Jan 31

Mohan Ramachandran (Buffalo):
On holomorphic convexity of reductive coverings of compact Kahler surfaces
Abstract: I will talk about the
following theorem. A reductive covering of a compact Kahler surface is
holomorphically convex if it does not have two ends. This is work in
collaboration with Napier.

Feb 7

Bill Menasco (Buffalo):
Short distances in the curve complex
Abstract: We will give a
preliminary report on recent joint work with Dan Margalit and Joan
Birman. The focus is an algorithm for determining
whether a filling pair of curves in an orientable closed surface of
genus greater than 1 has distance 3, 4, 5 or bigger. We will illustrate
the algorithm with a number of newly discovered filling pairs examples
of distance 4 in genus 2 and 3 surfaces. These examples were discovered
with the aid of a computer program implementing the algorithm for
distance 4 or greater. This computer program was developed by
the 201314 URGE cohort of Paul Glenn (UB), Kayla Morrell (Buffalo
State) and Matthew Morse (UB).

Mar 7

Jenny Wilson (Chicago):
Stability phenomena for sequences of representations of the classical Weyl groups
Abstract: Over the past two years Church, Ellenberg, Farb, and Nagpal have developed machinery for studying sequences of representations of the symmetric groups, using a concept they call an FImodule. Their work, which builds on results of Hemmer and others, provides a framework for describing various stability phenomena of these sequences. I will give an overview of their theory and describe how it generalizes to sequences of representations of the Weyl groups in type B/C and D. I will outline some applications, including stability results for the cohomology of the complements of Coxeter hyperplane arrangements.

Mar 14

Anh Tran (Ohio State):
On the AJ conjecture for pretzel knots
Abstract: This talk is about the AJ conjecture that relates two different knot invariants: the Apolynomial and the colored Jones polynomial of a knot in S^3. We will introduce the conjecture and the geometric picture behind it. We will discuss our approach to the AJ conjecture using the localized skein module. We will show that the conjecture holds true for those hyperbolic knots satisfying certain conditions, and in particular for some classes of twobridge knots and pretzel knots. This is joint work with Thang T.Q. Le.

Apr 4

Robert Lipshitz (Columbia):
The Jones polynomial, Khovanov homology and Khovanov homotopy
Abstract: We will start by recalling the definition of the Jones polynomial and a refinement of it, called Khovanov homology. We will then introduce a further refinement, called a Khovanov homotopy type, and sketch some applications of this refinement. (This last part is joint work with Sucharit Sarkar.)

Apr 11

Lenny Ng (Duke):
Knot contact homology and the augmentation polynomial
Abstract: Knot contact homology is a package of invariants of knots and links that
comes from counting holomorphic curves in the cotangent bundle to R^3
with boundary on the conormal bundle. Recently, one part of this
package, the augmentation polynomial, has shown up in some surprising
places, including relations to the Apolynomial, colored HOMFLY
polynomials, and physics work of Aganagic, Vafa, Gukov, and others. I
will give a brief overview of knot contact homology and discuss the
latest developments. This is partly joint work with Mina Aganagic,
Tobias Ekholm, and Cumrun Vafa.

Apr 18

Johanna Mangahas (Brown):
An algorithm to detect full irreducibility by bounding the volume of periodic free factors
Abstract: This is a sort of sequel (but selfcontained!) to my talk last year about how to bound the length of a canonical fixed curve of a reducible mapping class, and thus get a "listandcheck" algorithm for detecting pseudoAnosov elements, which have no fixed curves. Mapping class groups are a frequent point of reference for understanding Out(F), the group of outer automorphisms of the free group F. The "fully irreducible" elements of Out(F) are its version of pseudoAnosov mapping classes. I'll describe an analogous listandcheck method for identifying fully irreducible elements of Out(F). This is joint with Matt Clay and Alexandra Pettet.

May 2

Bill Menasco (Buffalo):
Efficient geodesics in the curve complex or "Box, glocks and socks"
Abstract: In the curve complex it is possible to have infinitely many geodesic paths between two vertices/curves. To deal with this nonfiniteness issue, Masur and Minsky introduced the notion of tight geodesicsgiven any two vertices in the curve graph there are only finitely many tight geodesics between them. In this talk we will discuss a new category of geodesics that also have this finiteness propertyefficient geodesics. We will then discuss possible applications. This is joint work with Joan Birman and Dan Margalit.
