-20142014-08-19T16:53:31Z<p>Rkent: Created page with "The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm. <br> For more information, contact [http://www.math.wisc.edu/~rkent ..."</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|[http://www.math.uiuc.edu/~dowdall/ Spencer Dowdall (UIUC)]<br />
|[[#Spencer Dowdall (UIUC)| ''Fibrations and polynomial invariants for free-by-cyclic groups'']]<br />
|[http://www.math.wisc.edu/~rkent Kent]<br />
|<br />
|-<br />
|February 7<br />
| <br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
| [http://www.math.vanderbilt.edu/~suvaini/ Ioana Suvaina (Vanderbilt)]<br />
| [[#Ioana Suvaina (Vanderbilt)| ''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|<br />
|-<br />
|February 28<br />
|[http://gt.postech.ac.kr/~jccha/ Jae Choon Cha (POSTECH, Korea)]<br />
|[[#Jae Choon Cha (POSTECH)| ''Universal bounds for the Cheeger-Gromov rho-invariants'']]<br />
|[http://www.math.wisc.edu/~maxim Maxim]<br />
|<br />
|-<br />
|March 7<br />
| Mustafa Kalafat (Michigan-State and Tunceli)<br />
|[[#Mustafa Kalafat (Michigan-State and Tunceli)| ''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature'']]<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''MOVED TO COLLOQUIUM SLOT'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
| Yongqiang Liu (UW-Madison and USTC-China)<br />
|[[#Yongqiang Liu| ''Nearby cycles and Alexander modules of hypersurface complements'']]<br />
|[http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
| April 18<br />
| [https://www.math.lsu.edu/~pdani/ Pallavi Dani (LSU)]<br />
| [[#Pallavi Dani (LSU)| ''Large-scale geometry of right-angled Coxeter groups.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 25<br />
| [http://www.math.sunysb.edu/~jsun/ Jingzhou Sun (Stony Brook)]<br />
| [[#Jingzhou Sun(Stony Brook)| ''On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space'']]<br />
|[http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Spencer Dowdall (UIUC)===<br />
''Fibrations and polynomial invariants for free-by-cyclic groups''<br />
<br />
The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial."<br />
<br />
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.<br />
<br />
===Ioana Suvaina (Vanderbilt)===<br />
''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach"<br />
<br />
The talk presents an explicit classification of the ALE Ricci flat Kahler surfaces (M,J,g), generalizing <br />
previous classification results of Kronheimer. The manifolds are related to Q-Gorenstein deformations <br />
of quotient singularities of type C^2/G, with G a finite subgroup of U(2). <br />
Using this classification, we show how these metrics can also be obtained by a construction of Tian-Yau.<br />
In particular, we find good compactifications of the underlying complex manifold M.<br />
<br />
===Jae Choon Cha (POSTECH)===<br />
''Universal bounds for the Cheeger-Gromov rho-invariants"<br />
<br />
Cheeger and Gromov showed that there is a universal bound of their L2 rho-invariants of a fixed smooth closed (4k-1)-manifold, using a deep analytic method. We give a new topological proof of the existence of a universal bound. For 3-manifolds, we give explicit estimates in terms of triangulations, Heegaard splittings, and surgery descriptions. The proof employs interesting ideas including controlled chain homotopy and a geometric reinterpretation of the Atiyah-Hirzebruch bordism spectral sequence. Applications include new results on the complexity of 3-manifolds.<br />
<br />
===Mustafa Kalafat (Michigan-State and Tunceli)===<br />
''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature''<br />
<br />
We show that a compact complex surface which admits a conformally Kahler metric g of positive orthogonal holomorphic bisectional curvature is biholomorphic to the complex projective plane. In addition, if g is a Hermitian metric which is Einstein, then the biholomorphism can be chosen to be an isometry via which g becomes a multiple of the Fubini-Study metric. This is joint work with C.Koca.<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
===Yongqiang Liu===<br />
''Nearby cycles and Alexander modules of hypersurface complements''<br />
<br />
For a polynomial transversal at infinity, we show that the Alexander modules of the hypersurface complement can be realized by the nearby cycle complex, and we obtain a divisibility result for the associated Alexander polynomial. As an application, we use nearby cycles to recover the mixed Hodge structure on the torsion Alexander modules, as defined by Dimca and Libgober.<br />
<br />
===Pallavi Dani (LSU)===<br />
''A finitely generated group can be endowed with a natural metric which<br />
is unique up to coarse isometries, or quasi-isometries. A fundamental<br />
question is to classify finitely generated groups up to<br />
quasi-isometry. I will report on the progress on this question in the<br />
case of right-angled Coxeter groups. In particular I will describe<br />
how topological features of the visual boundary can be used to<br />
classify a family of hyperbolic right-angled Coxeter groups. I will<br />
also discuss the connection with commensurability, an algebraic<br />
property which implies quasi-isometry, but is stronger in general.<br />
This is joint work with Anne Thomas.''<br />
<br />
===Jingzhou Sun (Stony Brook)===<br />
"On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space"<br />
<br />
Let X be a smooth hypersurface of degree d in the 3-dimensional complex projective space. <br />
By totally algebraic calculations, we prove that on the third Demailly-Semple jet bundle X_3 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 11, <br />
and that on the fourth Demailly-Semple jet bundle X_4 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 10, improving a recent result of Diverio.<br />
<br />
== Summer 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Monday, August 18, 2:25<br />
| <br />
| No seminar. David Epstein's lecture has been CANCELED.<br />
| <br />
|-<br />
|}<br />
<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=7977Geometry and Topology Seminar 2019-20202014-08-19T16:53:18Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|[http://www.math.uiuc.edu/~dowdall/ Spencer Dowdall (UIUC)]<br />
|[[#Spencer Dowdall (UIUC)| ''Fibrations and polynomial invariants for free-by-cyclic groups'']]<br />
|[http://www.math.wisc.edu/~rkent Kent]<br />
|<br />
|-<br />
|February 7<br />
| <br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
| [http://www.math.vanderbilt.edu/~suvaini/ Ioana Suvaina (Vanderbilt)]<br />
| [[#Ioana Suvaina (Vanderbilt)| ''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|<br />
|-<br />
|February 28<br />
|[http://gt.postech.ac.kr/~jccha/ Jae Choon Cha (POSTECH, Korea)]<br />
|[[#Jae Choon Cha (POSTECH)| ''Universal bounds for the Cheeger-Gromov rho-invariants'']]<br />
|[http://www.math.wisc.edu/~maxim Maxim]<br />
|<br />
|-<br />
|March 7<br />
| Mustafa Kalafat (Michigan-State and Tunceli)<br />
|[[#Mustafa Kalafat (Michigan-State and Tunceli)| ''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature'']]<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''MOVED TO COLLOQUIUM SLOT'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
| Yongqiang Liu (UW-Madison and USTC-China)<br />
|[[#Yongqiang Liu| ''Nearby cycles and Alexander modules of hypersurface complements'']]<br />
|[http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
| April 18<br />
| [https://www.math.lsu.edu/~pdani/ Pallavi Dani (LSU)]<br />
| [[#Pallavi Dani (LSU)| ''Large-scale geometry of right-angled Coxeter groups.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 25<br />
| [http://www.math.sunysb.edu/~jsun/ Jingzhou Sun (Stony Brook)]<br />
| [[#Jingzhou Sun(Stony Brook)| ''On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space'']]<br />
|[http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Spencer Dowdall (UIUC)===<br />
''Fibrations and polynomial invariants for free-by-cyclic groups''<br />
<br />
The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial."<br />
<br />
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.<br />
<br />
===Ioana Suvaina (Vanderbilt)===<br />
''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach"<br />
<br />
The talk presents an explicit classification of the ALE Ricci flat Kahler surfaces (M,J,g), generalizing <br />
previous classification results of Kronheimer. The manifolds are related to Q-Gorenstein deformations <br />
of quotient singularities of type C^2/G, with G a finite subgroup of U(2). <br />
Using this classification, we show how these metrics can also be obtained by a construction of Tian-Yau.<br />
In particular, we find good compactifications of the underlying complex manifold M.<br />
<br />
===Jae Choon Cha (POSTECH)===<br />
''Universal bounds for the Cheeger-Gromov rho-invariants"<br />
<br />
Cheeger and Gromov showed that there is a universal bound of their L2 rho-invariants of a fixed smooth closed (4k-1)-manifold, using a deep analytic method. We give a new topological proof of the existence of a universal bound. For 3-manifolds, we give explicit estimates in terms of triangulations, Heegaard splittings, and surgery descriptions. The proof employs interesting ideas including controlled chain homotopy and a geometric reinterpretation of the Atiyah-Hirzebruch bordism spectral sequence. Applications include new results on the complexity of 3-manifolds.<br />
<br />
===Mustafa Kalafat (Michigan-State and Tunceli)===<br />
''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature''<br />
<br />
We show that a compact complex surface which admits a conformally Kahler metric g of positive orthogonal holomorphic bisectional curvature is biholomorphic to the complex projective plane. In addition, if g is a Hermitian metric which is Einstein, then the biholomorphism can be chosen to be an isometry via which g becomes a multiple of the Fubini-Study metric. This is joint work with C.Koca.<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
===Yongqiang Liu===<br />
''Nearby cycles and Alexander modules of hypersurface complements''<br />
<br />
For a polynomial transversal at infinity, we show that the Alexander modules of the hypersurface complement can be realized by the nearby cycle complex, and we obtain a divisibility result for the associated Alexander polynomial. As an application, we use nearby cycles to recover the mixed Hodge structure on the torsion Alexander modules, as defined by Dimca and Libgober.<br />
<br />
===Pallavi Dani (LSU)===<br />
''A finitely generated group can be endowed with a natural metric which<br />
is unique up to coarse isometries, or quasi-isometries. A fundamental<br />
question is to classify finitely generated groups up to<br />
quasi-isometry. I will report on the progress on this question in the<br />
case of right-angled Coxeter groups. In particular I will describe<br />
how topological features of the visual boundary can be used to<br />
classify a family of hyperbolic right-angled Coxeter groups. I will<br />
also discuss the connection with commensurability, an algebraic<br />
property which implies quasi-isometry, but is stronger in general.<br />
This is joint work with Anne Thomas.''<br />
<br />
===Jingzhou Sun (Stony Brook)===<br />
"On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space"<br />
<br />
Let X be a smooth hypersurface of degree d in the 3-dimensional complex projective space. <br />
By totally algebraic calculations, we prove that on the third Demailly-Semple jet bundle X_3 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 11, <br />
and that on the fourth Demailly-Semple jet bundle X_4 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 10, improving a recent result of Diverio.<br />
<br />
== Summer 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Monday, August 18, 2:25<br />
| <br />
| No seminar. David Epstein's lecture has been CANCELED.<br />
| <br />
|-<br />
|}<br />
<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=7891Geometry and Topology Seminar 2019-20202014-08-06T22:00:50Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|[http://www.math.uiuc.edu/~dowdall/ Spencer Dowdall (UIUC)]<br />
|[[#Spencer Dowdall (UIUC)| ''Fibrations and polynomial invariants for free-by-cyclic groups'']]<br />
|[http://www.math.wisc.edu/~rkent Kent]<br />
|<br />
|-<br />
|February 7<br />
| <br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
| [http://www.math.vanderbilt.edu/~suvaini/ Ioana Suvaina (Vanderbilt)]<br />
| [[#Ioana Suvaina (Vanderbilt)| ''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|<br />
|-<br />
|February 28<br />
|[http://gt.postech.ac.kr/~jccha/ Jae Choon Cha (POSTECH, Korea)]<br />
|[[#Jae Choon Cha (POSTECH)| ''Universal bounds for the Cheeger-Gromov rho-invariants'']]<br />
|[http://www.math.wisc.edu/~maxim Maxim]<br />
|<br />
|-<br />
|March 7<br />
| Mustafa Kalafat (Michigan-State and Tunceli)<br />
|[[#Mustafa Kalafat (Michigan-State and Tunceli)| ''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature'']]<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''MOVED TO COLLOQUIUM SLOT'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
| Yongqiang Liu (UW-Madison and USTC-China)<br />
|[[#Yongqiang Liu| ''Nearby cycles and Alexander modules of hypersurface complements'']]<br />
|[http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
| April 18<br />
| [https://www.math.lsu.edu/~pdani/ Pallavi Dani (LSU)]<br />
| [[#Pallavi Dani (LSU)| ''Large-scale geometry of right-angled Coxeter groups.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 25<br />
| [http://www.math.sunysb.edu/~jsun/ Jingzhou Sun (Stony Brook)]<br />
| [[#Jingzhou Sun(Stony Brook)| ''On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space'']]<br />
|[http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Spencer Dowdall (UIUC)===<br />
''Fibrations and polynomial invariants for free-by-cyclic groups''<br />
