The GT seminar meets on Fridays
in Math
520, at 2 PM.
Organizer:
Walter Neumann.
Other
area seminars. Our e-mail
list. Archive of previous semesters
Fall 2017
| Date | Speaker | Title |
|---|---|---|
| Sept 8 | Conference for Lee Mosher, Princeton | Groups explored through geometry and dynamics |
| Sept 15 | Organizational meeting | |
| Sept 22 | Kyle Hayden, BC | Complex curves through a contact lens |
| Sept 29 | No seminar | |
| Oct 6 | Ilya Gekhtman, Yale | Counting loxodromics for actions of hyperbolic groups and other automatic groups |
| Oct 13 | Jenny Wilson, Stanford | Stability in the homology of configuration spaces |
| Oct 20 | Sam Taylor, Temple U. | Veering triangulations and fibered faces of 3--manifolds |
| Oct 27-29 | Conference in honor of Benson Farb in Chicago | "No Boundaries: Groups in Algebra, Geometry, and Topology" |
| Nov 3 | Martin Bridson, Oxford | Profinite rigidity and 3-manifolds |
| Nov 10 | Ralf Schiffler, U Conn | Cluster algebras and knot theory |
| Nov 17 | Eriko Hironaka, AMS | Topological vs Geometry Entropy in Flow Equivalence Classes of pseudo-Anosov maps |
| Dec 8 | Effie Kalfagianni, Michigan State U | Quantum representations and monodromies of fibered links |
Abstracts
Kyle Hayden, Boston College
Sept 22
Title: Complex curves through a contact lens
Abstract: Every four-dimensional Stein domain has a height function whose
regular level sets are contact three-manifolds. This allows us to study
complex curves in the Stein domain via their intersection with these contact
level sets, where we can comfortably apply three-dimensional tools. We use
this perspective to characterize the links in Stein-fillable contact
manifolds that bound complex curves in their Stein fillings. (Some of this
is joint work with Baykur, Etnyre, Hedden, Kawamuro, and Van Horn-Morris.)
Ilya Gekhtman, Yale
October 6
Title: Counting loxodromics for actions of hyperbolic groups and other
automatic groups
Abstract: We show that for arbitrary nonelementary actions $G\curvearrowright X$
of hyperbolic groups on Gromov hyperbolic spaces, translation length on average
grows linearly in word length. In particular, the proportion of loxodromic
elements in a large ball in the Cayley graph converges to 1.
This holds even when the action is not in any sense alignment preserving: for
example a dense free subgroup of $SL_2R$ acting on the hyperbolic plane, or a
hyperbolic subgroup of the mapping class group acting on the curve complex.
Along the way we described the behavior in the space $X$ of typical word geodesics
in the group: for example, with respect to the Patterson-Sullivan measure on the
boundary group, the orbit of almost every word geodesic logarithmically tracks a
geodesic in $X$.
We prove analogous counting results for more general groups, including relatively
hyperbolic groups with virtually abelian subgroups and right angled Artin and
Coxeter groups.
Our results hold more generally for automatic groups satisfying certain
properties: groups parametrized by paths in a finite directed graph. Indeed, the
automatic structure is what allows us to reduce the asymptotic geometry of the
Cayley graph of $G$ to a certain Markov chain on a finite graph and a family
of random walks on $G$ associated to vertices of the finite graph.
This is joint work with Sam Taylor and Giulio Tiozzo.
Jenny Wilson, Stanford
October 13
Title:Stability in the homology of configuration spaces
Abstract: This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of
distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of the
configuration spaces F_k(M) to become increasingly complicated. Church and others showed, however, that when M is
connected and open, there is a representation-theoretic sense in which these configuration spaces stabilize. In
this talk I will explain these stability patterns, and how they generalize homological stability results proved by
McDuff (with a stable range due to Segal) in the 1970s. I will describe higher-order stability phenomena established
in recent work joint with Jeremy Miller.
Sam Taylor, Temple U
October 20
Title: Veering triangulations and fibered faces of
3--manifolds
Abstract: Agol's veering triangulation for 3-manifolds that fiber over the
circle can be obtained very explicitly, via a construction of Gueritaud,
from the stable and unstable laminations of the monodromy. We study the way
in which these triangulations interact with the curve complexes of the
surface and its subsurfaces. This allows us to examine the “profile” of
subsurface projections associated to each fiber in a fibered face of the
Thurston norm ball, obtaining some bounds that do not depend on the
complexity of the fibers.
This is joint work with Yair Minsky.
Martin Bridson, Oxford
November 3
Title:Profinite rigidity and 3-manifolds
Abstract: There has recently been renewed vigour in pursuit of the old
question of the extent to which the finite images of a finitely presented
group determine the group, with a particular focus on groups that arise in
connection with low-dimensional topology. In this talk, I'll sketch what is
now known about the extent to which a 3-dimensional manifold is determined
by the finite images of its fundamental group, and I shall present recent
joint work with McReynolds, Reid and Spitler showing that certain hyperbolic
3-orbifold groups are distingusihed from all other finitely generated groups
by their finite quotients.
Ralph Schifler, U Conn
November 10
Title:Cluster algebras and knot theory.
Abstract: A cluster algebra is a commutative algebra with a special
combinatorial structure. Its generators, the cluster variables, are
Laurent polynomials in several variables. In knot theory, one of the
important knot invariants is the Jones polynomial, introduced by
Vaughan Jones in 1984. The Jones polynomial is a Laurent polynomial in
one variable. In this talk, I present a concrete relation between
cluster variables and Jones polynomials. For a certain class of knots,
the so-called 2-bridge knots, the Jones polynomials are
specializations of cluster variables. This is joint work with
Kyungyong Lee.
Eriko Hirnoaka, AMS
Nov 17
TitleTopological vs Geometry Entropy in Flow Equivalence Classes
of pseudo-Anosov maps
Abstract We show that the Alexander and Teichm\"uller norms of a
fibered face are equal when the associated flow equivalence class
contains an oriented fully-punctured element. As an application
we show that for fully-punctured pseudo-Anosov braid monodromies,
the normalized dilatations are dense in the interval [\phi^4, \infty)
where \phi is the golden ratio.
Effie Kalfagianni, Michigan State U
Dec 8
Title Quantum representations and monodromies of fibered links
Abstract Andersen, Masbaum and Ueno conjectured (2005) that
certain quantum representations of surface mapping class groups should send
pseudo-Anosov mapping classes to elements of infinite order (for large
enough level).
In this talk I will discuss work with Renaud Detcherry (MSU) that makes
progress on this conjecture in the case of surfaces with boundary.
Other relevant information.
Previous semesters:
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.