



3:304:00 

Tea 


4:005:00 

Talk: Benson Farb* 

Permutations and polynomiality in algebra and topology
Scanned Notes (notes by Bulent Tosun) 
5:30 

Social Gathering 

At Engine 11 




9:009:30 

Light refreshments 


9:3010:30 

Talk: Lenny Ng 

Knot contact homology and unknot detection
Scanned Notes (notes by Bulent Tosun)
Questions and comments from Lenny 
10:3011:00 

Tea Break 


11:0012:00 

Talk: Pallavi Dani 

Divergence in groups
Scanned Notes (notes by Bulent Tosun) 
12:002:00 

Lunch 


2:003:00 

Talk: Shelly Harvey 

Filtering smooth concordance classes of topologically slice knots
Slides from Talk 
3:004:00 

Extended Tea Break 


4:005:00 

Talk: Kate Petersen 

The Geometry of Character Varieties
Slides from Talk 
6:30 

Banquet 

At Baronda 




9:009:30 

Light refreshments 


9:3010:30 

Talk: Bulent Tosun 

Legendrian and transverse knots in cabled knot types
Slides from Talk 
10:3011:00 

Tea Break 


11:0012:00 

Talk: Josh Greene 

Conway mutation and alternating links
Scanned Notes (notes by Bulent Tosun)
Slides from Similar Talk
Questions and comments from Josh 
All talks will be in Skiles 006.
* This will be a colloquium talk.
Divergence in groups
Consider a pair of geodesics emanating from a point in a metric space. The
``divergence'' of the pair indicates how quickly they move away from each
other, by measuring how far one must travel to get between corresponding
points on the geodesics, without backtracking towards the basepoint.
Gersten used this idea to de fine a quasiisometry invariant for groups.
I will describe divergence in a variety of groups, and talk about a higher
dimensional analog. This will include joint work with A. Abrams, N. Brady,
M. Duchin and R. Young on rightangled Artin groups, and with A. Thomas on
rightangled Coxeter groups.
Permutations and polynomiality in algebra and topology
Tom Church, Jordan Ellenberg and I recently discovered that the ith Betti number of the space of configurations of n points on any manifold is given by a polynomial in n. Similarly for the moduli space of npointed genus g curves. Similarly for the dimensions of various spaces of homogeneous polynomials arising in algebraic combinatorics. Why? What do these disparate examples have in common? The goal of this talk will be to answer this question by explaining a simple underlying structure shared by these (and many other) examples in algebra and topology.
Conway mutation and alternating links
We will show that a pair of alternating links have homeomorphic branched doublecovers if and only if they are mutants. The proof involves some interesting combinatorial invariants coming from Heegaard Floer homology.
Filtering smooth concordance classes of topologically slice knots
Recall that two knots are concordant if they cobound a
smoothly embedded annulus in S^3 x I. The set of knots modulo
concordance forms a group, called the knot concordance group, C.
Inside this group lies a very interesting subgroup called the group of
topologically slice knots, denoted T. In this talk we will define two
monoid filtrations of T that approximate how close a knot is to being
(smoothly) slice in #_m CP(2) or #_m CP(2). Their intersection,
denoted T_n, is a filtration of T by subgroups. T /T_0 is large,
detected by the tau, s, and and deltainvariants, while T_0/T_1 is
detected by certain dinvariants. Going beyond this, our main result
is that T_1/T_2 has rank at least one. We also give evidence to
believe that Tn/Tn+1 has positive rank for all n.
Knot contact homology and unknot detection
Knot contact homology is an invariant of knotted submanifolds in R^n obtained by counting holomorphic curves in the cotangent bundle of R^n with certain boundary conditions. For knots in R^3, this produces a fairly strong knot invariant that can be formulated combinatorially. I will describe how this invariant is related to the fundamental group of the knot complement via "string topology", and deduce an elementary proof that knot contact homology detects the unknot. This is partly joint work with Kai Cieliebak, Tobias Ekholm, and Janko Latschev.
The Geometry of Character Varieties
The character variety, X(M), of a finite volume cusped
hyperbolic 3manifold M is in essence the moduli space of hyperbolic
structures on M. I will discuss how the geometry of these algebraic
sets is related to the topology of M and the structure of the
fundamental group of M. I will focus on curve components of X(M) and
the action of symmetries of M on X(M). This is partly joint with
Melissa Macasieb and Ronald van Luijk, and Ken Baker.
Legendrian and transverse knots in cabled knot types
In this talk we will exhibit many new phenomena in the structure of Legendrian and transverse knots
by giving a complete classification of all cables of the positive torus knots. We will also provide two structural
theorems to ensure when a cable of an arbitrary Legendrian simple knot type is also Legendrian simple. Part of
the results are joint work with John Etnyre and Douglas LaFountain.