<br />
The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial."<br />
<br />
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.<br />
<br />
===Ioana Suvaina (Vanderbilt)===<br />
''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach"<br />
<br />
The talk presents an explicit classification of the ALE Ricci flat Kahler surfaces (M,J,g), generalizing <br />
previous classification results of Kronheimer. The manifolds are related to Q-Gorenstein deformations <br />
of quotient singularities of type C^2/G, with G a finite subgroup of U(2). <br />
Using this classification, we show how these metrics can also be obtained by a construction of Tian-Yau.<br />
In particular, we find good compactifications of the underlying complex manifold M.<br />
<br />
===Jae Choon Cha (POSTECH)===<br />
''Universal bounds for the Cheeger-Gromov rho-invariants"<br />
<br />
Cheeger and Gromov showed that there is a universal bound of their L2 rho-invariants of a fixed smooth closed (4k-1)-manifold, using a deep analytic method. We give a new topological proof of the existence of a universal bound. For 3-manifolds, we give explicit estimates in terms of triangulations, Heegaard splittings, and surgery descriptions. The proof employs interesting ideas including controlled chain homotopy and a geometric reinterpretation of the Atiyah-Hirzebruch bordism spectral sequence. Applications include new results on the complexity of 3-manifolds.<br />
<br />
===Mustafa Kalafat (Michigan-State and Tunceli)===<br />
''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature''<br />
<br />
We show that a compact complex surface which admits a conformally Kahler metric g of positive orthogonal holomorphic bisectional curvature is biholomorphic to the complex projective plane. In addition, if g is a Hermitian metric which is Einstein, then the biholomorphism can be chosen to be an isometry via which g becomes a multiple of the Fubini-Study metric. This is joint work with C.Koca.<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
===Yongqiang Liu===<br />
''Nearby cycles and Alexander modules of hypersurface complements''<br />
<br />
For a polynomial transversal at infinity, we show that the Alexander modules of the hypersurface complement can be realized by the nearby cycle complex, and we obtain a divisibility result for the associated Alexander polynomial. As an application, we use nearby cycles to recover the mixed Hodge structure on the torsion Alexander modules, as defined by Dimca and Libgober.<br />
<br />
===Pallavi Dani (LSU)===<br />
''A finitely generated group can be endowed with a natural metric which<br />
is unique up to coarse isometries, or quasi-isometries. A fundamental<br />
question is to classify finitely generated groups up to<br />
quasi-isometry. I will report on the progress on this question in the<br />
case of right-angled Coxeter groups. In particular I will describe<br />
how topological features of the visual boundary can be used to<br />
classify a family of hyperbolic right-angled Coxeter groups. I will<br />
also discuss the connection with commensurability, an algebraic<br />
property which implies quasi-isometry, but is stronger in general.<br />
This is joint work with Anne Thomas.''<br />
<br />
===Jingzhou Sun (Stony Brook)===<br />
"On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space"<br />
<br />
Let X be a smooth hypersurface of degree d in the 3-dimensional complex projective space. <br />
By totally algebraic calculations, we prove that on the third Demailly-Semple jet bundle X_3 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 11, <br />
and that on the fourth Demailly-Semple jet bundle X_4 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 10, improving a recent result of Diverio.<br />
<br />
== Summer 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Monday, August 18, 2:25<br />
| <br />
| No seminar. David Epstein's lecture has been CANCELED.<br />
| <br />
|-<br />
|}<br />
<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=7059Geometry and Topology Seminar 2019-20202014-06-19T18:02:36Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|[http://www.math.uiuc.edu/~dowdall/ Spencer Dowdall (UIUC)]<br />
|[[#Spencer Dowdall (UIUC)| ''Fibrations and polynomial invariants for free-by-cyclic groups'']]<br />
|[http://www.math.wisc.edu/~rkent Kent]<br />
|<br />
|-<br />
|February 7<br />
| <br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
| [http://www.math.vanderbilt.edu/~suvaini/ Ioana Suvaina (Vanderbilt)]<br />
| [[#Ioana Suvaina (Vanderbilt)| ''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|<br />
|-<br />
|February 28<br />
|[http://gt.postech.ac.kr/~jccha/ Jae Choon Cha (POSTECH, Korea)]<br />
|[[#Jae Choon Cha (POSTECH)| ''Universal bounds for the Cheeger-Gromov rho-invariants'']]<br />
|[http://www.math.wisc.edu/~maxim Maxim]<br />
|<br />
|-<br />
|March 7<br />
| Mustafa Kalafat (Michigan-State and Tunceli)<br />
|[[#Mustafa Kalafat (Michigan-State and Tunceli)| ''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature'']]<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''MOVED TO COLLOQUIUM SLOT'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
| Yongqiang Liu (UW-Madison and USTC-China)<br />
|[[#Yongqiang Liu| ''Nearby cycles and Alexander modules of hypersurface complements'']]<br />
|[http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
| April 18<br />
| [https://www.math.lsu.edu/~pdani/ Pallavi Dani (LSU)]<br />
| [[#Pallavi Dani (LSU)| ''Large-scale geometry of right-angled Coxeter groups.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 25<br />
| [http://www.math.sunysb.edu/~jsun/ Jingzhou Sun (Stony Brook)]<br />
| [[#Jingzhou Sun(Stony Brook)| ''On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space'']]<br />
|[http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Spencer Dowdall (UIUC)===<br />
''Fibrations and polynomial invariants for free-by-cyclic groups''<br />
<br />
The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial."<br />
<br />
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.<br />
<br />
===Ioana Suvaina (Vanderbilt)===<br />
''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach"<br />
<br />
The talk presents an explicit classification of the ALE Ricci flat Kahler surfaces (M,J,g), generalizing <br />
previous classification results of Kronheimer. The manifolds are related to Q-Gorenstein deformations <br />
of quotient singularities of type C^2/G, with G a finite subgroup of U(2). <br />
Using this classification, we show how these metrics can also be obtained by a construction of Tian-Yau.<br />
In particular, we find good compactifications of the underlying complex manifold M.<br />
<br />
===Jae Choon Cha (POSTECH)===<br />
''Universal bounds for the Cheeger-Gromov rho-invariants"<br />
<br />
Cheeger and Gromov showed that there is a universal bound of their L2 rho-invariants of a fixed smooth closed (4k-1)-manifold, using a deep analytic method. We give a new topological proof of the existence of a universal bound. For 3-manifolds, we give explicit estimates in terms of triangulations, Heegaard splittings, and surgery descriptions. The proof employs interesting ideas including controlled chain homotopy and a geometric reinterpretation of the Atiyah-Hirzebruch bordism spectral sequence. Applications include new results on the complexity of 3-manifolds.<br />
<br />
===Mustafa Kalafat (Michigan-State and Tunceli)===<br />
''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature''<br />
<br />
We show that a compact complex surface which admits a conformally Kahler metric g of positive orthogonal holomorphic bisectional curvature is biholomorphic to the complex projective plane. In addition, if g is a Hermitian metric which is Einstein, then the biholomorphism can be chosen to be an isometry via which g becomes a multiple of the Fubini-Study metric. This is joint work with C.Koca.<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
===Yongqiang Liu===<br />
''Nearby cycles and Alexander modules of hypersurface complements''<br />
<br />
For a polynomial transversal at infinity, we show that the Alexander modules of the hypersurface complement can be realized by the nearby cycle complex, and we obtain a divisibility result for the associated Alexander polynomial. As an application, we use nearby cycles to recover the mixed Hodge structure on the torsion Alexander modules, as defined by Dimca and Libgober.<br />
<br />
===Pallavi Dani (LSU)===<br />
''A finitely generated group can be endowed with a natural metric which<br />
is unique up to coarse isometries, or quasi-isometries. A fundamental<br />
question is to classify finitely generated groups up to<br />
quasi-isometry. I will report on the progress on this question in the<br />
case of right-angled Coxeter groups. In particular I will describe<br />
how topological features of the visual boundary can be used to<br />
classify a family of hyperbolic right-angled Coxeter groups. I will<br />
also discuss the connection with commensurability, an algebraic<br />
property which implies quasi-isometry, but is stronger in general.<br />
This is joint work with Anne Thomas.''<br />
<br />
===Jingzhou Sun (Stony Brook)===<br />
"On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space"<br />
<br />
Let X be a smooth hypersurface of degree d in the 3-dimensional complex projective space. <br />
By totally algebraic calculations, we prove that on the third Demailly-Semple jet bundle X_3 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 11, <br />
and that on the fourth Demailly-Semple jet bundle X_4 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 10, improving a recent result of Diverio.<br />
<br />
== Summer 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>Monday, August 18, 2:25 in 901!</b><br />
| David Epstein (Warwick University)<br />
|[[#David Epstein (Warwick University)| ''Machine Learning and Topology'']]<br />
| [http://www.math.wisc.edu/~robbin/ Robbin]<br />
|-<br />
|}<br />
<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick University)===<br />
''Machine Learning and Topology''<br />
<br />
Modern scientists, particularly biologists, have to deal with datasets that<br />
live in high-dimensional spaces. A typical image has 1000 x 1000 pixels, and<br />
each pixel has an real-valued intensity, so that we can regard the image as a<br />
point in the space R^1,000,000. The objective of a lot of modern research is to<br />
find ways to drastically reduce the dimension from a million to a dimension<br />
that human brains are capable of understanding|ideally this means to dimension 1 or 2, or, reluctantly, dimension 3, but any reduction in dimension<br />
is helpful.<br />
<br />
Suppose, for example, there is a disease that typically shows a one-<br />
dimensional progression, getting steadily worse. It might be possible to detect this deterioration with a sequence of images made from blood samples.<br />
This progression can be modelled as a curve, so 1-dimensional, in R^1,000,000.<br />
Stochastic factors are always present in biological measurements. So the<br />
model would consist of a probability distribution that clusters in the vicinity<br />
of a curve.<br />
<br />
How might one find (an approximation to) the curve, given only the point<br />
cloud in the higher dimensional euclidean space? More generally, suppose<br />
that the point cloud is clustered round a patch of surface (dimension 2) or a k-<br />
dimensional non-linear patch in R^n. How can one recover (an approximation<br />
to) the patch? More generally still (more mathematically complete, but<br />
further from biological applications), given a point cloud in R^n that clusters<br />
round a compact k-dimensional submanifold, possibly with boundary, how<br />
might one find (an approximation to) the submanifold?<br />
<br />
If one succeeds in finding the k-dimensional submanifold, one can then<br />
project the point cloud onto the submanifold, and examine its properties<br />
in a space of dimension k rather in dimension n. This approach to dimension reduction will be applicable to only some point clouds, and completely<br />
different techniques will be applicable in different cases.<br />
<br />
The talk will describe some partial progress towards achieving the above<br />
objectives, with a sketch plan for further progress. Manifold learning is a<br />
topic being worked on by hundreds of researchers, and, as an outsider, I am<br />
not claiming originality. I would be interested to learn of others following<br />
similar lines of investigation.<br />
<br />
A main tool is the use of (multi-dimensional) splines.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=7058Geometry and Topology Seminar 2019-20202014-06-19T18:00:25Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|[http://www.math.uiuc.edu/~dowdall/ Spencer Dowdall (UIUC)]<br />
|[[#Spencer Dowdall (UIUC)| ''Fibrations and polynomial invariants for free-by-cyclic groups'']]<br />
|[http://www.math.wisc.edu/~rkent Kent]<br />
|<br />
|-<br />
|February 7<br />
| <br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
| [http://www.math.vanderbilt.edu/~suvaini/ Ioana Suvaina (Vanderbilt)]<br />
| [[#Ioana Suvaina (Vanderbilt)| ''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|<br />
|-<br />
|February 28<br />
|[http://gt.postech.ac.kr/~jccha/ Jae Choon Cha (POSTECH, Korea)]<br />
|[[#Jae Choon Cha (POSTECH)| ''Universal bounds for the Cheeger-Gromov rho-invariants'']]<br />
|[http://www.math.wisc.edu/~maxim Maxim]<br />
|<br />
|-<br />
|March 7<br />
| Mustafa Kalafat (Michigan-State and Tunceli)<br />
|[[#Mustafa Kalafat (Michigan-State and Tunceli)| ''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature'']]<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''MOVED TO COLLOQUIUM SLOT'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
