The GT seminar meets on Fridays
in Math 520, at 2 PM.
Organizer:
Abhijit Champanerkar.
Other
area seminars. Our e-mail
list. Archive of previous semesters
Date | Speaker | Title |
---|---|---|
January 22 | Organizational meeting | 2pm Room 520 |
January 29 | Alan Reid (UT Austin & IAS) | Profinite rigidity for 1-punctured torus bundles |
February 5 | Andre de Carvalho (Brazil & IAS) | Organizing horseshoe braids |
February 12 | Richard Kent (UWisconsin & IAS) | Spacious knots |
February 19 | Joan Birman (Barnard) | Efficient geodesics and an effective algorithm for distance in the complex of curves |
February 26 | John Etnyre (GeorgiaTech & IAS) | Solid tori and the classification of contact structures on small Seifert fibered spaces |
March 4 | Jeff Danciger (UT Austin) | Proper affine actions of right angled Coxeter groups |
March 11 | No Seminar | |
March 18 | No Seminar | Spring break |
March 25 | Nancy Wrinkle (Northeastern Illinois University) | The ribbonlength of knot diagrams |
April 1st | Sarah Koch (Michigan) | Deforming rational maps |
April 6th, 2:30 pm Room 528 Note different date, time and room |
Saddat Oyku Yurttas (Turkey) | Counting curves of an integral lamination |
April 15th | Josh Greene (Boston College) | Alternating links and definite surfaces |
April 22nd | Khalid Bou-Rabee (City College, CUNY) | Intersection growths of groups |
April 29th | Keiko Kawamuro (U of Iowa) | Quasi-right-veering braids and quasi-positive braids |
May 6th, 2:30 pm Math 507 Note different time and room |
Greg Kuperberg (UC Davis) | Knots and 3-manifolds from the viewpoint of NP and BQP |
Abstracts
Alan Reid, UT Austin & IAS
Jan 29th, 2016
Title: Profinite rigidity for 1-punctured torus bundles
Abstract: This talk will discuss the question: To what extent are the
fundamental groups of finite volume hyperbolic 3-manifolds determined by
their finite quotients amongst the fundamental groups of compact
3-manifolds. We will show that this is the case for hyperbolic 1-punctured
torus bundles.
Andre de Carvalho, Brazil & IAS
Feb 5th, 2016
Title: Organizing horseshoe braids
Abstract: We will discuss the braids associated to periodic
orbits of Smale's horseshoe map. Roughly speaking, we say a braid
forces another if every homeomorphism of the disk which has a
periodic orbit with the first braid type must also have one with
the second. We will describe a conjecture about how forcing
organizes horseshoe braids. Part of this conjecture concerns the
conjugacy problem among horseshoe braids, of which we'll see a
recent proof (joint with Toby Hall; as is everything else in the
talk). The proof sheds light on the structure of horseshoe braids
and knots. Central to it are infinite braids associated to
certain horseshoe homoclinic orbits. If time permits, we'll also
discuss the complementary (hyperbolic) 3-manifolds and geometric
limits of some sequences, all of which is related to the above
proof.
Richard Kent, UWisconsin & IAS
Feb 12th, 2016
Title: Spacious knots
Abstract: Brock and Dunfield showed that there are integral homology
spheres whose thick parts are very thick and take up most of the
volume. Precisely, they show that, given R big and r small, there is
an integral homology 3-sphere whose R-thick part has volume (1-r)
volume(M). Purcell and I find knots in the 3-sphere with this
property, answering a question of Brock and Dunfield.
Joan Birman , Barnard
Feb 19th, 2016
Title: Efficient geodesics and an effective algorithm for distance in the complex of curves
Abstract: This is a report on joint work with Margalit and
Menasco. We give an algorithm for determining the distance between two
vertices of the complex of curves. While there already exist such
algorithms, for example by Leasure, Shackleton, and Webb, our approach
is new, simple, and more effective for small distances. Our method
gives a new preferred finite set of geodesics between any two vertices
of the complex, called efficient geodesics, which are different from
the tight geodesics introduced by Masur and Minsky.
