Seminars and Colloquia by Series

Duality exact sequences in contact homology

Series
Geometry Topology Seminar
Time
Monday, February 2, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
John Etnyre – School of Mathematics, Georgia Tech
I will discuss a "duality" among the linearized contact homology groups of a Legendrian submanifold in certain contact manifolds (in particular in Euclidean (2n+1)-space). This duality is expressed in a long exact sequence relating the linearized contact homology, linearized contact cohomology and the ordinary homology of the Legendrian submanifold. One can use this structure to ease difficult computations of linearized contact homology in high dimensions and further illuminate the proof of cases of the Arnold Conjecture for the double points of an exact Lagrangian in complex n- space.

Broken Lefschetz fibrations and Floer theoretical invariants

Series
Geometry Topology Seminar
Time
Monday, December 1, 2008 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Yanki Lekili – MIT
A broken fibration is a map from a smooth 4-manifold to S^2 with isolated Lefschetz singularities and isolated fold singularities along circles. These structures provide a new framework for studying the topology of 4-manifolds and a new way of studying Floer theoretical invariants of low dimensional manifolds. In this talk, we will first talk about topological constructions of broken Lefschetz fibrations. Then, we will describe Perutz's 4-manifold invariants associated with broken fibrations and a TQFT-like structure corresponding to these invariants. The main goal of this talk is to sketch a program for relating these invariants to Ozsváth-Szabó invariants.

On Cannon's conjecture

Series
Geometry Topology Seminar
Time
Monday, November 24, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Sa'ar Hersonsky – University of Georgia
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.

Multiple knots in a manifold with the same surgeries yielding S^3

Series
Geometry Topology Seminar
Time
Friday, November 21, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Ken Baker – University of Miami
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.

Branched covers and nonpositive curvature

Series
Geometry Topology Seminar
Time
Friday, November 7, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Igor Belegradek – School of Mathematics, Georgia Tech
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.

The four-vertex-property and topology of surfaces with constant curvature

Series
Geometry Topology Seminar
Time
Monday, October 27, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Mohammad Ghomi – School of Mathematics, Georgia Tech
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.

A new topological bound for energy of fluid flows

Series
Geometry Topology Seminar
Time
Friday, October 24, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Rafal Komendarczyk – University of Pennsylvania
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.

Ribbon graphs and knots

Series
Geometry Topology Seminar
Time
Monday, October 20, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Iain Moffatt – University of Southern Alabama
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.

Knots in contact 3-manifolds

Series
Geometry Topology Seminar
Time
Friday, October 10, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Vera Vertesi – School of Mathematics, Georgia Tech
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).

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