| Yongqiang Liu (UW-Madison and USTC-China)<br />
|[[#Yongqiang Liu| ''Nearby cycles and Alexander modules of hypersurface complements'']]<br />
|[http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
| April 18<br />
| [https://www.math.lsu.edu/~pdani/ Pallavi Dani (LSU)]<br />
| [[#Pallavi Dani (LSU)| ''Large-scale geometry of right-angled Coxeter groups.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 25<br />
| [http://www.math.sunysb.edu/~jsun/ Jingzhou Sun (Stony Brook)]<br />
| [[#Jingzhou Sun(Stony Brook)| ''On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space'']]<br />
|[http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Spencer Dowdall (UIUC)===<br />
''Fibrations and polynomial invariants for free-by-cyclic groups''<br />
<br />
The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial."<br />
<br />
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.<br />
<br />
===Ioana Suvaina (Vanderbilt)===<br />
''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach"<br />
<br />
The talk presents an explicit classification of the ALE Ricci flat Kahler surfaces (M,J,g), generalizing <br />
previous classification results of Kronheimer. The manifolds are related to Q-Gorenstein deformations <br />
of quotient singularities of type C^2/G, with G a finite subgroup of U(2). <br />
Using this classification, we show how these metrics can also be obtained by a construction of Tian-Yau.<br />
In particular, we find good compactifications of the underlying complex manifold M.<br />
<br />
===Jae Choon Cha (POSTECH)===<br />
''Universal bounds for the Cheeger-Gromov rho-invariants"<br />
<br />
Cheeger and Gromov showed that there is a universal bound of their L2 rho-invariants of a fixed smooth closed (4k-1)-manifold, using a deep analytic method. We give a new topological proof of the existence of a universal bound. For 3-manifolds, we give explicit estimates in terms of triangulations, Heegaard splittings, and surgery descriptions. The proof employs interesting ideas including controlled chain homotopy and a geometric reinterpretation of the Atiyah-Hirzebruch bordism spectral sequence. Applications include new results on the complexity of 3-manifolds.<br />
<br />
===Mustafa Kalafat (Michigan-State and Tunceli)===<br />
''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature''<br />
<br />
We show that a compact complex surface which admits a conformally Kahler metric g of positive orthogonal holomorphic bisectional curvature is biholomorphic to the complex projective plane. In addition, if g is a Hermitian metric which is Einstein, then the biholomorphism can be chosen to be an isometry via which g becomes a multiple of the Fubini-Study metric. This is joint work with C.Koca.<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
===Yongqiang Liu===<br />
''Nearby cycles and Alexander modules of hypersurface complements''<br />
<br />
For a polynomial transversal at infinity, we show that the Alexander modules of the hypersurface complement can be realized by the nearby cycle complex, and we obtain a divisibility result for the associated Alexander polynomial. As an application, we use nearby cycles to recover the mixed Hodge structure on the torsion Alexander modules, as defined by Dimca and Libgober.<br />
<br />
===Pallavi Dani (LSU)===<br />
''A finitely generated group can be endowed with a natural metric which<br />
is unique up to coarse isometries, or quasi-isometries. A fundamental<br />
question is to classify finitely generated groups up to<br />
quasi-isometry. I will report on the progress on this question in the<br />
case of right-angled Coxeter groups. In particular I will describe<br />
how topological features of the visual boundary can be used to<br />
classify a family of hyperbolic right-angled Coxeter groups. I will<br />
also discuss the connection with commensurability, an algebraic<br />
property which implies quasi-isometry, but is stronger in general.<br />
This is joint work with Anne Thomas.''<br />
<br />
===Jingzhou Sun (Stony Brook)===<br />
"On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space"<br />
<br />
Let X be a smooth hypersurface of degree d in the 3-dimensional complex projective space. <br />
By totally algebraic calculations, we prove that on the third Demailly-Semple jet bundle X_3 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 11, <br />
and that on the fourth Demailly-Semple jet bundle X_4 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 10, improving a recent result of Diverio.<br />
<br />
== Summer 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>Monday, August 18, 2:25 in 901!</b><br />
| David Epstein (Warwick University)<br />
|[[#David Epstein (Warwick University)| ''Machine Learning and Topology'']]<br />
| [http://www.math.wisc.edu/~robbin/ Robbin]<br />
|-<br />
|}<br />
<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick University)===<br />
''Machine Learning and Topology''<br />
<br />
Modern scientists, particularly biologists, have to deal with datasets that<br />
live in high-dimensional spaces. A typical image has 1000 x 1000 pixels, and<br />
each pixel has an real-valued intensity, so that we can regard the image as a<br />
point in the space R^1,000,000. The objective of a lot of modern research is to<br />
find ways to drastically reduce the dimension from a million to a dimension<br />
that human brains are capable of understanding|ideally this means to di-<br />
mension 1 or 2, or, reluctantly, dimension 3, but any reduction in dimension<br />
is helpful.<br />
<br />
Suppose, for example, there is a disease that typically shows a one-<br />
dimensional progression, getting steadily worse. It might be possible to de-<br />
tect this deterioration with a sequence of images made from blood samples.<br />
This progression can be modelled as a curve, so 1-dimensional, in R^1,000,000.<br />
Stochastic factors are always present in biological measurements. So the<br />
model would consist of a probability distribution that clusters in the vicinity<br />
of a curve.<br />
<br />
How might one find (an approximation to) the curve, given only the point<br />
cloud in the higher dimensional euclidean space? More generally, suppose<br />
that the point cloud is clustered round a patch of surface (dimension 2) or a k-<br />
dimensional non-linear patch in Rn. How can one recover (an approximation<br />
to) the patch? More generally still (more mathematically complete, but<br />
further from biological applications), given a point cloud in Rn that clusters<br />
round a compact k-dimensional submanifold, possibly with boundary, how<br />
might one find (an approximation to) the submanifold?<br />
<br />
If one succeeds in finding the k-dimensional submanifold, one can then<br />
project the point cloud onto the submanifold, and examine its properties<br />
in a space of dimension k rather in dimension n. This approach to dimen-<br />
sion reduction will be applicable to only some point clouds, and completely<br />
different techniques will be applicable in different cases.<br />
<br />
The talk will describe some partial progress towards achieving the above<br />
objectives, with a sketch plan for further progress. Manifold learning is a<br />
topic being worked on by hundreds of researchers, and, as an outsider, I am<br />
not claiming originality. I would be interested to learn of others following<br />
similar lines of investigation.<br />
<br />
A main tool is the use of (multi-dimensional) splines.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=7040Geometry and Topology Seminar 2019-20202014-06-05T20:16:22Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|[http://www.math.uiuc.edu/~dowdall/ Spencer Dowdall (UIUC)]<br />
|[[#Spencer Dowdall (UIUC)| ''Fibrations and polynomial invariants for free-by-cyclic groups'']]<br />
|[http://www.math.wisc.edu/~rkent Kent]<br />
|<br />
|-<br />
|February 7<br />
| <br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
| [http://www.math.vanderbilt.edu/~suvaini/ Ioana Suvaina (Vanderbilt)]<br />
| [[#Ioana Suvaina (Vanderbilt)| ''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|<br />
|-<br />
|February 28<br />
|[http://gt.postech.ac.kr/~jccha/ Jae Choon Cha (POSTECH, Korea)]<br />
|[[#Jae Choon Cha (POSTECH)| ''Universal bounds for the Cheeger-Gromov rho-invariants'']]<br />
|[http://www.math.wisc.edu/~maxim Maxim]<br />
|<br />
|-<br />
|March 7<br />
| Mustafa Kalafat (Michigan-State and Tunceli)<br />
|[[#Mustafa Kalafat (Michigan-State and Tunceli)| ''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature'']]<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''MOVED TO COLLOQUIUM SLOT'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
| Yongqiang Liu (UW-Madison and USTC-China)<br />
|[[#Yongqiang Liu| ''Nearby cycles and Alexander modules of hypersurface complements'']]<br />
|[http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
| April 18<br />
| [https://www.math.lsu.edu/~pdani/ Pallavi Dani (LSU)]<br />
| [[#Pallavi Dani (LSU)| ''Large-scale geometry of right-angled Coxeter groups.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 25<br />
| [http://www.math.sunysb.edu/~jsun/ Jingzhou Sun (Stony Brook)]<br />
| [[#Jingzhou Sun(Stony Brook)| ''On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space'']]<br />
|[http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Spencer Dowdall (UIUC)===<br />
''Fibrations and polynomial invariants for free-by-cyclic groups''<br />
<br />
The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial."<br />
<br />
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.<br />
<br />
===Ioana Suvaina (Vanderbilt)===<br />
''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach"<br />
<br />
The talk presents an explicit classification of the ALE Ricci flat Kahler surfaces (M,J,g), generalizing <br />
previous classification results of Kronheimer. The manifolds are related to Q-Gorenstein deformations <br />
of quotient singularities of type C^2/G, with G a finite subgroup of U(2). <br />
Using this classification, we show how these metrics can also be obtained by a construction of Tian-Yau.<br />
In particular, we find good compactifications of the underlying complex manifold M.<br />
<br />
===Jae Choon Cha (POSTECH)===<br />
''Universal bounds for the Cheeger-Gromov rho-invariants"<br />
<br />
Cheeger and Gromov showed that there is a universal bound of their L2 rho-invariants of a fixed smooth closed (4k-1)-manifold, using a deep analytic method. We give a new topological proof of the existence of a universal bound. For 3-manifolds, we give explicit estimates in terms of triangulations, Heegaard splittings, and surgery descriptions. The proof employs interesting ideas including controlled chain homotopy and a geometric reinterpretation of the Atiyah-Hirzebruch bordism spectral sequence. Applications include new results on the complexity of 3-manifolds.<br />
<br />
===Mustafa Kalafat (Michigan-State and Tunceli)===<br />
''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature''<br />
<br />
We show that a compact complex surface which admits a conformally Kahler metric g of positive orthogonal holomorphic bisectional curvature is biholomorphic to the complex projective plane. In addition, if g is a Hermitian metric which is Einstein, then the biholomorphism can be chosen to be an isometry via which g becomes a multiple of the Fubini-Study metric. This is joint work with C.Koca.<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
===Yongqiang Liu===<br />
''Nearby cycles and Alexander modules of hypersurface complements''<br />
<br />
For a polynomial transversal at infinity, we show that the Alexander modules of the hypersurface complement can be realized by the nearby cycle complex, and we obtain a divisibility result for the associated Alexander polynomial. As an application, we use nearby cycles to recover the mixed Hodge structure on the torsion Alexander modules, as defined by Dimca and Libgober.<br />
<br />
===Pallavi Dani (LSU)===<br />
''A finitely generated group can be endowed with a natural metric which<br />
is unique up to coarse isometries, or quasi-isometries. A fundamental<br />
question is to classify finitely generated groups up to<br />
quasi-isometry. I will report on the progress on this question in the<br />
case of right-angled Coxeter groups. In particular I will describe<br />
how topological features of the visual boundary can be used to<br />
classify a family of hyperbolic right-angled Coxeter groups. I will<br />
also discuss the connection with commensurability, an algebraic<br />
property which implies quasi-isometry, but is stronger in general.<br />
This is joint work with Anne Thomas.''<br />
<br />
===Jingzhou Sun (Stony Brook)===<br />
"On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space"<br />
<br />
Let X be a smooth hypersurface of degree d in the 3-dimensional complex projective space. <br />
By totally algebraic calculations, we prove that on the third Demailly-Semple jet bundle X_3 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 11, <br />
and that on the fourth Demailly-Semple jet bundle X_4 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 10, improving a recent result of Diverio.<br />
<br />
== Summer 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>Monday, August 18, 2:25 in 901!</b><br />
| David Epstein (Warwick University)<br />
|[[#David Epstein (Warwick University)| ''Machine Learning and Topology'']]<br />
| [http://www.math.wisc.edu/~robbin/ Robbin]<br />
|-<br />
|}<br />
<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick University)===<br />
''Machine Learning and Topology''<br />
<br />
