Monday, December 1, 2008 - 14:30 , Location: Skiles 269 , Sandra Ritz , University of South Carolina , Organizer: John Etnyre
We will begin with an overview of the Burau representation of the braid group. This will be followed by an introduction to a contact category on 3-manifolds, with a brief discussion of its relation to the braid group.
Monday, November 24, 2008 - 14:00 , Location: Skiles 269 , Sa'ar Hersonsky , University of Georgia , Organizer: John Etnyre
Cannon: "A f.g. negatively curved group with boundary homeomorphic to the round two sphere is Kleinian". We shall outline a combinatorial (complex analysis motivated) approach to this interesting conjecture (following Cannon, Cannon-Floyd-Parry). If time allows we will hint on another approach (Bonk-Kleiner) (as well as ours). The talk should be accessible to graduate students with solid background in: complex analysis, group theory and basic topology.
Friday, November 21, 2008 - 14:00 , Location: Skiles 269 , Ken Baker , University of Miami , Organizer: John Etnyre
Lickorish observed a simple way to make two knots in S^3 that produced the same manifold by the same surgery. Many have extended this result with the most dramatic being Osoinach's method (and Teragaito's adaptation) of creating infinitely many distinct knots in S^3 with the same surgery yielding the same manifold. We will turn this line of inquiry around and examine relationships within such families of corresponding knots in the resulting surgered manifold.
Friday, November 7, 2008 - 14:00 , Location: Skiles 269 , Igor Belegradek , School of Mathematics, Georgia Tech , Organizer: Igor Belegradek
In the 1980s Gromov showed that curvature (in the triangle comparison sense) decreases under branched covers. In this expository talk I shall prove Gromov's result, and then discuss its generalization (due to Allcock) that helps show that some moduli spaces arising in algebraic geometry have contractible universal covers. The talk should be accessible to those interested in geometry/topology.
Monday, October 27, 2008 - 14:00 , Location: Skiles 269 , Mohammad Ghomi , School of Mathematics, Georgia Tech , Organizer: John Etnyre
We prove that every metric of constant curvature on a compact 2-manifold M with boundary bdM induces (at least) four vertices, i.e., local extrema of geodesic curvature, on bdM, if, and only if, M is simply connected. Indeed, when M is not simply connected, we construct hyperbolic, parabolic, and elliptic metrics of constant curvature on M which induce only two vertices on bdM. Furthermore, we characterize the sphere as the only closed orientable Riemannian 2-manifold M which has the four-vertex-property, i.e., the boundary of every compact surface immersed in M has 4 vertices.
Friday, October 24, 2008 - 14:00 , Location: Skiles 269 , Rafal Komendarczyk , University of Pennsylvania , Organizer: John Etnyre
In many physical situations we are interested in topological lower bounds for L^2-energy of volume preserving vector fields. Such situations include for instance evolution of a magnetic field in ideal magnetohydrodynamics. Classical energy bounds involve topological invariants like helicity which measure linkage of orbits in the flow. In this talk I will present a new lower bound in terms of the third order helicity, which is an invariant measuring a third order linkage of orbits. I will also discuss how the third order helicity can be derived from the Milnor's \mu-bar invariant for 3-component links.
Monday, October 20, 2008 - 14:00 , Location: Skiles 269 , Iain Moffatt , University of Southern Alabama , Organizer: Stavros Garoufalidis
In this talk I will describe some relations between embedded graphs, their polynomials and the Jones polynomial of an associated link. I will explain how relations between graphs, links and their polynomials leads to the definition of the partial dual of a ribbon graph. I will then go on to show that the realizations of the Jones polynomial as the Tutte polynomial of a graph, and as the topological Tutte polynomial of a ribbon graph are related, surprisingly, by the homfly polynomial.
Friday, October 10, 2008 - 14:00 , Location: Skiles 269 , Vera Vertesi , School of Mathematics, Georgia Tech , Organizer: John Etnyre
In this talk I will give a purely combinatorial description of Knot Floer Homology for knots in the three-sphere (Manolescu-Ozsvath-Szabo- Thurston). In this homology there is a naturally associated invariant for transverse knots. This invariant gives a combinatorial but still an effective way to distinguish transverse knots (Ng-Ozsvath-Thurston). Moreover it leads to the construction of an infinite family of non-transversely simple knot-types (Vertesi).
Monday, October 6, 2008 - 14:00 , Location: Skiles 269 , A. Sikora , SUNY Buffalo , Organizer: Thang Le
W. Goldman proved that the SL(2)-character variety X(F) of a closed surface F is a holonomic symplectic manifold. He also showed that the Sl(2)-characters of every 3-manifold with boundary F form an isotropic subspace of X(F). In fact, for all 3-manifolds whose SL(2)-representations are easy to analyze, these representations form a Lagrangian space. In this talk, we are going to construct explicit examples of 3-manifolds M bounding surfaces of arbitrary genus, whose spaces of SL(2)-characters have dimension as small as possible. We discuss relevance of this problem to quantum and classical low-dimensional topology.
Friday, October 3, 2008 - 14:00 , Location: Skiles 269 , Tony Pantev , Dept of Mathematics, University of Penn , Organizer: Stavros Garoufalidis
I will describe a framework which relates large N duality to the geometry of degenerating Calabi-Yau spaces and the Hitchin integrable system. I will give a geometric interpretation of the Dijkgraaf-Vafa large N quantization procedure in this context.