Wednesday, August 27, 2014 - 14:00 , Location: Skiles 006 , James Conway , Georgia Tech , Organizer: James Conway
We will define transverse surgery, and study its effects on open books, the Heegaard Floer contact invariant, and tightness. We show that surgery on the connected binding of a genus g open book that supports a tight contact structure preserves tightness if the surgery coefficient is greater than 2g-1. We also give criteria for when positive contact surgery on Legendrian knots will result in an overtwisted manifold.
Monday, August 25, 2014 - 14:05 , Location: Skiles 00-TBA , Oyku Yurttas , Georgia Tech , Organizer: Dan Margalit
In this talk I will explain the Dynnikov’s coordinate system, which puts global coordinates on the boundary of Teichmuller space of the finitely punctured disk, and the update rules which describe the action of the Artin braid generators in terms of Dynnikov’s coordinates. If time permits, I will list some applications of this coordinate system. These applications include computing the geometric intersection number of two curves, computing the dilatation and moreover studying the dynamics of a given pseudo-Anosov braid on the finitely punctured disk.
Thursday, July 10, 2014 - 12:05 , Location: Skiles 005 , Andy Wand , University of Nantes , Organizer: John Etnyre
A well known result of Giroux tells us that isotopy classes ofcontact structures on a closed three manifold are in one to onecorrespondence with stabilization classes of open book decompositions ofthe manifold. We will introduce a characterization of tightness of acontact structure in terms of corresponding open book decompositions, andshow how this can be used to resolve the question of whether tightness ispreserved under Legendrian surgery.
Monday, June 16, 2014 - 14:00 , Location: Skiles 006 , Atreyee Bhattacharya , Indian Institute Of Science , Organizer: John Etnyre
In this talk we will discuss an ODE associated to the evolution of curvature along the Ricci flow. We talk about the stability of certain fixed points of this ODE (up to a suitable normalization). These fixed points include curvature of a large class of symmetric spaces.
Monday, May 5, 2014 - 14:05 , Location: Skiles 006 , Dan Margalit , Georgia Institute of Technology , Organizer: Dan Margalit
In joint work with Joan Birman and Bill Menasco, we describe a new finite set of geodesics connecting two given vertices of the curve complex. As an application, we give an effective algorithm for distance in the curve complex.
Monday, April 21, 2014 - 14:00 , Location: Skiles 006 , Faramarz Vafaee , MSU , Organizer: John Etnyre
Heegaard Floer theory consists of a set of invariants of three-and four-dimensional manifolds. Three-manifolds with the simplest HeegaardFloer invariants are called L-spaces and the name stems from the fact thatlens spaces are L-spaces. The primary focus of this talk will be on thequestion of which knots in the three-sphere admit L-space surgeries. Wewill also discuss about possible characterizations of L-spaces that do notreference Heegaard Floer homology.
Wednesday, April 16, 2014 - 14:00 , Location: Skiles 006 , Jeremy Van Horn-Morris , University of Arkansas , Organizer: John Etnyre
A monoidal subset of a group is any set which is closed under the product (and contains the identity). The standard example is Dehn^+, the set of maps whcih can be written as a product of right-handed Dehn twists. Using open book decompositions, many properties of contact 3-manifolds are encoded as monoidal subsets of the mapping class group. By a related construction, contact topology also produces a several monoidal subsets of the braid group. These generalize the notion of positive braids and Rudolphs ideas of quasipositive and strongly quasipositive. We'll discuss the construction of these monoids and some of the many open questions.
Monday, April 14, 2014 - 14:00 , Location: Skiles 006 , David Krcatovich , MSU , Organizer: John Etnyre
The set of knots up to a four-dimensional equivalence relation can be given the structure of a group, called the (smooth) knot concordance group. We will discuss how to compute concordance invariants using Heegaard Floer homology. We will then introduce the idea of a "reduced" knot Floer complex, see how it can be used to simplify computations, and give examples of how it can be helpful in distinguishing knots which are not concordant.
Friday, April 11, 2014 - 13:05 , Location: Skiles 006 , Christian Zickert , University of Maryland , email@example.com , Organizer: Stavros Garoufalidis
The Ptolemy coordinates are efficient coordinates for computingboundary-unipotent representations of a 3-manifold group in SL(2,C). Wedefine a slightly modified version which allows you to computerepresentations that are not necessarily boundary-unipotent. This givesrise to a new algorithm for computing the A-polynomial.