Suppose we do lots of experiments on various gases, measuring their pressure P, volume V, absolute temperature T and quantity Q (in moles). This gives lot of points in 4 dimensions, with experimental error in observing them. The question is: how can we recover (an approximation to) the 3d-submanifold P.V=const.T.Q? (This is the Ideal Gas Law.) In general, given a point cloud in n-space, clustered round a manifold, how can one recover the manifold? A main tool is splines.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=7021Geometry and Topology Seminar 2019-20202014-05-29T23:22:19Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|[http://www.math.uiuc.edu/~dowdall/ Spencer Dowdall (UIUC)]<br />
|[[#Spencer Dowdall (UIUC)| ''Fibrations and polynomial invariants for free-by-cyclic groups'']]<br />
|[http://www.math.wisc.edu/~rkent Kent]<br />
|<br />
|-<br />
|February 7<br />
| <br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
| [http://www.math.vanderbilt.edu/~suvaini/ Ioana Suvaina (Vanderbilt)]<br />
| [[#Ioana Suvaina (Vanderbilt)| ''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|<br />
|-<br />
|February 28<br />
|[http://gt.postech.ac.kr/~jccha/ Jae Choon Cha (POSTECH, Korea)]<br />
|[[#Jae Choon Cha (POSTECH)| ''Universal bounds for the Cheeger-Gromov rho-invariants'']]<br />
|[http://www.math.wisc.edu/~maxim Maxim]<br />
|<br />
|-<br />
|March 7<br />
| Mustafa Kalafat (Michigan-State and Tunceli)<br />
|[[#Mustafa Kalafat (Michigan-State and Tunceli)| ''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature'']]<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''MOVED TO COLLOQUIUM SLOT'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
| Yongqiang Liu (UW-Madison and USTC-China)<br />
|[[#Yongqiang Liu| ''Nearby cycles and Alexander modules of hypersurface complements'']]<br />
|[http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
| April 18<br />
| [https://www.math.lsu.edu/~pdani/ Pallavi Dani (LSU)]<br />
| [[#Pallavi Dani (LSU)| ''Large-scale geometry of right-angled Coxeter groups.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 25<br />
| [http://www.math.sunysb.edu/~jsun/ Jingzhou Sun (Stony Brook)]<br />
| [[#Jingzhou Sun(Stony Brook)| ''On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space'']]<br />
|[http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Spencer Dowdall (UIUC)===<br />
''Fibrations and polynomial invariants for free-by-cyclic groups''<br />
<br />
The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial."<br />
<br />
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.<br />
<br />
===Ioana Suvaina (Vanderbilt)===<br />
''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach"<br />
<br />
The talk presents an explicit classification of the ALE Ricci flat Kahler surfaces (M,J,g), generalizing <br />
previous classification results of Kronheimer. The manifolds are related to Q-Gorenstein deformations <br />
of quotient singularities of type C^2/G, with G a finite subgroup of U(2). <br />
Using this classification, we show how these metrics can also be obtained by a construction of Tian-Yau.<br />
In particular, we find good compactifications of the underlying complex manifold M.<br />
<br />
===Jae Choon Cha (POSTECH)===<br />
''Universal bounds for the Cheeger-Gromov rho-invariants"<br />
<br />
Cheeger and Gromov showed that there is a universal bound of their L2 rho-invariants of a fixed smooth closed (4k-1)-manifold, using a deep analytic method. We give a new topological proof of the existence of a universal bound. For 3-manifolds, we give explicit estimates in terms of triangulations, Heegaard splittings, and surgery descriptions. The proof employs interesting ideas including controlled chain homotopy and a geometric reinterpretation of the Atiyah-Hirzebruch bordism spectral sequence. Applications include new results on the complexity of 3-manifolds.<br />
<br />
===Mustafa Kalafat (Michigan-State and Tunceli)===<br />
''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature''<br />
<br />
We show that a compact complex surface which admits a conformally Kahler metric g of positive orthogonal holomorphic bisectional curvature is biholomorphic to the complex projective plane. In addition, if g is a Hermitian metric which is Einstein, then the biholomorphism can be chosen to be an isometry via which g becomes a multiple of the Fubini-Study metric. This is joint work with C.Koca.<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
===Yongqiang Liu===<br />
''Nearby cycles and Alexander modules of hypersurface complements''<br />
<br />
For a polynomial transversal at infinity, we show that the Alexander modules of the hypersurface complement can be realized by the nearby cycle complex, and we obtain a divisibility result for the associated Alexander polynomial. As an application, we use nearby cycles to recover the mixed Hodge structure on the torsion Alexander modules, as defined by Dimca and Libgober.<br />
<br />
===Pallavi Dani (LSU)===<br />
''A finitely generated group can be endowed with a natural metric which<br />
is unique up to coarse isometries, or quasi-isometries. A fundamental<br />
question is to classify finitely generated groups up to<br />
quasi-isometry. I will report on the progress on this question in the<br />
case of right-angled Coxeter groups. In particular I will describe<br />
how topological features of the visual boundary can be used to<br />
classify a family of hyperbolic right-angled Coxeter groups. I will<br />
also discuss the connection with commensurability, an algebraic<br />
property which implies quasi-isometry, but is stronger in general.<br />
This is joint work with Anne Thomas.''<br />
<br />
===Jingzhou Sun (Stony Brook)===<br />
"On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space"<br />
<br />
Let X be a smooth hypersurface of degree d in the 3-dimensional complex projective space. <br />
By totally algebraic calculations, we prove that on the third Demailly-Semple jet bundle X_3 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 11, <br />
and that on the fourth Demailly-Semple jet bundle X_4 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 10, improving a recent result of Diverio.<br />
<br />
== Summer 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 18, <b>2:25 in 901!</b><br />
| David Epstein (Warwick University)<br />
|[[#David Epstein (Warwick University)| ''Machine Learning and Topology'']]<br />
| [http://www.math.wisc.edu/~robbin/ Robbin]<br />
|-<br />
|}<br />
<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick University)===<br />
''Machine Learning and Topology''<br />
<br />
Suppose we do lots of experiments on various gases, measuring their pressure P, volume V, absolute temperature T and quantity Q (in moles). This gives lot of points in 4 dimensions, with experimental error in observing them. The question is: how can we recover (an approximation to) the 3d-submanifold P.V=const.T.Q? (This is the Ideal Gas Law.) In general, given a point cloud in n-space, clustered round a manifold, how can one recover the manifold? A main tool is splines.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=7020Geometry and Topology Seminar 2019-20202014-05-29T23:21:01Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|[http://www.math.uiuc.edu/~dowdall/ Spencer Dowdall (UIUC)]<br />
|[[#Spencer Dowdall (UIUC)| ''Fibrations and polynomial invariants for free-by-cyclic groups'']]<br />
|[http://www.math.wisc.edu/~rkent Kent]<br />
|<br />
|-<br />
|February 7<br />
| <br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
| [http://www.math.vanderbilt.edu/~suvaini/ Ioana Suvaina (Vanderbilt)]<br />
| [[#Ioana Suvaina (Vanderbilt)| ''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|<br />
|-<br />
|February 28<br />
|[http://gt.postech.ac.kr/~jccha/ Jae Choon Cha (POSTECH, Korea)]<br />
|[[#Jae Choon Cha (POSTECH)| ''Universal bounds for the Cheeger-Gromov rho-invariants'']]<br />
|[http://www.math.wisc.edu/~maxim Maxim]<br />
|<br />
|-<br />
|March 7<br />
| Mustafa Kalafat (Michigan-State and Tunceli)<br />
|[[#Mustafa Kalafat (Michigan-State and Tunceli)| ''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature'']]<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''MOVED TO COLLOQUIUM SLOT'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
| Yongqiang Liu (UW-Madison and USTC-China)<br />
|[[#Yongqiang Liu| ''Nearby cycles and Alexander modules of hypersurface complements'']]<br />
|[http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
| April 18<br />
| [https://www.math.lsu.edu/~pdani/ Pallavi Dani (LSU)]<br />
| [[#Pallavi Dani (LSU)| ''Large-scale geometry of right-angled Coxeter groups.'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 25<br />
| [http://www.math.sunysb.edu/~jsun/ Jingzhou Sun (Stony Brook)]<br />
| [[#Jingzhou Sun(Stony Brook)| ''On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space'']]<br />
|[http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Spencer Dowdall (UIUC)===<br />
''Fibrations and polynomial invariants for free-by-cyclic groups''<br />
<br />
The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial."<br />
<br />
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.<br />
<br />
===Ioana Suvaina (Vanderbilt)===<br />
''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach"<br />
<br />
The talk presents an explicit classification of the ALE Ricci flat Kahler surfaces (M,J,g), generalizing <br />
previous classification results of Kronheimer. The manifolds are related to Q-Gorenstein deformations <br />
of quotient singularities of type C^2/G, with G a finite subgroup of U(2). <br />
Using this classification, we show how these metrics can also be obtained by a construction of Tian-Yau.<br />
In particular, we find good compactifications of the underlying complex manifold M.<br />
<br />
===Jae Choon Cha (POSTECH)===<br />
''Universal bounds for the Cheeger-Gromov rho-invariants"<br />
<br />
Cheeger and Gromov showed that there is a universal bound of their L2 rho-invariants of a fixed smooth closed (4k-1)-manifold, using a deep analytic method. We give a new topological proof of the existence of a universal bound. For 3-manifolds, we give explicit estimates in terms of triangulations, Heegaard splittings, and surgery descriptions. The proof employs interesting ideas including controlled chain homotopy and a geometric reinterpretation of the Atiyah-Hirzebruch bordism spectral sequence. Applications include new results on the complexity of 3-manifolds.<br />
<br />
===Mustafa Kalafat (Michigan-State and Tunceli)===<br />
''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature''<br />
<br />
We show that a compact complex surface which admits a conformally Kahler metric g of positive orthogonal holomorphic bisectional curvature is biholomorphic to the complex projective plane. In addition, if g is a Hermitian metric which is Einstein, then the biholomorphism can be chosen to be an isometry via which g becomes a multiple of the Fubini-Study metric. This is joint work with C.Koca.<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
===Yongqiang Liu===<br />
''Nearby cycles and Alexander modules of hypersurface complements''<br />
<br />
For a polynomial transversal at infinity, we show that the Alexander modules of the hypersurface complement can be realized by the nearby cycle complex, and we obtain a divisibility result for the associated Alexander polynomial. As an application, we use nearby cycles to recover the mixed Hodge structure on the torsion Alexander modules, as defined by Dimca and Libgober.<br />
<br />
===Pallavi Dani (LSU)===<br />
''A finitely generated group can be endowed with a natural metric which<br />
is unique up to coarse isometries, or quasi-isometries. A fundamental<br />
question is to classify finitely generated groups up to<br />
quasi-isometry. I will report on the progress on this question in the<br />
case of right-angled Coxeter groups. In particular I will describe<br />
how topological features of the visual boundary can be used to<br />
classify a family of hyperbolic right-angled Coxeter groups. I will<br />
also discuss the connection with commensurability, an algebraic<br />
property which implies quasi-isometry, but is stronger in general.<br />
This is joint work with Anne Thomas.''<br />
<br />
===Jingzhou Sun (Stony Brook)===<br />
"On the Demailly-Semple jet bundles of hypersurfaces in the 3-dimensional complex projective space"<br />
<br />
Let X be a smooth hypersurface of degree d in the 3-dimensional complex projective space. <br />
By totally algebraic calculations, we prove that on the third Demailly-Semple jet bundle X_3 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 11, <br />
and that on the fourth Demailly-Semple jet bundle X_4 of X, <br />
the Demailly-Semple line bundle is big for d not ness than 10, improving a recent result of Diverio.<br />
<br />
== Summer 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|August 18, <b>2:25 in 901!</b><br />
| David Epstein (Warwick University)<br />
|[[#David Epstein (Warwick University)| ''Machine Learning and Topology'']]<br />
|<br />
|-<br />
|}<br />
<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick University)===<br />
''Machine Learning and Topology''<br />
<br />
Suppose we do lots of experiments on various gases, measuring their pressure P, volume V, absolute temperature T and quantity Q (in moles). This gives lot of points in 4 dimensions, with experimental error in observing them. The question is: how can we recover (an approximation to) the 3d-submanifold P.V=const.T.Q? (This is the Ideal Gas Law.) In general, given a point cloud in n-space, clustered round a manifold, how can one recover the manifold? A main tool is splines.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=6640Geometry and Topology Seminar 2019-20202014-02-14T12:36:25Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|[http://www.math.uiuc.edu/~dowdall/ Spencer Dowdall (UIUC)]<br />
|[[#Spencer Dowdall (UIUC)| ''Fibrations and polynomial invariants for free-by-cyclic groups'']]<br />
|[http://www.math.wisc.edu/~rkent Kent]<br />
|<br />
|-<br />
