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

## Abstracts

**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**: New Approach to Quantum Teichmuller Theory

**Abstract**: The Jones polynomial invariant of links in R^3 extends to links in thickened surfaces, leading to the notion of the skein algebra of a surface, which can be thought as quantizating
the Teichmuller space. The algebraic structure of skein algebras remain rather mysterious. We will prove some fundamental properties of these objects using the theory of measured foliations
and pseudo-Anosov diffeomorphisms of surfaces.

**Lee Mosher,** Rutgers Newark

April 6

**Title**:Some hyperbolic actions of subgroups of Aut(F_n) (joint with Michael Handel)

**Abstract**: In the course of our theorem on the H^2_b-alternative for Out(F_n) — every finitely generated subgroup of Out(F_n) is either virtually abelian or has second bounded cohomology of uncountable dimension — thinking about natural embeddings of Aut(F_k) into Out(F_n) led us to subgroups of Aut(F_k) which have interesting new hyperbolic actions arising from “suspension” constructions, generalizing a thread of hyperbolic suspension constructions which goes back to a theorem of W. Thurston. In this talk we will describe these suspension constructions, emphasizing how they arise in the context of proving the H^2_b-alternative, and we will speculate on what may unify them.

**Neil Hoffman,** OK state

April 13

**Title**:Unifying unexpected lens space surgeries

**Abstract**: The Berge Conjecture attempts to classify knots in $S^3$ which admit a (non-trivial)
lens space surgery. After providing some background for this problem, we will discuss why the
natural generalization of this conjecture to knots in lens spaces which admit a second lens
space surgery fails. Following this discussion, we will see how to make some sense of these
counter-examples. This is joint work with Ken Baker, Nathan Dunfield, and Joan Licata.

**Olga Plamemevskaya**, Stony Brook

April 20

**Title**: Planar open books and links of surface singularities

**Abstract**: Due to work of Giroux, contact structures on 3-manifolds can be topologically described by their open books decompositions (which in turn can be encoded via fibered
links). A contact structure is called planar if it admits an open book with fibers of genus 0. Symplectic fillings of such contact structures can be understood, by a theorem of
Wendl, via Lefschetz fibrations with the same planar fiber. Using this together with topological considerations, we prove new obstructions to planarity (in terms of intersection
form of a Stein filling or presence of certain symplectic surfaces in a weak symplectic filling) and obtain a few corollaries.
In particular, we show that the canonical contact structure on a link of a normal surface singularity is planar if and only if the singularity is minimal. For hypersurface
singularities, planarity is equivalent to having singularity of type A_n. (Joint work with P. Ghiggini and M. Golla.)

**Pallavi Dani**, LSU

Apr 27

**Title**: Subgroup distortion in hyperbolic groups

**Abstract**: The distortion function of a subgroup measures the extent to which
the intrinsic word metric of the subgroup differs from the metric induced by
the ambient group. Ol'shanskii showed that there are almost no restrictions
on which functions arise as distortion functions of subgroups of finitely
presented groups. This prompts one to ask what happens if one forces the
ambient group to be particularly nice, say, for example, to be hyperbolic. I
will survey which functions are known to be distortion functions of
subgroups of hyperbolic groups. I will then describe joint work with Tim
Riley which adds to this list: we construct free subgroups
of hyperbolic groups with distortion functions $2^{n^{p/q}}$, for all
integers $p > q > 0$.

# 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.## Other area seminars.

- 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.