Seminars and Colloquia by Series

Isotopies of links carried by Matsuda branched surfaces

Series
Geometry Topology Seminar
Time
Monday, August 16, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Bill MenascoUniversity of Buffalo
We introduce two related sets of topological objects in the 3-sphere, namely a set of two-component exchangable links termed "iterated doubling pairs", and a see of associated branched surfaces called "Matsuda branched surfaces". Together these two sets possess a rich internal structure, and allow us to present two theorems that provide a new characterization of topological isotopy of braids, as well as a new characterization of transversal isotopy of braids in the 3-sphere endowed with the standard contact structure. This is joint work with Doug Lafountain, and builds upon previous seminal work of Hiroshi Matsuda.

Positivity of monodromies of open book decompositions

Series
Geometry Topology Seminar
Time
Tuesday, June 15, 2010 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Andy WandBerkeley and Max Planck Institute
I will describe some results concerning factorizations ofdiffeomorphisms of compact surfaces with boundary. In particular, Iwill describe a refinement of the well-known \emph{right-veering}property, and discuss some applications to the problem ofcharacterization of geometric properties of contact structures interms of monodromies of supporting open book decompositions.

On the categorification of the quantum Casimir

Series
Geometry Topology Seminar
Time
Monday, April 26, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
A. BeliakovaUniversity of Zurich
In the talk, I will gently introduce the Lauda-Khovanov 2-category, categorifying the idempotent form of the quantum sl(2). Then I will define a complex, whose Euler characteristic is the quantum Casimir. Finally, I will show that this complex naturally belongs to the center of the 2-category. The talk is based on the joint work with Aaron Lauda and Mikhail Khovanov.

The topology at infinity of real algebraic manifolds

Series
Geometry Topology Seminar
Time
Friday, April 2, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Clint McCroryUGA
A noncompact smooth manifold X has a real algebraic structure if and only if X is tame at infinity, i.e. X is the interior of a compact manifold with boundary. Different algebraic structures on X can be detected by the topology of an algebraic compactification with normal crossings at infinity. The resulting filtration of the homology of X is analogous to Deligne's weight filtration for nonsingular complex algebraic varieties.

"On the unification of quantum invariants of 3-manifolds" by Qi Chen

Series
Geometry Topology Seminar
Time
Friday, February 26, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Qi ChenWinston-Salem State University
For every quantum group one can define two invariants of 3-manifolds:the WRT invariant and the Hennings invariant. We will show that theseinvariants are equivalentfor quantum sl_2 when restricted to the rational homology 3-spheres.This relation can be used to solve the integrality problem of the WRT invariant.We will also show that the Hennings invariant produces integral TQFTsin a more natural way than the WRT invariant.

The Jones slopes of a knot

Series
Geometry Topology Seminar
Time
Monday, November 30, 2009 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Stavros GaroufalidisGeorgia Tech
I will discuss a conjecture that relates the degree of the Jones polynomial of a knot and its parallels with the slopes of incompressible surfaces in the knot complement. I will present examples, as well as computational challenges.

Geometry, computational complexity and algebraic number fields

Series
Geometry Topology Seminar
Time
Monday, November 23, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Hong-Van LeMathematical Institute of Academy of Sciences of the Czech Republic
In 1979 Valiant gave algebraic analogs to algorithmic complexity problem such as $P \not = NP$. His central conjecture concerns the determinantal complexity of the permanents. In my lecture I shall propose geometric and algebraic methods to attack this problem and other lower bound problems based on the elusive functions approach by Raz. In particular I shall give new algorithms to get lower bounds for determinantal complexity of polynomials over $Q$, $R$ and $C$.

On the Legendrian and transverse classification of cabled knot types

Series
Geometry Topology Seminar
Time
Monday, November 9, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Bulent TosunGa Tech
In 3-dimensional contact topology one of the main problem is classifying Legendrian (transverse) knots in certain knot type up to Legendrian ( transverse) isotopy. In particular we want to decide if two (one in case of transverse knots) classical invariants of this knots are complete set of invariants. If it is, then we call this knot type Legendrian (transversely) simple knot type otherwise it is called Legendrian (transversely) non-simple. In this talk, by tracing the techniques developed by Etnyre and Honda, we will present some results concerning the complete Legendrian and transverse classification of certain cabled knots in the standard tight contact 3-sphere. Moreover we will provide an infinite family of Legendrian and transversely non-simple prime knots.

Schur Weyl duality and the colored Jones polynomial

Series
Geometry Topology Seminar
Time
Wednesday, October 28, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Roland van der VeenUniversity of Amsterdam
We recall the Schur Weyl duality from representation theory and show how this can be applied to express the colored Jones polynomial of torus knots in an elegant way. We'll then discuss some applications and further extensions of this method.

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