|February 7<br />
| <br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
| [http://www.math.vanderbilt.edu/~suvaini/ Ioana Suvaina (Vanderbilt)]<br />
| [[#Ioana Suvaina (Vanderbilt)| ''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|<br />
|-<br />
|February 28<br />
|[http://gt.postech.ac.kr/~jccha/ Jae Choon Cha (POSTECH, Korea)]<br />
|[[#Jae Choon Cha (POSTECH)| ''Universal bounds for the Cheeger-Gromov rho-invariants'']]<br />
|[http://www.math.wisc.edu/~maxim Maxim]<br />
|<br />
|-<br />
|March 7<br />
| Mustafa Kalafat (Michigan-State and Tunceli)<br />
|[[#Mustafa Kalafat (Michigan-State and Tunceli)| ''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature'']]<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
| <br />
|<br />
|<br />
|-<br />
| April 18<br />
| [https://www.math.lsu.edu/~pdani/ Pallavi Dani (LSU)]<br />
| [[#Pallavi Dani (LSU)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 25<br />
| [http://www.math.sunysb.edu/~jsun/ Jingzhou Sun (Stony Brook)]<br />
| [[#Jingzhou Sun(Stony Brook)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Spencer Dowdall (UIUC)===<br />
''Fibrations and polynomial invariants for free-by-cyclic groups''<br />
<br />
The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial."<br />
<br />
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.<br />
<br />
===Ioana Suvaina (Vanderbilt)===<br />
''ALE Ricci flat Kahler surfaces from a Tian-Yau construction approach"<br />
<br />
The talk presents an explicit classification of the ALE Ricci flat Kahler surfaces (M,J,g), generalizing <br />
previous classification results of Kronheimer. The manifolds are related to Q-Gorenstein deformations <br />
of quotient singularities of type C^2/G, with G a finite subgroup of U(2). <br />
Using this classification, we show how these metrics can also be obtained by a construction of Tian-Yau.<br />
In particular, we find good compactifications of the underlying complex manifold M.<br />
<br />
===Jae Choon Cha (POSTECH)===<br />
''Universal bounds for the Cheeger-Gromov rho-invariants"<br />
<br />
Cheeger and Gromov showed that there is a universal bound of their L2 rho-invariants of a fixed smooth closed (4k-1)-manifold, using a deep analytic method. We give a new topological proof of the existence of a universal bound. For 3-manifolds, we give explicit estimates in terms of triangulations, Heegaard splittings, and surgery descriptions. The proof employs interesting ideas including controlled chain homotopy and a geometric reinterpretation of the Atiyah-Hirzebruch bordism spectral sequence. Applications include new results on the complexity of 3-manifolds.<br />
<br />
===Mustafa Kalafat (Michigan-State and Tunceli)===<br />
''Conformally Kahler Surfaces and Orthogonal Holomorphic Bisectional Curvature''<br />
<br />
We show that a compact complex surface which admits a conformally Kahler metric g of positive orthogonal holomorphic bisectional curvature is biholomorphic to the complex projective plane. In addition, if g is a Hermitian metric which is Einstein, then the biholomorphism can be chosen to be an isometry via which g becomes a multiple of the Fubini-Study metric. This is joint work with C.Koca.<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
===Pallavi Dani (LSU)===<br />
''TBA''<br />
<br />
===Jingzhou Sun(Stony Brook)===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=6499Geometry and Topology Seminar 2019-20202014-01-30T15:04:44Z<p>Rkent: /* Spring 2014 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|[http://www.math.uiuc.edu/~dowdall/ Spencer Dowdall (UIUC)]<br />
|[[#Spencer Dowdall (UIUC)| ''Fibrations and polynomial invariants for free-by-cyclic groups'']]<br />
|[http://www.math.wisc.edu/~rkent Kent]<br />
|<br />
|-<br />
|February 7<br />
| <br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
| [http://www.math.vanderbilt.edu/~suvaini/ Ioana Suvaina (Vanderbilt)]<br />
| [[#Ioana Suvaina (Vanderbilt)| ''TBA'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|<br />
|-<br />
|February 28<br />
|[http://gt.postech.ac.kr/~jccha/ Jae Choon Cha (POSTECH, Korea)]<br />
|[[#Jae Choon Cha (POSTECH)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~maxim Maxim]<br />
|<br />
|-<br />
|March 7<br />
| <br />
|<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
| <br />
|<br />
|<br />
|-<br />
| April 18<br />
| [https://www.math.lsu.edu/~pdani/ Pallavi Dani (LSU)]<br />
| [[#Pallavi Dani (LSU)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 25<br />
| [http://www.math.sunysb.edu/~jsun/ Jingzhou Sun (Stony Brook)]<br />
| [[#Jingzhou Sun(Stony Brook)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~bwang Wang]<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Spencer Dowdall (UIUC)===<br />
''Fibrations and polynomial invariants for free-by-cyclic groups''<br />
<br />
The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial."<br />
<br />
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
===Pallavi Dani (LSU)===<br />
''TBA''<br />
<br />
===Jingzhou Sun(Stony Brook)===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=6498Geometry and Topology Seminar 2019-20202014-01-30T15:02:50Z<p>Rkent: /* Spring 2014 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|[http://www.math.uiuc.edu/~dowdall/ Spencer Dowdall (UIUC)]<br />
|[[#Spencer Dowdall (UIUC)| ''Fibrations and polynomial invariants for free-by-cyclic groups'']]<br />
|[http://www.math.wisc.edu/~rkent Kent]<br />
|<br />
|-<br />
|February 7<br />
| <br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
| [http://www.math.vanderbilt.edu/~suvaini/ Ioana Suvaina (Vanderbilt)]<br />
| [[#Ioana Suvaina (Vanderbilt)| ''TBA'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|<br />
|-<br />
|February 28<br />
|[http://gt.postech.ac.kr/~jccha/ Jae Choon Cha (POSTECH, Korea)]<br />
|[[#Jae Choon Cha (POSTECH)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~maxim Maxim]<br />
|<br />
|-<br />
|March 7<br />
| <br />
|<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
| <br />
|<br />
|<br />
|-<br />
| April 18<br />
| [https://www.math.lsu.edu/~pdani/ Pallavi Dani (LSU)]<br />
| [[#Pallavi Dani (LSU)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 25<br />
| [http://www.math.sunysb.edu/~jsun/ Jingzhou Sun(Stony Brook)]<br />
| [[#Jingzhou Sun(Stony Brook)| ''TBA'']]<br />
|[Wang]<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Spencer Dowdall (UIUC)===<br />
''Fibrations and polynomial invariants for free-by-cyclic groups''<br />
<br />
The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial."<br />
<br />
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
===Pallavi Dani (LSU)===<br />
''TBA''<br />
<br />
===Jingzhou Sun(Stony Brook)===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=6460Geometry and Topology Seminar 2019-20202014-01-24T03:21:04Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|[http://www.math.uiuc.edu/~dowdall/ Spencer Dowdall (UIUC)]<br />
|[[#Spencer Dowdall (UIUC)| ''Fibrations and polynomial invariants for free-by-cyclic groups'']]<br />
|[http://www.math.wisc.edu/~rkent Kent]<br />
|<br />
|-<br />
|February 7<br />
| Reserved for special Colloquium<br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
|<br />
|<br />
|<br />
|-<br />
|February 28<br />
|[http://gt.postech.ac.kr/~jccha/ Jae Choon Cha (POSTECH, Korea)]<br />
|[[#Jae Choon Cha (POSTECH)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~maxim Maxim]<br />
|<br />
|-<br />
|March 7<br />
| <br />
|<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
| [http://www.math.vanderbilt.edu/~suvaini/ Ioana Suvaina (Vanderbilt)]<br />
| [[#Ioana Suvaina (Vanderbilt)| ''TBA'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|April 18<br />
| <br />
|<br />
|<br />
|-<br />
|April 25<br />
| [http://www.math.sunysb.edu/~jsun/ Jingzhou Sun(Stony Brook)]<br />
| [[#Jingzhou Sun(Stony Brook)| ''TBA'']]<br />
|[Wang]<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Spencer Dowdall (UIUC)===<br />
''Fibrations and polynomial invariants for free-by-cyclic groups''<br />
<br />
The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial."<br />
<br />
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
===Jingzhou Sun(Stony Brook)===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=6438Geometry and Topology Seminar 2019-20202014-01-22T21:30:19Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|[http://www.math.uiuc.edu/~dowdall/ Spencer Dowdall (UIUC)]<br />
|[[#Spencer Dowdall (UIUC)| ''Fibrations and polynomial invariants for free-by-cyclic groups'']]<br />
|[http://www.math.wisc.edu/~rkent Kent]<br />
|<br />
|-<br />
|February 7<br />
|<br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
|<br />
|<br />
|<br />
|-<br />
|February 28<br />
|[http://gt.postech.ac.kr/~jccha/ Jae Choon Cha (POSTECH, Korea)]<br />
|[[#Jae Choon Cha (POSTECH)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~maxim Maxim]<br />
|<br />
|-<br />
|March 7<br />
| <br />
|<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
| [http://www.math.vanderbilt.edu/~suvaini/ Ioana Suvaina (Vanderbilt)]<br />
| [[#Ioana Suvaina (Vanderbilt)| ''TBA'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|April 18<br />
| <br />
|<br />
|<br />
|-<br />
|April 25<br />
| [http://www.math.sunysb.edu/~jsun/ Jingzhou Sun(Stony Brook)]<br />
| [[#Jingzhou Sun(Stony Brook)| ''TBA'']]<br />
|[Wang]<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Spencer Dowdall (UIUC)===<br />
''Fibrations and polynomial invariants for free-by-cyclic groups''<br />
<br />
The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial."<br />
<br />
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
===Jingzhou Sun(Stony Brook)===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=6437Geometry and Topology Seminar 2019-20202014-01-22T20:44:18Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|[http://www.math.uiuc.edu/~dowdall/ Spencer Dowdall (UIUC)]<br />
|[[#Spencer Dowdall (UIUC)| ''Fibrations and polynomial invariants for free-by-cyclic groups'']]<br />
|[http://www.math.wisc.edu/~rkent Kent]<br />
|<br />
|-<br />
|February 7<br />
|<br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
|<br />
|<br />
|<br />
|-<br />
|February 28<br />
|[http://gt.postech.ac.kr/~jccha/ Jae Choon Cha (POSTECH, Korea)]<br />
|[[#Jae Choon Cha (POSTECH)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~maxim Maxim]<br />
|<br />
|-<br />
|March 7<br />
| <br />
|<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
| [http://www.math.vanderbilt.edu/~suvaini/ Ioana Suvaina (Vanderbilt)]<br />
| [[#Ioana Suvaina (Vanderbilt)| ''TBA'']]<br />
| [http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|April 18<br />
| <br />
|<br />
|<br />
|-<br />
|April 25<br />
| [http://www.math.sunysb.edu/~jsun/ Jingzhou Sun(Stony Brook)]<br />
| [[#Jingzhou Sun(Stony Brook)| ''TBA'']]<br />
|[Wang]<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Spencer Dowdall (UIUC)===<br />
''Fibrations and polynomial invariants for free-by-cyclic groups''<br />
<br />
The beautiful theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology M^1(M;R) whose integral points all correspond to fibrations of M, and the dynamical features of these fibrations are all encoded by McMullen's "Teichmuller polynomial."<br />
<br />
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygonal cone C in the first cohomology of G whose integral points all correspond to algebraically and dynamically interesting splittings of G. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is joint work with Ilya Kapovich and Christopher J. Leininger.<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
===JingZhou Sun(Stony Brook)===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6318Colloquia/Fall182014-01-05T20:42:04Z<p>Rkent: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2013 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)<br />
|Riemann-Roch for Graphs and Applications<br />
|Ellenberg<br />
|-<br />
|Sept 13<br />
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)<br />
|A hop, skip, and a jump through the degrees of relative provability<br />
|<br />
|-<br />
|Sept 20<br />
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)<br />
|Flat connections and quantum groups<br />
|Gurevich<br />
|-<br />
|'''Wed, Sept 25, 2:30PM in B139'''<br />
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss] (Indiana University)<br />
|Taylor Series in Homotopy Theory<br />
|Meyer<br />
|-<br />
|'''Wed, Sept 25''' (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication-Avoiding Algorithms for Linear Algebra and Beyond<br />
|Gurevich<br />
|-<br />
|'''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Implementing Communication-Avoiding Algorithms<br />
|Gurevich<br />
|-<br />
|Sept 27 (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays<br />
|Gurevich<br />
|-<br />
|Oct 4<br />
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)<br />
|Galois groups of Schubert problems<br />
|Caldararu<br />
|-<br />
|Oct 11<br />
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)<br />
|[[Colloquia#October 11: Amie Wilkinson (Chicago) | Robust mechanisms for chaos]]<br />
|WIMAW (Cladek)<br />
|-<br />
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability I]]<br />
|Valko<br />
|-<br />
|'''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability II]]<br />
|Valko<br />
|-<br />
|<strike>Oct 18</strike><br />
|No colloquium due to the distinguished lecture<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)<br />
|[[Colloquia#October 25: Paul Garrett (Minnesota) | Boundary-value problems, generalized functions, and zeros of zeta functions]]<br />
|Gurevich<br />
|<br />
|<br />
|-<br />
|Nov 1<br />
|[http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)<br />
|On sets of large doubling, Lambda(4) sets, and error-correcting codes<br />
|Stovall<br />
|-<br />
|Nov 8<br />
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)<br />
