Seminars and Colloquia by Series

Friday, October 17, 2014 - 14:05 , Location: Skiles 006 , Balazs Strenner , U Wisconsin , Organizer: Dan Margalit
Construction of pseudo-Anosov elements of mapping class groups of surfaces is a non-trivial task. In 1988, Penner gave a very general construction of pseudo-Anosov mapping classes, and he conjectured that all pseudo-Anosov mapping classes arise this way up to finite power. This conjecture was known to be true on some simple surfaces, including the torus. In joint work with Hyunshik Shin, we resolve this conjecture for all surfaces.
Monday, October 13, 2014 - 14:05 , Location: Skiles 006 , Andreas Arvanitoyeorgos , University of Patras , , Organizer: Stavros Garoufalidis
A Riemannian manifold (M, g) is called Einstein if the Ricci tensor satisfies Ric(g)=\lambda g. For a Riemannian homogeneous space (M=G/H,g), where G is a Lie group and H a closed subgroup of G, the problem is to classify all G-invariant Einstein metrics.   In the present talk I will discuss progress on this problem on two important classes of homogeneous spaces, namely generalized flag manifolds and Stiefel manifolds. A generalized flag manifold is a compact homogeneous space M=G/H=G/C(S), where G is a compact semisimple Lie group and C(S) is the centralizer of a torus in G.  Equivalently, it is the orbit of the adjoint representation of G. A (real) Stiefel manifold is the set of orthonormal k-frames in R^n and is diffeomorphic to the homogeneous space SO(n)/SO(n-k).One main difference between these spaces is that in the first case the isotropy representationdecomposes into a sum of irreducible and {\it non equivalent} subrepresentations, whereas in thesecond case the isotropy representation contains equivalent summands. In both cases, when the number of isotropy summands increases, various difficulties appear, such as description of Ricci tensor, G-invariant metrics, as well as solving  the Einstein equation, which reduces to an  algebraic system of equations.  In many cases such systems involve parameters and we use Grobner bases techniques to prove existence of positive solutions.Based on joint works with I. Chrysikos (Brno), Y. Sakane (Osaka) and M. Statha (Patras)
Monday, October 6, 2014 - 14:00 , Location: Skiles 006 , Ryo Furukawa , University of Tokyo , Organizer: John Etnyre
In this talk we consider the contact embeddings of contact 3-manifolds to S^5 with the standard contact structure.Every closed 3-manifold can be embedded to S^5 smoothly by Wall's theorem. The only known necessary condition to a contact embedding to the standard S^5 is the triviality of the Euler class of the contact structure. On the other hand there are not so much examples of contact embeddings.I will explain the systematic construction of contact embeddings of some contact structures (containing non Stein fillable ones) on torus bundles and Lens spaces.If time permits I will explain relation between above construction and some polynomials on \mathbb C^3.
Friday, September 26, 2014 - 11:05 , Location: Skiles 006 , Vaughan Jones , University of Vanderbilt , , Organizer: Stavros Garoufalidis
Monday, September 22, 2014 - 14:00 , Location: Skiles 006 , David Gay , University of Georgia , Organizer: John Etnyre
This is joint work with Rob Kirby. Trisections are to 4-manifolds as Heegaard splittings are to 3-manifolds; a Heegaard splitting splits a 3-manifolds into 2 pieces each of which looks like a regular neighborhood of a bouquet of circles in R^3 (a handlebody), while a trisection splits a 4-manifold into 3 pieces of each of which looks like a regular neighborhood of a bouquet of circles in R^4. All closed, oriented 4-manifolds (resp. 3-manifolds) have trisections (resp. Heegaard splittings), and for a fixed manifold these are unique up to a natural stabilization operation. The striking parallels between the two dimensions suggest a plethora of interesting open questions, and I hope to present as many of these as I can.
Monday, September 15, 2014 - 14:05 , Location: Skiles 006 , Nick Salter , University of Chicago , Organizer: Dan Margalit
An essential feature of the theory of 3-manifolds fibering over the circle is that they often admit infinitely many distinct structures as a surface bundle. In four dimensions, the story is much more rigid: a given 4-manifold admits only finitely many fiberings as a surface bundle over a surface. But how many is “finitely many”? Can a 4-manifold possess three or more distinct surface bundle structures? In this talk, we will survey some of the beautiful classical examples of surface bundles over surfaces with multiple fiberings, and discuss some of our own work. This includes a rigidity result showing that a class of surface bundles have no second fiberings whatsoever, as well as the first example of a 4-manifold admitting three distinct surface bundle structures, and our progress on a quantitative version of the “how many?” question.
Monday, September 1, 2014 - 14:00 , Location: Skiles 006 , None , None , Organizer: John Etnyre
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.