January 24 
Joan Licata (IAS) 
Legendrian knot invariants in Seifert fibered spaces
Knot theory beyond the threesphere has seen increased attention in recent years, and in this talk I'll focus on knot theory in Seifert fibered spaces. In particular, we'll consider Legendrian knots in Seifert fibered spaces equipped with a special contact form. This setting gives rise to both topological and contact geometric questions, and I'll describe some of the ingredients used to prove the Legendrian nonsimplicity of an infinite family of knot types representing torsion homology classes. This is joint work with J. Sabloff.

January 31 
Anastasiia Tsvietkova (UTK) 
An alternative approach to hyperbolic structures on link complements
Thurston demonstrated that every link in S3 is a torus link, a satellite link or a hyperbolic link and these three categories are mutually exclusive. It also follows from work of Menasco that an alternating link represented by a prime diagram is either hyperbolic or a (2, n)�torus link. A new method for computing the hyperbolic structure of the complement of a hyperbolic link, based on ideal polygons bounding the regions of a diagram of the link rather than decomposition of the complement into ideal tetrahedra, was suggested by M. Thistlethwaite. The method is applicable to all diagrams of hyperbolic links under a few mild restrictions. The talk will introduce the basics of the method. Some applications will be discussed, including a surprising rigidity property of certain tangles, a new numerical invariant for tangles, and formulas that allow one to calculate the volume of 2�bridged links directly from the diagram. 
February 7 
David Rose (Duke) 
A categorification of quantum sl_3 projectors and the sl_3 ReshetikhinTuraev invariants of tangles
We discuss a recent result of the speaker giving a categorification of quantum sl_3 projectors and the sl_3 ReshetikhinTuraev invariants of framed tangles. In more detail, we will review Kuperberg's diagrammatic description of the category of representations of quantum sl_3 (which gives a combinatorial method for computing the quantum sl_3 invariant of links) as well as Morrison and Nieh's geometric categorification of this structure. We then show that there exist elements in Morrison and Nieh's categorification which correspond to projection onto highest weight irreducible summands and use these elements to construct a categorification of the sl_3 ReshetikhinTuraev invariant, that is, a link homology theory from which the sl_3 invariant can be obtained by taking the graded Euler characteristic.

February 14 
Ben Cooper (UVA) 
Homological generalizations of Hecke algebras
(In preparation) A family of algebras related to recent research in quantum topology and representation theory will be generalized using tools from topology. 
February 28 
Stefan Schwede (Bonn) 
Equivariant properties of symmetric products
The filtration on the infinite symmetric product of spheres by number of factors provides a sequence of spectra between the sphere spectrum and the integral EilenbergMac Lane spectrum. This filtration has received a lot of attention and the subquotients are interesting stable homotopy types.
In this talk I will discuss the equivariant stable homotopy types, for finite groups, obtained from this filtration for the infinite symmetric product of representation spheres. The filtration is more complicated than in the nonequivariant case, and already on the zeroth homotopy groups an interesting filtration of the augmentation ideal of the Burnside rings arises. Our method is by `global' homotopy theory, i.e., we study the simultaneous behaviour for all finite groups at once. In this context, the equivariant subquotients are no longer rationally trivial, nor even concentrated in dimension 0. 
March 13 
Slava Krushkal (UVA) 
Slicing the Hopf link 
March 22 
Matt Hogancamp (UVA) 
Categorification of Generalized JonesWenzl Projectors
The projections of tensor powers of the fundamental representation of quantum sl_2 onto the symmetric powers are called the JonesWenzl projectors. These have important applications to topology and have been categorified by previous authors. In this talk, we discuss a categorification of the entire decomposition of these tensor powers into irreducibles, and applications. This is joint work with Ben Cooper. 
March 27 
Margaret Doig (Indiana) 
Finite surgeries
It is well known that any 3manifold can be obtained by Dehn surgery on a link but not which ones can be obtained from a knot or which knots can produce them. We investigate these two questions for elliptic Seifert fibered spaces (other than lens spaces) using the Heegaard Floer ``correction terms'' or ``dinvariants'' associated to a 3manifold Y and its torsion Spin^c structures. If H_1(Y ) is finite and small, the correction terms completely identify the manifolds which can be realized as knot surgeries and the knots which realize them; even when H_1(Y ) is larger (but still finite), the invariants help identify the manifolds and place restrictions on the knots. 
April 3 
James Conant (UTK) 
Iterating the Whitney move
The Whitney move allows one to remove pairs of algebraically canceling intersections of an nmanifold embedded in a (2n)manifold, where n > 2. It is wellknown to fail when the ambient dimension is 4 because the Whitney disk that guides the move is not generically embedded. This leads to the idea of a Whitney tower, where one can pair the intersections of Whitney disks by �higherorder� Whitney disks, and repeat the process with these Whitney disks. We give a complete list of obstructions for a link in the 3sphere to bound a Whitney tower of order n into the 4ball, in terms of Milnor invariants, higherorder SatoLevine invariants and higherorder Arf invariants. This is joint work with Rob Schneiderman and Peter Teichner. 
April 19 
Charles Frohman (University of Iowa) 
SU(3) representations of web groups
I will explain a TQFT using the homology of representation spaces of the fundamental groups of the complements of webs in S^3. ( A web is an oriented trivalent graph all of whose vertices are sources and sinks.) This will be related to the sl_3 polynomial of links. 
April 24 
Tom Mark (UVA) 
Floer homology and fractional Dehn twists
A fibered knot K in a 3manifold Y gives rise to a contact structure on Y, which may or may not be tight. Composing the monodromy of K with sufficiently many right Dehn twists parallel to K always gives a tight contact structure (on a new 3manifold), while after sufficiently many left twists the contact structure becomes overtwisted. I'll describe some work in progress that gives a bound on the number of twists required, depending only on Y. In particular, this proves a somewhat surprising fact, that the fractional Dehn twist coefficient of the monodromy of any fibered knot in Y is bounded by a constant determined by the Floer homology of Y. 
May 1 
Andras Stipsicz (IAS) 
Knots in lattice homology
We introduce a filtration on the lattice homology of a negative definite plumbing tree associated to a further vertex and show how to determine lattice homologies of surgeries on this last vertex. We discuss the relation with Heegaard Floer homology. 