Seminars and Colloquia by Series

Monday, September 27, 2010 - 15:45 , Location: Skiles 269 , Dan Rutherford , Duke University , Organizer: John Etnyre

This is the first talk in the Emory-Ga Tech-UGA joint seminar. The second talk will follow at 5.

A smooth knot in a contact 3-manifold is called Legendrian if it is always tangent to the contact planes. In this talk, I will discuss Legendrian knots in R^3 and the solid torus where knots can be conveniently viewed using their `front projections'. In particular, I will describe how certain decompositions of front projections known as `normal rulings' (introduced by Fuchs and Chekanov-Pushkar) can be used to give combinatorial descriptions for parts of the HOMFLY-PT and Kauffman polynomials. I will conclude by discussing recent generalizations to Legendrian solid torus links. It is usual to identify the `HOMFLY-PT skein module' of the solid torus with the ring of symmetric functions. In this context, normal rulings can be used to give a knot theory description of the standard scalar product determined by taking the Schur functions to form an orthonormal basis.
Monday, September 20, 2010 - 14:00 , Location: Skiles 114 , Xavier Fernandes , Emory University , Organizer: John Etnyre
We adapt techniques derived from the study of quasi-flats in Right Angled Artin Groups, and apply them to 2-dimensional Graph Braid Groups to show that the groups B_2(K_n) are quasi-isometrically distinct for all n.
Monday, September 13, 2010 - 14:00 , Location: Skiles 114 , Jason McGibbon , University of Massachusetts , Organizer: John Etnyre
Knot contact homology (KCH) is a combinatorially defined topological invariant of smooth knots introduced by Ng. Work of Ekholm, Etnyre, Ng and Sullivan shows that KCH is the contact homology of the unit conormal lift of the knot. In this talk we describe a monodromy result for knot contact homology,namely that associated to a path of knots there is a connecting homomorphism which is invariant under homotopy. The proof of this result suggests a conjectural interpretation for KCH via open strings, which we will describe.
Monday, September 6, 2010 - 14:00 , Location: Skiles , No Speaker , --- , Organizer: John Etnyre
Monday, August 30, 2010 - 14:00 , Location: Skiles 114 , Mohammad Ghomi , Ga Tech , Organizer: John Etnyre
We discuss necessary and sufficient conditions of a subset X of the sphere S^n to be the image of the unit normal vector field (or Gauss map) of a closed orientable hypersurface immersed in Euclidean space R^{n+1}.
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.

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