|[[Colloquia#November 8: Tim Riley (Cornell) | Hydra groups]]<br />
|Dymarz<br />
|-<br />
|Nov 15 and later<br />
|Reserved<br />
|<br />
|Street<br />
|-<br />
|Nov 22<br />
|[http://www.math.uchicago.edu/~tj/ Tianling Jin] (University of Chicago)<br />
|Solutions of some Monge-Ampere equations with degeneracy or singularities.<br />
|Bolotin<br />
|-<br />
|'''Mon, Nov 25, 4PM'''<br />
|[https://web.math.princeton.edu/~linlin/ Lin Lin] (Lawrence Berkeley National Lab)<br />
|Fast algorithms for electronic structure analysis<br />
|Jin<br />
|-<br />
|'''Tue, Nov 26, 4PM, B139'''<br />
|[http://www.math.cornell.edu/m/People/Faculty/conley Clinton Conley] (Cornell)<br />
|[[Colloquia#November 26 (Tuesday): Clinton Conley (Cornell) | Descriptive set-theoretic graph theory]]<br />
|Lempp<br />
|-<br />
|'''Mon, Dec 2, 4PM'''<br />
|[http://www.math.northwestern.edu/~slm/ Simon Marshall] (Northwestern)<br />
|[[Colloquia#December 2 (Monday): Simon Marshall (Northwestern) | Semiclassical estimates for eigenfunctions on locally symmetric spaces]]<br />
|Denissov<br />
|-<br />
|'''Wed, Dec 4, 4PM'''<br />
|[http://math.berkeley.edu/~svs/ Steven Sam] (Berkeley)<br />
|Free Resolutions and Symmetry<br />
|Boston <br />
|-<br />
|'''Fri, Dec 6'''<br />
|[http://math.mit.edu/~hand/ Paul Hand] (MIT)<br />
|[[Colloquia#December 6: Paul Hand (MIT) | Simplifications of the lifting approach for quadratic signal recovery problems]]<br />
|Thiffeault<br />
|-<br />
|'''Fri, Dec. 6 and Sat Dec. 7'''<br />
|<br />
|[http://www.math.umn.edu/~stant001/askey80 Conference in honor of Dick Askey]<br />
|<br />
|-<br />
|'''Mon, Dec. 9, 4pm, VV B239'''<br />
|[http://www.cims.nyu.edu/~jacob/ Jacob Bedrossian] (Courant Institute)<br />
|Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations<br />
|Bolotin<br />
|-<br />
|'''Wed, Dec 11, 4PM'''<br />
|[http://math.jhu.edu/~lwang/ Lu Wang] (Johns Hopkins)<br />
|Rigidity of Self-shrinkers of Mean Curvature Flow<br />
|Viaclovsky <br />
|-<br />
|'''Fri, Dec. 13, 2:25pm, VV 901'''<br />
|[http://chanwookim.wordpress.com/ Chanwoo Kim] (Cambridge)<br />
|Regularity of the Boltzmann equation in convex domains<br />
|Bolotin<br />
|-<br />
|'''Tues, Dec 17, 4PM'''<br />
|[http://www.statslab.cam.ac.uk/~ps422/ Perla Sousi] (Cambridge)<br />
|[[Colloquia#December 17: Perla Sousi (Cambridge) | The effect of drift on the volume of the Wiener sausage]]<br />
|Seppalainen <br />
|-<br />
|'''Wed, Dec 18, 4PM'''<br />
|[http://users.math.yale.edu/~dc597/ Dustin Cartwright] (Yale)<br />
|[[Colloquia#December 18: Dustin Cartwright (Yale) | Tropical Complexes]]<br />
|Gurevich<br />
|}<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Mon, Jan 6, 4PM'''<br />
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC) <br />
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]<br />
|Caldararu<br />
|-<br />
|'''Wed, Jan 8, 4PM'''<br />
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland) <br />
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]<br />
|Kent<br />
|-<br />
|Jan 10, 4PM<br />
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale) <br />
|Convergence of Fourier series and multilinear analysis<br />
|Denissov<br />
|-<br />
|Jan 17<br />
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth) <br />
|<br />
|Thiffeault<br />
|-<br />
|'''Thu, Jan 23, 2:25, VV901'''<br />
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)<br />
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]<br />
|Seppalainen<br />
|-<br />
|Jan 24<br />
|[http://www.yanivplan.com/ Yaniv Plan] (Stanford)<br />
|<br />
|Thiffeault<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 28<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|<br />
|Spagnolie<br />
|-<br />
|March 7<br />
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)<br />
|<br />
|Seeger<br />
|-<br />
|March 14<br />
|<br />
|<br />
|<br />
|- <br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The Two Weight Inequality for the Hilbert Transform<br />
|Street<br />
|-<br />
|April 4<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|<br />
|Mari-Beffa<br />
|-<br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|'''Monday, April 28''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|A mystery concerning algebraic plane curves<br />
|Maxim<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new<br />
|Maxim<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Easy solution of polynomial equations over finite fields<br />
|Maxim<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sep 6: Matt Baker (GA Tech) ===<br />
''Riemann-Roch for Graphs and Applications''<br />
<br />
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).<br />
<br />
===Sep 13: Uri Andrews (UW-Madison) ===<br />
''A hop, skip, and a jump through the degrees of relative provability''<br />
<br />
The topic of this talk arises from two directions. On the one hand, Gödel's incompleteness theorem tell us that given any sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic, there is a statement that is true but not provable in T. On the other hand, over the past seventy years, a number of researchers studying witnessing functions for various combinatorial statements have realized the importance of fast-growing functions and the fact that their totality is often not provable over a given sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic (e.g. the Paris-Harrington and the Kirby-Paris theorems).<br />
<br />
I will talk about the structure induced by giving the order (for a fixed T) of relative provability for totality of algorithms. That is, for algorithms describing functions f and g, we say f ≤ g if T along with the totality of g suffices to prove the totality of f. It turns out that this structure is rich, and encodes many facets of the nature of provability over sufficiently strong, consistent, effectively axiomatizable theories for first-order arithmetic. (Work joint with Mingzhong Cai, David Diamondstone, Steffen Lempp, and Joseph S. Miller.)<br />
<br />
===Sep 20: Valerio Toledano Laredo (Northeastern)===<br />
''Flat connections and quantum groups''<br />
<br />
Quantum groups are natural deformations of the Lie algebra of<br />
nxn matrices, and more generally of semisimple Lie algebras.<br />
They first arose in the mid eighties in the study of solvable<br />
models in statistical mechanics.<br />
<br />
I will explain how these algebraic objects can serve as natural<br />
receptacles for the (transcendental) monodromy of flat connections<br />
arising from representation theory.<br />
<br />
These connections exist in rational, trigonometric and elliptic<br />
forms, and lead to quantum groups of increasing interest and<br />
complexity.<br />
<br />
===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===<br />
''Taylor Series in Homotopy Theory''<br />
<br />
I will discuss Goodwillie's calculus of functors on topological spaces. To mimic the set-up in real analysis, topological spaces are considered small if their nontrivial homotopy groups start only in higher dimensions. They can be considered close only in relation to a map between them, but a map allows us to construct the difference between two spaces, and two spaces are close if the difference between them is small. Spaces can be summed (in different ways) by taking twisted products of them. It is straightforward to construct the analogs of constant, linear, and higher degree homogenous functors, and they can be assembled into "polynomials" and "infinite sums". There are notions of differentiability and higher derivatives, of Taylor towers, and of analytic functions.<br />
<br />
What might look like a game of analogies is an extremely useful tool because when one looks at functors that map topological spaces not into the category of topological spaces, but into the category of spectra (the stabilized version of the category of spaces, which will be explained), many of them are, in fact, analytic, so they can be constructed from the homogenous functors of different degrees. And we can use appropriate analogs of calculus theorems to understand them better. I will conclude with some recent work of Randy McCarthy and myself, applying Goodwillie's calculus to algebraic K-theory calculations.<br />
<br />
===Sep 25: Jim Demmel (Berkeley) ===<br />
''Communication Avoiding Algorithms for Linear Algebra and Beyond''<br />
<br />
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. <br />
<br />
===Sep 26: Jim Demmel (Berkeley) ===<br />
''Implementing Communication Avoiding Algorithms''<br />
<br />
Designing algorithms that avoiding communication, attaining<br />
lower bounds if possible, is critical for algorithms to minimize runtime and<br />
energy on current and future architectures. These new algorithms can have <br />
new numerical stability properties, new ways to encode answers, and new data<br />
structures, not just depend on loop transformations (we need those too!).<br />
We will illustrate with a variety of examples including direct linear algebra<br />
(eg new ways to perform pivoting, new deterministic and randomized<br />
eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize<br />
Krylov subspace methods) and direct n-body algorithms, on architectures<br />
ranging from multicore to distributed memory to heterogeneous.<br />
The theory describing communication avoiding algorithms can give us a large<br />
design space of possible implementations, so we use autotuning to find<br />
the fastest one automatically. Finally, on parallel architectures one can<br />
frequently not expect to get bitwise identical results from multiple runs,<br />
because of dynamic scheduling and floating point nonassociativity; <br />
this can be a problem for reasons from debugging to correctness.<br />
We discuss some techniques to get reproducible results at modest cost.<br />
<br />
===Sep 27: Jim Demmel (Berkeley) ===<br />
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''<br />
<br />
Our goal is to minimize communication, i.e. moving data, since it increasingly<br />
dominates the cost of arithmetic in algorithms. Motivated by this, attainable<br />
communication lower bounds have been established by many authors for a <br />
variety of algorithms including matrix computations.<br />
<br />
The lower bound approach used initially by Irony, Tiskin and Toledo <br />
for O(n^3) matrix multiplication, and later by Ballard et al <br />
for many other linear algebra algorithms, depends on a geometric result by <br />
Loomis and Whitney: this result bounds the volume of a 3D set <br />
(representing multiply-adds done in the inner loop of the algorithm) <br />
using the product of the areas of certain 2D projections of this set <br />
(representing the matrix entries available locally, i.e., without communication).<br />
<br />
Using a recent generalization of Loomis' and Whitney's result, we generalize <br />
this lower bound approach to a much larger class of algorithms, <br />
that may have arbitrary numbers of loops and arrays with arbitrary dimensions, <br />
as long as the index expressions are affine combinations of loop variables.<br />
In other words, the algorithm can do arbitrary operations on any number of <br />
variables like A(i1,i2,i2-2*i1,3-4*i3+7*i_4,…).<br />
Moreover, the result applies to recursive programs, irregular iteration spaces, <br />
sparse matrices, and other data structures as long as the computation can be<br />
logically mapped to loops and indexed data structure accesses. <br />
<br />
We also discuss when optimal algorithms exist that attain the lower bounds; <br />
this leads to new asymptotically faster algorithms for several problems.<br />
<br />
===October 4: Frank Sottile (Texas A&M) ===<br />
''Galois groups of Schubert problems''<br />
<br />
Work of Jordan from 1870 showed how Galois theory<br />
can be applied to enumerative geometry. Hermite earlier<br />
showed the equivalence of Galois groups with geometric <br />
monodromy groups, and in 1979 Harris used this to study <br />
Galois groups of many enumerative problems. Vakil gave <br />
a geometric-combinatorial criterion that implies a Galois <br />
group contains the alternating group. With Brooks and <br />
Martin del Campo, we used Vakil's criterion to show that <br />
all Schubert problems involving lines have at least <br />
alternating Galois group. White and I have given a new <br />
proof of this based on 2-transitivity.<br />
<br />
My talk will describe this background and sketch a <br />
current project to systematically determine Galois groups <br />
of all Schubert problems of moderate size on all small <br />
classical flag manifolds, investigating at least several <br />
million problems. This will use supercomputers employing <br />
several overlapping methods, including combinatorial <br />
criteria, symbolic computation, and numerical homotopy <br />
continuation, and require the development of new <br />
algorithms and software.<br />
<br />
===October 11: Amie Wilkinson (Chicago) ===<br />
<br />
''Robust mechanisms for chaos''<br />
<br />
What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?<br />
<br />
In addressing this question, I'll focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I'll describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.<br />
<br />
===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===<br />
<br />
''Integrable probability I and II''<br />
<br />
The goal of the talks is to describe the emerging field of integrable<br />
probability, whose goal is to identify and analyze exactly solvable<br />
probabilistic models. The models and results are often easy to describe,<br />
yet difficult to find, and they carry essential information about broad<br />
universality classes of stochastic processes.<br />
<br />
<br />
===October 25: Paul Garrett (Minnesota)=== <br />
<br />
''Boundary-value problems, generalized functions, and zeros of zeta functions''<br />
