Seminars and Colloquia by Series

Monday, August 23, 2010 - 14:00 , Location: Skiles 114 , John Etnyre , Ga Tech , Organizer: John Etnyre
The study of Legendrian and transversal knots has been an essential part of contact topology for quite some time now, but until recently their study in overtwisted contact structures has been virtually ignored. In the past few years that has changed. I will review what is know about such knots and discuss recent work on the "geography" and "botany" problem. 
Monday, August 16, 2010 - 14:00 , Location: Skiles 171 , Bill Menasco , University of Buffalo , Organizer: John Etnyre
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.
Tuesday, June 15, 2010 - 15:30 , Location: Skiles 171 , Andy Wand , Berkeley and Max Planck Institute , Organizer: John Etnyre
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.
Monday, April 26, 2010 - 15:00 , Location: Skiles 269 , A. Beliakova , University of Zurich , Organizer: Thang Le
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.
Friday, April 2, 2010 - 14:00 , Location: Skiles 269 , Clint McCrory , UGA , clint@math.uga.edu , Organizer: Mohammad Ghomi
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.
Friday, February 26, 2010 - 14:00 , Location: Skiles 269 , Qi Chen , Winston-Salem State University , Organizer: Thang Le
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.
Sunday, January 10, 2010 - 15:00 , Location: TBA , Matt Clay , Allegheny College , Organizer: Dan Margalit
Monday, November 30, 2009 - 14:05 , Location: Skiles 269 , Stavros Garoufalidis , Georgia Tech , stavros@math.gatech.edu , Organizer: Stavros Garoufalidis
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.
Monday, November 23, 2009 - 14:00 , Location: Skiles 269 , Hong-Van Le , Mathematical Institute of Academy of Sciences of the Czech Republic , Organizer: Thang Le
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 $C$.
Monday, November 9, 2009 - 14:00 , Location: Skiles 269 , Bulent Tosun , Ga Tech , Organizer: John Etnyre
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.

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