John Etnyre , GeorgiaTech & IAS
Feb 27th, 2016
Title: Solid tori and the classification of contact structures
on small Seifert fibered spaces
Abstract: Tight contact structures have been classified on most
small Seifert fibered spaces, but there are infinite families that
have resisted classification despite many attempts. These are the most
interesting families in that they contain examples that do not admit
tight contact structures and examples of tight but non-fillable
contact structures. In this talk I will discuss an approach to the
classification on new infinite subsets of these families and
illustrates how studying embeddings of solid tori in contact manifolds
can be used to construct and distinguish tight contact structures.
Jeff Danciger , UT Austin
March 4th, 2016
Title: Proper affine actions of right angled Coxeter groups
Abstract: We prove that any right-angled Coxeter group on k
generators admits a proper action by affine transformations on \mathbb
R^{k(k-1)/2}. As a corollary many interesting groups admit proper
affine actions, including surface groups, hyperbolic three-manifold
groups, and Gromov hyperbolic groups of arbitrarily large virtual
cohomological dimension. Joint work with Francois Gueritaud and Fanny
Kassel.
Nancy Wrinkle , Northeastern Illinois University
March 25th, 2016
Title: The ribbonlength of knot diagrams
Abstract: The ropelength problem asks to minimize the length of
a knotted space curve such that a unit tube around the curve remains
embedded. A two-dimensional analog has a much more combinatorial
flavor: we require a unit-width ribbon around a knot diagram to be
immersed with consistent crossing information. The ribbonlength is the
length of the diagram divided by its width. Attempting to characterize
critical points for ribbonlength leads us to new results about the
medial axis of an immersed disk in the plane, including a certain
topological stability for thin disks. This is joint work with
Elizabeth Denne and John M. Sullivan.
Sarah Koch, Michigan
April 1st, 2016
Title: Deforming rational maps
Abstract: For a rational map on the Riemann sphere, there is an
associated deformation space (originally defined by
A. Epstein). Epstein proved that this deformation space is a complex
submanifold of a certain Teichmueller space. The arguments in his
proof are local; not much is known about the global topology of the
deformation space in general. We present a concrete example of this
construction in which the topology can be relatively understood. These
deformation spaces are related to dynamically defined subvarieties in
the moduli space of rational maps. I will mention some fundamental
open questions in complex dynamics concerning the topology of these
objects. This is joint work with E. Hironaka.
Saddat Oyku Yurttas, Dicle University, Turkey,
April 6th, 2016, 2:30 - 3:30 pm, Room 528
Note different date, time and room
Title: Counting curves of an integral lamination
Abstract: An integral lamination on the n-punctured disk is a
non-empty disjoint union of finitely many essential simple closed
curves, up to isotopy. A beautiful method of describing such
laminations is given by the Dynnikov coordinate system. In the case n
= 3, the Dynnikov coordinates of an integral lamination consist of a
pair of integers, and the number of connected components of the
lamination is the greatest common divisor of these integers. No
analogous formula is known when n > 3. In this talk we describe an
efficient algorithm for calculating the number of components of an
integral lamination from its Dynnikov coordinates. This is joint work
with Toby Hall.
Josh Greene , Boston College
April 15th, 2016
Title: Alternating links and definite surfaces
Abstract: I will describe a characterization of alternating
links in terms intrinsic to the link complement and use it to deduce
some properties of these links, including new proofs of some of Tait's
conjectures that previously required the use of the Jones polynomial.
Khalid Bou-Rabee , City College, CUNY
April 22nd, 2016
Title: Intersection growths of groups
Abstract: Intersection growth concerns the asymptotic behavior
of the index of the intersection of all subgroups of a group that have
index at most $n$. We motivate studying this growth and explore some
examples with a focus on nilpotent groups and zeta functions. This
covers joint work with Ian Biringer, Martin Kassabov, and Francesco
Matucci.
Keiko Kawamuro , U of Iowa
April 29th, 2016
Title: Quasi-right-veering braids and quasi-positive braids
Abstract: In the first half of this talk, I define a
quasi-right-veering braid in a general open books then show its
connection to tight contact structure. In the second half of the
talk, I compare sub-monoids of the braid group B_n and sub-monoids of
the mapping class group Mod(S) and answer some questions raised by
Etnyre and Van Horn-Morris. This is joint work with Tetsuya Ito.
Greg Kuperberg , UC Davis
May 6th, 2016, 2:30 pm Math 507
Note different time and room
Title: Knots and 3-manifolds from the viewpoint of NP and BQP
Abstract:
Other relevant information.
Previous semesters:
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.