Seminars and Colloquia by Series

Monday, November 19, 2012 - 14:00 , Location: Skiles 006 , Ramon Vera , Durham University , Organizer: John Etnyre
We discuss two concepts of low-dimensional topology in higher dimensions: near-symplectic manifolds and overtwisted contact structures. We present a generalization of near-symplectic 4-manifolds to dimension 6. By near-symplectic, we understand a closed 2-form that is symplectic outside a small submanifold where it degenerates. This approach uses some singular mappings called generalized broken Lefschetz fibrations. An application of this setting appears in contact topology. We find that a contact 5-manifold, which appears naturally in this context, is PS-overtwisted. This property can be detected in a rather simple way.
Monday, November 12, 2012 - 14:00 , Location: Skiles 006 , Youlin Li , Shanghai Jiaotong University and Ga Tech , Organizer: John Etnyre
We classify the Legendrian torus knots in S1XS2 with tight contact structure up to isotopy. This is a joint work with Feifei Chen and Fan Ding.
Monday, October 29, 2012 - 14:00 , Location: Skiles 006 , Yankı Lekili , University of Cambridge & Simons Center , Organizer: John Etnyre
We study some finite quotients of the A_n Milnor fibre which coincide with the Stein surfaces that appear in Fintushel and Stern's rational blowdown construction. We show that these Stein surfaces have no exact Lagrangian submanifolds by using the already available and deep understanding of the Fukaya category of the A_n Milnor fibre coming from homological mirror symmetry. On the contrary, we find Floer theoretically essential monotone Lagrangian tori, finitely covered by the monotone tori that we studied in the A_n Milnor fibre. We conclude that these Stein surfaces have non-vanishing symplectic cohomology. This is joint work with M. Maydanskiy.
Wednesday, October 24, 2012 - 14:00 , Location: Skiles 006 , Tetsuya Ito , UBC , Organizer: John Etnyre
We will give an overview of open book foliation method by emphasizing the aspect that it is a generalization of Birman-Menasco's braid foliation theory. We explain how surfaces in open book reflects topology and (contact) geometry of underlying 3-manifolds, and will give several applications. This talk is based on joint work with Keiko Kawamuro.
Monday, October 15, 2012 - 14:00 , Location: Skiles 006 , none , none , Organizer: John Etnyre
Monday, October 8, 2012 - 14:05 , Location: Skiles 006 , Rodrigo Montes , Univerity of Curitiba, Brazil , ristow@ufpr.br , Organizer: Mohammad Ghomi
 In this talk we introduce the notions of the  contact angle and of the holomorphic angle for  immersed surfaces in $S^{2n+1}$.  We deduce formulas for the Laplacian and for the Gaussian curvature, and we will classify minimal surfaces in $S^5$   with the two angles constant. This classification gives a 2-parameter family of minimal flat  tori  of $S^5$. Also, we will  give an alternative proof of the classification of minimal Legendrian surfaces in $S^5$ with constant Gaussian curvature. Finally, we will show some remarks and generalizations  of this classification.    
Monday, October 1, 2012 - 14:00 , Location: Skiles 006 , Keiko Kawamuro , University of Iowa , Organizer: John Etnyre
The fractional Dehn twist coefficient (FDTC), defined by Honda-Kazez-Matic, is an invariant of mapping classes. In this talk we study properties of FDTC by using open book foliation method, then obtain results in geometry and contact geometry of the open-book-manifold of a mapping class. This is joint work with Tetsuya Ito.
Monday, September 24, 2012 - 14:00 , Location: Skiles 006 , Olga Plamenevskaya , SUNY - Stony Brook , Organizer: John Etnyre
By a classical result of Eliashberg, contact manifolds in dimension 3 come in two flavors: tight (rigid) and overtwisted (flexible). Characterized by the presence of an "overtwisted disk", the overtwisted contact structures form a class where isotopy and homotopy classifications are equivalent.In higher dimensions, a class of flexible contact structures is yet to be found. However, some attempts to generalize the notion of an overtwisted disk have been made. One such object is a "plastikstufe" introduced by Niederkruger following some ideas of Gromov. We show that under certain conditions, non-isotopic contact structures become isotopic after connect-summing with a contact sphere containing a plastikstufe. This is a small step towards finding flexibility in higher dimensions. (Joint with E. Murphy, K. Niederkruger, and A. Stipsicz.)
Monday, September 17, 2012 - 14:00 , Location: Skiles 006 , Shea Vela-Vick , LSU , Organizer: John Etnyre
The Heegaard Floer package provides a robust tool for studying contact 3-manifolds and their subspaces. Within the sphere of Heegaard Floer homology, several invariants of Legendrian and transverse knots have been defined. The first such invariant, constructed by Ozsvath, Szabo and Thurston, was defined combinatorially using grid diagrams. The second invariant was obtained by geometric means using open book decompositions by Lisca, Ozsvath, Stipsicz and Szabo. We show that these two previously defined invariant agree. Along the way, we define a third, equivalent Legendrian/transverse invariant which arises naturally when studying transverse knots which are braided with respect to an open book decomposition.
Monday, September 10, 2012 - 14:05 , Location: Skiles 006 , Richard Kent , U Wisconsin , Organizer: Dan Margalit
It is a theorem of Bass, Lazard, and Serre, and, independently, Mennicke, that the special linear group SL(n,Z) enjoys the congruence subgroup property when n is at least 3.  This property is most quickly described by saying that the profinite completion of the special linear group injects into the special linear group of the profinite completion of Z.  There is a natural analog of this property for mapping class groups of surfaces.  Namely, one may ask if the profinite completion of the mapping class group embeds in the outer automorphism group of the profinite completion of the surface group. M. Boggi has a program to establish this property for mapping class groups, which couches things in geometric terms, reducing the conjecture to determining the homotopy type of a certain space.  I'll discuss what's known, and what's needed to continue his attack.

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