Columbia Geometric Topology Seminar

Spring/Fall 2018

The GT seminar meets on Fridays at 2:00pm Fridays in room 520 (with room 622 from 11 to 1 as an overflow for additional talks).
Organizer: Walter Neumann.
Other area seminars. Our e-mail list. Archive of previous semesters

Spring 2018

Date Speaker Title
Jan 26 Chen Lei, Chicago From point-picking to sections of surface bundles
Feb 2 Joseph Maher, CSI Random mapping classes have generic foliations
11:15am Room 622
Liming Pang, NYU Some configuration and related covering spaces arising in generalizing intersection theoretic approaches to Jones polynomials
Feb 16 Hoang Nguyen, UWM Distortion of surfaces in 3-manifolds
Feb 23 Abhijit Champanerkar, CSI Geometry of biperiodic alternating links
Mar 2 Jing Tao, OU Geometry of the Thurston Metric on Teichmuller Space
Mar 9. Spencer Dowdall, Vanderbilt Abstract commensurations of big mapping class groups
Mar 16 No seminar Spring Break 12-16 March
Mar 23 Joe Quinn, UANM Shapes of Hilbert-Blumenthal surfaces and some quaternionic generalizations (joint work with Alberto Verjovsky)
Mar 30 Adam Sikora, SUNY Buffalo TBA
Apr 6 Lee Mosher, Rutgers Newark TBA
Apr 13 Neil Hoffman, OK state TBA
Apr 20. Olga Plamemevskaya, Stony Brook TBA
April 27 Pallavi Dani, LSU TBA

Fall 2018

Date Speaker Title
TBA Tullia Dymarz, Wisconsin



Chen Lei, Chicago
Jan 26, 11:15pm
Title:From point-picking to sections of surface bundles
Abstract: Given any n points on a manifold, how can we systematically and continuously find a new point? What if we ask them to be distinct? In this talk, I will try to answer this question in surfaces. Then I will connect this question to sections of surface bundles. The slogan is "there is no center of mass on closed hyperbolic surfaces".

Joseph Maher, CSI
Feb 2
Title: Random mapping classes have generic foliations
Abstract: A pseudo-Anosov element of the mapping class group determines a quadratic differential, which lies in the principal stratum if all zeroes are simple, equivalently, if the corresponding foliations have trivalent singularities. We show that this occurs with asymptotic probability one for random walks on the mapping class group, and furthermore, the hitting measure on the boundary gives weight zero to foliations with saddle connections. This is joint work with Vaibhav Gadre.

Liming Pang, NYU
Feb 9 NOTE TIME: 11:15am Room 622
Title: Some configuration and related covering spaces arising in generalizing intersection theoretic approaches to Jones polynomials
Abstract: In this talk we'll present some results on configuration spaces of points in surfaces with a view towards generalizing Bigelow's intersection theoretic approach to the Jones polynomial by considering an intersection number of two submanifolds in a cover of an associated space. We use an interesting homomorphism sending braids on a punctured torus to a group which is a central extension of Z x Z by Z (very similar to the discrete Heisenberg group). This map can be used to construct two layers of covering spaces analogous to Bigelow's covering spaces.

Hoang Nguyen, UWM
Feb 16
Title:Distortion of surfaces in 3-manifolds
Abstract: In the 3-manifold theory, a great deal of interest has focused on the study of immersed surfaces in 3-manifolds in last decades. One reason is that studying immersed surfaces will help us to understand the structures of 3-manifolds. For instance, cubulation is used in the work of Wise and Agol to resolve the Virtuallly Haken conjecture on the hyperbolic manifolds. Wise observed that the following problem is important in the study of of cubulations of 3-manifold groups: Determine the distortion of surface subgroups in 3-manifold groups. The answer to this problem has been answered by Bonahon-Thurston in the hyperbolic case. In this talk, I will give a solution to this problem in the non-geometric 3-manifold case.

Abhijit Champanerkar, CSI
Feb 23
Title:Geometry of biperiodic alternating links
Abstract: In this talk we will study the hyperbolic geometry of alternating link complements in the thickened torus. We give conditions which imply that such link complements are hyperbolic and admit a positively oriented, unimodular geometric triangulation, and determine upper and lower volume bounds. For links which arise from semi-regular Euclidean tilings, called semi-regular links, we determine the complete hyperbolic structure on their complement. This has a number of nice consequences like determining exact volumes, arithmeticity and commensurability for this class of links. We will also discuss the Volume Density Conjecture and examples.

Jing Tao, OU
March 2
Title: Geometry of the Thurston Metric on Teichmuller Space
Abstract: The Thurston metric is an asymmetric metric on Teichmuller Space defined using Lipschitz constants of maps between hyperbolic surfaces. This metric was introduced by Thurston in the late 80's, who showed this metric is geodesic, though geodesics are not necessarily unique, and induced by an asymmetric Finsler norm on tangent space. In this talk, I will survey some recent advances in this field, particular on the coarse geometry of the geodesics in the Thurston metric, and some finer properties in the case of the punctured torus. This talk is based on joint work with David Dumas, Anna Lenzhen, and Kasra Rafi.

Spencer Dowdall, Vanderbilt
March 9
Title: Abstract commensurations of big mapping class groups
Abstract: It is a classic result of Ivanov that the mapping class group of a finite-type surface is equal to its own automorphism group. Relatedly, it is well-known that non-homeomorphic surfaces cannot have isomorphic mapping class groups. In the setting of ``big mapping class groups'' of infinite-type surfaces, the situation is more complicated due tot he fact that the sheer enormity and variety of behavior prevents group elements from having canonical descriptions in terms of normal forms. This talk will present work with Juliette Bavard and Kasra Rafi overcoming these difficulties and extending the above results to big mapping class groups. In particular, we show that any isomorphism between big mapping class groups is induced by a homeomorphism of the surfaces and that each big mapping class group is equal to its abstract commensurator.

Joe Quinn, UANM,
March 23
Title: Shapes of Hilbert-Blumenthal surfaces and some quaternionic generalizations (joint work with Alberto Verjovsky)
Abstract: I will explain a generalization of the classical Hilbert-Blumenthal surfaces to quaternionic surfaces over products of hyperbolic 4- and 5-space. I will present some new results improving on the geometric accuracy and visualizability of fundamental domains for classical Hilbert-Blumenthal surfaces, and then I'll discuss our progress on an ongoing project generalizing this to the higher dimensional quaternionic cases. i

Adam Sikora, SUNY Buffalo
March 30
Title: TBA
Abstract: TBA

Lee Mosher, Rutgers Newark
April 6
Title: TBA
Abstract: TBA

Neil Hoffman, OK state
April 13
Title: TBA
Abstract: TBA

Olga Plamemevskaya, Stony Brook
April 20
Title: TBA
Abstract: TBA

Pallavi Dani, LSU
Apr 27
Title: TBA
Abstract: TBA

Other relevant information.

Previous semesters:

Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, 2010/11, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006.

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