<br />
Modern analysis (Beppo Levi, Sobolev, Friedrichs, Schwartz) illuminates work of D. Hejhal and Y. Colin de Verdiere from 30 years<br />
ago, clarifying, as in P. Cartier's letter to A. Weil, "how the Riemann Hypothesis was not proven". (Joint with E. Bombieri.)<br />
<br />
===November 1: Allison Lewko (Columbia University) ===<br />
<br />
''On sets of large doubling, Lambda(4) sets, and error-correcting codes''<br />
<br />
We investigate the structure of finite sets A of integers such that A+A is large, presenting a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. We will begin with a brief history of the problem and its connection to the study of Lambda(4) sets in harmonic analysis, and then we will discuss our counterexample and its construction from error-correcting codes. We will conclude by describing some related open problems.<br />
This is joint work with Mark Lewko.<br />
<br />
===November 8: Tim Riley (Cornell)===<br />
<br />
''Hydra groups''<br />
<br />
A few years ago Will Dison and I constructed a family of<br />
finitely generated groups whose workings include a string-rewriting<br />
phenomenon of extraordinary duration which is reminiscent of Hercules'<br />
battle with the hydra. I will describe this and the investigations it<br />
spurred in hyperbolic geometry, combinatorial group theory, and a<br />
problem of how to calculate efficiently with hugely compressed<br />
representations of integers.<br />
<br />
===November 22: Tianling Jin (University of Chicago)===<br />
<br />
''Solutions of some Monge-Ampere equations with degeneracy or singularities''<br />
<br />
We will first give a new proof of a celebrated theorem of<br />
Jorgens which states that every classical convex solution of det(Hess<br />
u)=1 in R^2 has to be a second order polynomial. Our arguments do not use<br />
complex analysis, and will be applied to establish such Liouville type<br />
theorems for solutions some degenerate Monge-Ampere equations. We will<br />
also discuss some results on existence, regularity, classification, and<br />
asymptotic behavior of solutions of some Monge-Ampere equations with<br />
isolated and line singularities. This is joint work with J. Xiong.<br />
<br />
===Monday, Nov 25: Lin Lin (Lawrence Berkeley National Lab)===<br />
<br />
''Fast algorithms for electronic structure analysis''<br />
<br />
Kohn-Sham density functional theory (KSDFT) is the most widely used<br />
electronic structure theory for molecules and condensed matter systems. For<br />
a system with N electrons, the standard method for solving KSDFT requires<br />
solving N eigenvectors for an O(N) * O(N) Kohn-Sham Hamiltonian matrix.<br />
The computational cost for such procedure is expensive and scales as<br />
O(N^3). We have developed pole expansion plus selected inversion (PEXSI)<br />
method, in which KSDFT is solved by evaluating the selected elements of the<br />
inverse of a series of sparse symmetric matrices, and the overall algorithm<br />
scales at most O(N^2) for all materials including insulators,<br />
semiconductors and metals. The PEXSI method can be used with orthogonal or<br />
nonorthogonal basis set, and the physical quantities including electron<br />
density, energy, atomic force, density of states, and local density of<br />
states are calculated accurately without using the eigenvalues and<br />
eigenvectors. The recently developed massively parallel PEXSI method has<br />
been implemented in SIESTA, one of the most popular electronic structure<br />
software using atomic orbital basis set. The resulting method can allow<br />
accurate treatment of electronic structure in a unprecedented scale. We<br />
demonstrate the application of the method for solving graphene-like<br />
structures with more than 20,000 atoms, and the method can be efficiently<br />
parallelized 10,000 - 100,000 processors on Department of Energy (DOE) high<br />
performance machines.<br />
<br />
===November 26 (Tuesday): Clinton Conley (Cornell)===<br />
<br />
''Descriptive set-theoretic graph theory''<br />
<br />
Familiar graph-theoretic problems (for example, vertex coloring) exhibit a<br />
stark change of character when measurability constraints are placed on the<br />
structures and functions involved. While discussing some ramifications in<br />
descriptive set theory, we also pay special attention to interactions with<br />
probability (concerning random colorings of Cayley graphs) and ergodic<br />
theory (characterizing various dynamical properties of groups). The talk<br />
will include joint work with Alexander Kechris, Andrew Marks, Benjamin<br />
Miller, and Robin Tucker-Drob.<br />
<br />
<br />
===December 2 (Monday): Simon Marshall (Northwestern)===<br />
<br />
''Semiclassical estimates for eigenfunctions on locally symmetric spaces''<br />
<br />
Let M be a compact Riemannian manifold, and f an L^2-normalised Laplace<br />
eigenfunction on M. If p > 2, a theorem of Sogge tells us how large the L^p<br />
norm of f can be in terms of its Laplace eigenvalue. For instance, when p<br />
is infinity this is asking how large the peaks of f can be. I will present<br />
an analogue of Sogge's theorem for eigenfunctions of the full ring of<br />
invariant differential operators on a locally symmetric space, and discuss<br />
some links between this result and number theory.<br />
<br />
===December 4 (Wednesday): Steven Sam (Berkeley)===<br />
<br />
''Free Resolutions and Symmetry''<br />
<br />
This talk is about the use of symmetry in the study of modules and free resolutions in commutative algebra and algebraic geometry, and specifically how it clarifies, organizes, and rigidifies calculations, and how it enables us to find finiteness in situations where it a priori does not seem to exist. I will begin the talk with an example coming from classical invariant theory and determinantal ideals using just some basic notions from linear algebra. Then I will explain some of my own work which builds on this setting in several directions. Finally, I'll discuss a recent program on twisted commutative algebras, developed jointly with Andrew Snowden, which formalizes the synthesis of representation theory and commutative algebra and leads to new finiteness results in seemingly infinite settings.<br />
<br />
===December 6: Paul Hand (MIT)===<br />
<br />
''Simplifications of the Lifting Approach for Quadratic Signal Recovery Problems''<br />
<br />
Many signal recovery problems are quadratic in nature, such as phase<br />
retrieval and sparse principal component analysis. Such problems in<br />
R^n can be convexified by introducing n^2 variables corresponding to<br />
each quadratic combination of unknowns. This approach often gives<br />
rise to an n x n matrix recovery problem that is convex and has<br />
provable recovery guarantees. Because the dimensionality has been<br />
squared, it is an important task to find simplifications that make<br />
computation more tractable. We will discuss two examples where the<br />
lifting approach can be simplified while retaining recovery<br />
guarantees. These examples will be the phase retrieval problem and a<br />
special case of sparse principal component analysis.<br />
<br />
===December 9 (Monday): Jacob Bedrossian (Courant Institute)===<br />
<br />
''Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations''<br />
<br />
We prove asymptotic stability of shear flows close to the<br />
planar, periodic Couette flow in the 2D incompressible Euler equations.<br />
That is, given an initial perturbation of the Couette flow small in a<br />
suitable regularity class, specifically Gevrey space of class smaller than<br />
2, the velocity converges strongly in L2 to a shear flow which is also<br />
close to the Couette flow. The vorticity is asymptotically mixed to small<br />
scales by an almost linear evolution and in general enstrophy is lost in<br />
the weak limit. The strong convergence of the velocity field is sometimes<br />
referred to as inviscid damping, due to the relationship with Landau<br />
damping in the Vlasov equations. Joint work with Nader Masmoudi.<br />
<br />
===Wednesday, Dec 11: Lu Wang (Johns Hopkins)===<br />
<br />
''Rigidity of Self-shrinkers of Mean Curvature Flow''<br />
<br />
The study of mean curvature flow not only is fundamental in geometry, topology and analysis, but also has important applications in applied mathematics, for instance, image processing. One of the most important problems in mean curvature flow is to understand the possible singularities of the flow and self-shrinkers, i.e., self-shrinking solutions of the flow, provide the singularity models.<br />
<br />
In this talk, I will describe the rigidity of asymptotic structures of self-shrinkers. First, I show the uniqueness of properly embedded self-shrinkers asymptotic to any given regular cone. Next, I give a partial affirmative answer to a conjecture of Ilmanen under an infinite order asymptotic assumption, which asserts that the only two-dimensional properly embedded self-shrinker asymptotic to a cylinder along some end is itself the cylinder. The feature of our results is that no completeness of self-shrinkers is required.<br />
<br />
The key ingredients in the proof are a novel reduction of unique continuation for elliptic operators to backwards uniqueness for parabolic operators and the Carleman type techniques. If time permits, I will discuss some applications of our approach to shrinking solitons of Ricci flow.<br />
<br />
===Friday, Dec 13: Chanwoo Kim (Cambridge)===<br />
<br />
''Regularity of the Boltzmann equation in convex domains''<br />
<br />
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical <math>C^{1}</math> solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct <math>W^{1,p}</math> solutions for 1< p<2 and weighted <math>W^{1,p}</math> solutions for <math>2\leq p\leq \infty</math> as well. On the other hand, we show second derivatives do not exist up to the boundary in general by constructing counterexamples for all boundary conditions. This is a joint work with Guo, Tonon, Trescases.<br />
<br />
===December 17: Perla Sousi (Cambridge)===<br />
<br />
''The effect of drift on the volume of the Wiener sausage''<br />
<br />
The Wiener sausage at time t is the algebraic sum of a Brownian path on [0,t] and a ball. Does the expected volume of the Wiener sausage increase when we add drift?<br />
How do you compare the expected volume of the usual Wiener sausage to one defined as the algebraic sum of the Brownian path and a square (in 2D) or a cube (in higher dimensions)? We will answer these questions using their relation to the detection problem for Poisson Brownian motions, and rearrangement inequalities on the sphere (with Y. Peres). We will also discuss generalisations of this to Levy processes (with A. Drewitz and R. Sun) as well as an adversarial detection problem and its connections to Kakeya sets (with Babichenko, Peres, Peretz and Winkler).<br />
<br />
<br />
===December 18: Dustin Cartwright (Yale)===<br />
<br />
''Tropical Complexes''<br />
<br />
Tropical geometry is a way of understanding algebraic varieties by the limiting behavior of their degenerations. Through tropicalization, algebraic operations are replaced with combinatorial constructions and piecewise linear functions. I will introduce tropical complexes, which a way of understanding the geometry of algebraic varieties through combinatorics. Tropical complexes are Delta-complexes together with additional integral data, for which one has parallels and concrete comparisons with the behavior of algebraic varieties. <br />
<br />
===January 6: Aaron Lauda (USC)===<br />
<br />
''An introduction to diagrammatic categorification''<br />
<br />
Categorification seeks to reveal a hidden layer in mathematical<br />
structures. Often the resulting structures can be combinatorially<br />
complex objects making them difficult to study. One method of<br />
overcoming this difficulty, that has proven very successful, is to<br />
encode the categorification into a diagrammatic calculus that makes<br />
computations simple and intuitive.<br />
<br />
In this talk I will review some of the original considerations that<br />
led to the categorification philosophy. We will examine how the<br />
diagrammatic perspective has helped to produce new categorifications<br />
having profound applications to algebra, representation theory, and<br />
low-dimensional topology.<br />
<br />
===January 8: Karin Melnick (Maryland)===<br />
<br />
''Normal forms for local flows on parabolic geometries''<br />
<br />
The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.<br />
<br />
===January 10, 4PM: Yen Do (Yale)===<br />
<br />
''Convergence of Fourier series and multilinear analysis''<br />
<br />
Almost everywhere convergence of the Fourier series of square <br />
integrable functions was first proved by Lennart Carleson in 1966, and <br />
the proof has lead to deep developments in various multilinear settings. <br />
In this talk I would like to introduce a brief history of the subject <br />
and sketch some recent developments, some of these involve my joint <br />
works with collaborators.<br />
<br />
===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===<br />
''Intertwinings, wave equations and growth models''<br />
<br />
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal. <br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The Two Weight Inequality for the Hilbert Transform''<br />
<br />
The individual two weight inequality for the Hilbert transform <br />
asks for a real variable characterization of those pairs of weights <br />
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). <br />
This question arises naturally in different settings, most famously <br />
in work of Sarason. Answering in the positive a deep <br />
conjecture of Nazarov-Treil-Volberg, the mapping property <br />
