|Friday Sept 9||Organizational meeting||2pm Room 520|
|September 16||Hung C Tran (UGA)||Geometric embedding properties of Bestvina-Brady subgroups|
|September 22 THURSDAY 2:40pm!||BoGwang Jeon||The Unlikely Intersection Theory and the Cosmetic Surgery Conjecture|
|September 30||No GT seminar|
|October 7||Henry Segerman, Oklahoma State||Connectivity of triangulations without degree one edges under 2-3 and 3-2 moves|
|October 14||Mehdi Yazdi (Princeton)||On Thurston's Euler class one conjecture|
|October 21||David Hume, MSRI and Oxford||The wide world of relative hyperbolicity|
|November 4||No GT Seminar||Symplectic Seminar|
|November 11||Tim Susse, U Nebraska||TBA|
|November 18||Daniel Groves, UIC||TBA|
|November 25||No Seminar||Happy Thanksgiving|
|December 1||Cornelia Drutu, Oxford University||TBA|
|December 2||David Futer, Temple U||TBA|
|December 9||Hongbin Sun, UCB||NonLERFness of arithmetic hyperbolic manifold groups|
|Spring Semester||Ahn Tran, UT Dallas|
Hung C Tran, UGA
Title: Geometric embedding properties of Bestvina-Brady subgroups
We compute the subgroup distortion of Bestvina-Brady subgroups. We use the result of this computation to show that for each integer $n\geq 3$, there is a free subgroup of rank $n$ of some right-angled Artin group whose inclusion is not a quasi-isometric embedding. This corollary answers the question of Carr about the minimum rank $n$ such that some right-angled Artin group has a free subgroup of rank $n$ whose inclusion is not a quasi-isometric embedding. It is also well-known that a right-angled Artin group $A_\Gamma$ is the fundamental group of a graph manifold whenever the defining graph $\Gamma$ is a tree. We show that the Bestvina-Brady subgroup $H_\Gamma$ in this case is a horizontal surface subgroup.
BoGwang Jeon, Columbia
THURSDAY September 22, 2:40pm
Title: The Unlikely Intersection Theory and the Cosmetic Surgery Conjecture
The main result of this talk is the following theorem: Let M be a 1-cusped hyperbolic 3-manifold whose cusp shape is not quadratic, and M(p/q) be its p/q-Dehn filled manifold. If p/q is not equal to p'/q' for sufficiently large |p|+|q| and |p'|+|q'|, there is no orientation preserving isometry between M(p/q) and M(p'/q'). This resolves the conjecture of C. Gordon, which is so called the Cosmetic Surgery Conjecture, for hyperbolic 3-manifolds belonging to the aforementioned class except for possibly finitely many exceptions for each manifold. We also consider its generalization to more cusped manifolds. The key ingredient of the proof is the unlikely intersection theory developed by E. Bombieri, D. Masser, and U. Zannier.
Henry Segerman, Oklahoma State U
Title: Connectivity of triangulations without degree one edges under 2-3 and 3-2 moves.
Matveev and Piergallini independently showed that, with a small number of known exceptions, any triangulation of a three-manifold can be transformed into any other triangulation of the same three-manifold with the same number of vertices, via a sequence of 2-3 and 3-2 moves. We can interpret this as showing that the "2-3 Pachner graph" of such triangulations is connected. This is useful for defining invariants of a three-manifold based on the triangulation. However, there are "would-be" invariants that can only be defined on triangulations with certain properties, for example 1-efficiency or having only essential edges. Unfortunately, there are no similar connectivity results for the subgraphs of the Pachner graph with such properties. In this talk, I will describe a new connectivity result for a weaker property than either 1-efficiency or essential edges: that of a triangulation having no degree one edges.
Mehdi Yazdi, Princeton
Title: On Thurston's Euler class one conjecture
In 1976, Thurston proved that taut foliations on closed hyperbolic 3–manifolds have Euler class of norm at most one, and conjectured that, conversely, any Euler class with norm equal to one is Euler class of a taut foliation. I construct counterexamples to this conjecture and suggest an alternative conjecture.
David Hume, MSRI and Oxford
Title: The wide world of relative hyperbolicity
I will describe part of a joint project with Matthew Cordes in which, for a given finitely generated group $H$ satisfying some very mild assumptions, we build infinitely many quasi-isometry types of 1-ended groups $G_i$ which are hyperbolic relative to $H$. With care, one can even ensure that all the $G_i$ satisfy Kazhdan's property T. The invariant we use is a refinement of the stable dimension which we introduced in a previous paper.
Tim Susse, University of Nebraska
Title: To be announced
Daniel Groves, University of Illinois at Chicago
Title: To be announced
David Futer, Temple University
Title: To be announced
Hongbin Sun, UCB
Title: NonLERFness of arithmetic hyperbolic manifold groups
Abstract: We will show that, for "almost" all arithmetic hyperbolic manifolds with dimension >3, their fundamental groups are not LERF. The main ingredient in the proof is a study of certain graph of groups with hyperbolic 3-manifold groups being the vertex groups. We will also show that a compact irreducible 3-manifold with empty or tori boundary does not support a geometric structure if and only if its fundamental group is not LERF.
Other relevant information.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.
- Columbia Symplectic Geometry/Gauge Theory Seminar
- All Columbia Math Dept Seminars
- CUNY Geometry and Topology Seminar
- CUNY Complex Analysis & Dynamics Seminar
- CUNY Magnus Seminar
- Princeton Topology Seminar.