of the Hilbert transform is characterized by a triple of conditions, <br />
the first being a two-weight Poisson A2 on the pair of weights, <br />
with a pair of so-called testing inequalities, uniform over all <br />
intervals. This is the first result of this type for a singular <br />
integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)<br />
<br />
== Past talks ==<br />
<br />
Last year's schedule: [[Colloquia 2012-2013]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=6274Geometry and Topology Seminar 2019-20202013-11-16T03:33:48Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
The celebrated Poincare-Hopf theorem states that a vector ﬁeld <math>X</math> on a manifold<br />
<math>M</math> has nonempty zero set <math>Z(X)</math>, provided <math>M</math> is compact with empty boundary and<br />
<math>M</math> has nonzero Euler characteristic. Surprising little is known about the set of<br />
common zeros of two or more vector ﬁelds, especially when <math>M</math> is not compact.<br />
One of the few results in this direction is a remarkable theorem of Christian<br />
Bonatti (Bol. Soc. Brasil. Mat. 22 (1992), 215–247), stated below. When <math>Z(X)</math> is<br />
compact, <math>i(X)</math> denotes the intersection number of <math>X</math> with the zero section of the<br />
tangent bundle.<br />
<br />
<math>\cdot </math> Assume <math> dim_{\mathbb{R}(M)} ≤ 4</math>, <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Then<br />
every analytic vector ﬁeld commuting with <math>X</math> has a zero in <math>Z(X)</math>.<br />
In this talk I will discuss the following analog of Bonatti’s theorem. Let <math>\mathfrak{g}</math> be<br />
a Lie algebra of analytic vector ﬁelds on a real or complex 2-manifold <math>M</math>, and set<br />
<math>Z(g) := \cap_{Y \in \mathfrak{g}} Z(Y)</math>.<br />
<br />
• Assume <math>X</math> is analytic, <math>Z(X)</math> is compact and <math>i(X) \neq 0</math>. Let <math>\mathfrak{g}</math> be generated by<br />
analytic vector ﬁelds <math>Y</math> on <math>M</math> such that the vectors <math>[X,Y]p</math> and <math>Xp</math> are linearly<br />
dependent at all <math>p \in M</math>. Then <math>Z(\mathfrak{g}) \cap Z(X) \neq \emptyset </math>.<br />
Related results on Lie group actions, and nonanalytic vector ﬁelds, will also be<br />
treated.<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|<br />
|<br />
|<br />
|-<br />
|February 7<br />
|<br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
|<br />
|<br />
|<br />
|-<br />
|February 28<br />
| <br />
|<br />
|<br />
|-<br />
|March 7<br />
| <br />
|<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
|<br />
|<br />
|<br />
|-<br />
|April 18<br />
| <br />
|<br />
|<br />
|-<br />
|April 25<br />
| <br />
|<br />
|<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=6264Geometry and Topology Seminar 2019-20202013-11-12T19:35:26Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''On generalizing a theorem of A. Borel'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''On generalizing a theorem of A. Borel''<br />
<br />
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.<br />
<br />
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>.<br />
<br />
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.<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|<br />
|<br />
|<br />
|-<br />
|February 7<br />
|<br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
|<br />
|<br />
|<br />
|-<br />
|February 28<br />
| <br />
|<br />
|<br />
|-<br />
|March 7<br />
| <br />
|<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
|<br />
|<br />
|<br />
|-<br />
|April 18<br />
| <br />
|<br />
|<br />
|-<br />
|April 25<br />
| <br />
|<br />
|<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=6155Geometry and Topology Seminar 2019-20202013-10-27T01:51:57Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs I'']]<br />
| local<br />
|-<br />
|December 13<br />
| Sean Paul (Wisconsin)<br />
| [[#Sean Paul (Wisconsin)| ''(Semi)stable Pairs II'']]<br />
| local<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''TBA''<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs I''<br />
<br />
===Sean Paul (Wisconsin)===<br />
''(Semi)stable Pairs II''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|<br />
|<br />
|<br />
|-<br />
|February 7<br />
|<br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
|<br />
|<br />
|<br />
|-<br />
|February 28<br />
| <br />
|<br />
|<br />
|-<br />
|March 7<br />
| <br />
|<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
|<br />
|<br />
|<br />
|-<br />
|April 18<br />
| <br />
|<br />
|<br />
|-<br />
|April 25<br />
| <br />
|<br />
|<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=6062Geometry and Topology Seminar 2019-20202013-10-09T17:24:26Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| [http://www.math.wisc.edu/~robbin/ Joel Robbin (Wisconsin)]<br />
| [[#Joel Robbin (Wisconsin) | ''GIT and <math>\mu</math>-GIT'']]<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| Morris Hirsch (Wisconsin)<br />
| [[#Morris Hirsch (Wisconsin)| ''Common zeros for Lie algebras of vector fields on real and complex <br />
2-manifolds.'']]<br />
| local<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| <br />
|<br />
|<br />
|-<br />
|December 13<br />
| <br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
GIT and <math>\mu</math>-GIT<br />
<br />
Many problems in differential geometry can be reduced to solving a PDE of form<br />
<br><br><br />
<math><br />
\mu(x)=0<br />
</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. <br />
In Hamiltonian dynamics the moment map was introduced to use a group action to reduce the number of degrees of freedom in the ODE. <br />
It was soon discovered that the moment map could be applied to Geometric Invariant Theory: <br />
if a compact Lie group <math>G</math> acts on a projective algebraic variety <math>X</math>, <br />
then the complexification <math>G^c</math> also acts and there is an isomorphism of orbifolds <br />
<br><br><br />
<math><br />
X^s/G^c=X//G:=\mu^{-1}(0)/G<br />
</math><br />
<br><br><br />
between the space of orbits of Mumford's stable points and the Marsden-Weinstein quotient. <br />
<br />
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. <br />
The theory works for compact Kaehler manifolds, not just projective varieties. <br />
I will describe our paper in this talk; the following Monday Dietmar will give more details in the Geometric Analysis Seminar.<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''TBA''<br />
<br />
===Morris Hirsch (Wisconsin)===<br />
''Common zeros for Lie algebras of vector fields on real and complex 2-manifolds.''<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|<br />
|<br />
|<br />
|-<br />
|February 7<br />
|<br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
|<br />
|<br />
|<br />
|-<br />
|February 28<br />
| <br />
|<br />
|<br />
|-<br />
|March 7<br />
| <br />
|<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
|<br />
|<br />
|<br />
|-<br />
|April 18<br />
| <br />
|<br />
|<br />
|-<br />
|April 25<br />
| <br />
|<br />
|<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=5909Geometry and Topology Seminar 2019-20202013-09-18T19:54:31Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| Joel Robbin (Wisconsin)<br />
| ''TBA''<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''Uniformly quasi-regular mappings on sub-Riemannian manifolds'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| Khalid Bou-Rabee (Minnesota)<br />
| [[#Khalid Bou-Rabee (Minnesota)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 22<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| <br />
|<br />
|<br />
|-<br />
|December 13<br />
| <br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
''TBA''<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''Uniformly quasi-regular mappings on sub-Riemannian manifolds''<br />
<br />
Abstract:<br />
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: <br />
1) Every lens space admits a uniformly QR (UQR) mapping f. <br />
2) Every UQR mapping leaves invariant a measurable conformal structure. <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
===Khalid Bou-Rabee (Minnesota)===<br />
''TBA''<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|<br />
|<br />
|<br />
|-<br />
|February 7<br />
|<br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
|<br />
|<br />
|<br />
|-<br />
|February 28<br />
| <br />
|<br />
|<br />
|-<br />
|March 7<br />
| <br />
|<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
|<br />
|<br />
|<br />
|-<br />
|April 18<br />
| <br />
|<br />
|<br />
|-<br />
|April 25<br />
| <br />
|<br />
|<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=5875Geometry and Topology Seminar 2019-20202013-09-14T18:40:22Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| Joel Robbin (Wisconsin)<br />
| ''TBA''<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| <br />
|<br />
|<br />
|-<br />
|November 22<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| <br />
|<br />
|<br />
|-<br />
|December 13<br />
| <br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Joel Robbin (Wisconsin)===<br />
''TBA''<br />
<br />
===Anton Lukyanenko (Illinois)===<br />
''TBA''<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|<br />
|<br />
|<br />
|-<br />
|February 7<br />
|<br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
|<br />
|<br />
|<br />
|-<br />
|February 28<br />
| <br />
|<br />
|<br />
|-<br />
|March 7<br />
| <br />
|<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
|<br />
|-<br />
|March 28<br />
|<br />
|<br />
|<br />
|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
|<br />
|<br />
|<br />
|-<br />
|April 18<br />
| <br />
|<br />
|<br />
|-<br />
|April 25<br />
| <br />
|<br />
|<br />
|-<br />
|May 2<br />
| <br />
|<br />
|<br />
|-<br />
|May 9<br />
| <br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Matthew Kahle (Ohio)===<br />
''TBA''<br />
<br />
<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkenthttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=5874Geometry and Topology Seminar 2019-20202013-09-14T18:33:45Z<p>Rkent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2013==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 6<br />
| <br />
|<br />
|<br />
|-<br />
|September 13, <b>10:00 AM in 901!</b><br />
| [http://www.ma.utexas.edu/users/zupan/ Alex Zupan] (Texas)<br />
| [[#Alex Zupan (Texas)| ''Totally geodesic subgraphs of the pants graph'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|September 20<br />
| <br />
|<br />
|<br />
|-<br />
|September 27<br />
| <br />
|<br />
|<br />
|-<br />
|October 4<br />
| <br />
|<br />
|<br />
|-<br />
|October 11<br />
| <br />
|<br />
|<br />
|-<br />
|October 18<br />
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois)<br />
|[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']]<br />
| [http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|October 25<br />
| Joel Robbin (Wisconsin)<br />
|<br />
| local<br />
|-<br />
|November 1<br />
| [http://lukyanenko.net/ Anton Lukyanenko (Illinois)]<br />
| [[#Anton Lukyanenko (Illinois)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
<br />
|-<br />
|November 8<br />
| Neil Hoffman (Melbourne)<br />
| [[#Neil Hoffman (Melbourne)| ''Verified computations for hyperbolic 3-manifolds'']]<br />
|[http://www.math.wisc.edu/~rkent/ Kent]<br />
|-<br />
|November 15<br />
| <br />
|<br />
|<br />
|-<br />
|November 22<br />
| <br />
|<br />
|<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 6<br />
| <br />
|<br />
|<br />
|-<br />
|December 13<br />
| <br />
|<br />
|<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Zupan (Texas)===<br />
''Totally geodesic subgraphs of the pants graph''<br />
<br />
Abstract:<br />
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.<br />
<br />
===Jayadev Athreya (Illinois)===<br />
''Gap Distributions and Homogeneous Dynamics''<br />
<br />
Abstract: <br />
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.<br />
<br />
===Neil Hoffman (Melbourne)===<br />
''Verified computations for hyperbolic 3-manifolds''<br />
<br />
Abstract:<br />
Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?<br />
<br />
While this question can be answered in the negative if M is known to<br />
be reducible or toroidal, it is often difficult to establish a<br />
certificate of hyperbolicity, and so computer methods have developed<br />
for this purpose. In this talk, I will describe a new method to<br />
establish such a certificate via verified computation and compare the<br />
method to existing techniques.<br />
<br />
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi,<br />
Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 24<br />
| <br />
|<br />
|<br />
|-<br />
|January 31<br />
|<br />
|<br />
|<br />
|-<br />
|February 7<br />
|<br />
|<br />
|<br />
|-<br />
|February 14<br />
| <br />
|<br />
|<br />
|-<br />
|February 21<br />
|<br />
|<br />
|<br />
|-<br />
|February 28<br />
| <br />
|<br />
|<br />
|-<br />
|March 7<br />
| <br />
|<br />
|<br />
|-<br />
|March 14<br />
| <br />
|<br />
|<br />
|-<br />
|Spring Break<br />
|<br />
|<br />
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|-<br />
|March 28<br />
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|-<br />
| April 4<br />
| [http://matthewkahle.org/ Matthew Kahle (Ohio)]<br />
| [[#Matthew Kahle (Ohio)| ''TBA'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Dymarz]<br />
|-<br />
|April 11<br />
|<br />
|<br />
|<br />
|-<br />
|April 18<br />
| <br />
|<br />
|<br />
|-<br />
|April 25<br />
| <br />
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|-<br />
|May 2<br />
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|-<br />
|May 9<br />
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|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Rkent