Seminars and Colloquia by Series

The colored HOMFLY polynomial is q-holonomic

Series
Geometry Topology Seminar
Time
Monday, December 10, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Stavros Garoufalidis – Georgia Tech –
I will explain how to construct a 4-variable knot invariant which expresses a recursion for the colored HOMFLY polynomial of a knot, and its implications on (a) asymptotics (b) the SL2 character variety of the knot (c) mirror symmetry.

The topology of a subspace of the Legendrian curves in a closed contact 3-manifold

Series
Geometry Topology Seminar
Time
Monday, November 26, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ali Maalaoui – Rutgers University
In this talk we are going to present a theorem that can be seen as related to S. Smale's theorem on the topology of the space of Legendrian loops. The framework will be slightly different and the space of Legendrian curves will be replaced by a smaller space $C_{\beta}$, that appears to be convenient in some variational problems in contact form geometry. We will also talk about the applications and the possible extensions of this result. This is a joint work with V. Martino.

Near-symplectic 6-manifolds with PS-overtwisted contact submanifolds

Series
Geometry Topology Seminar
Time
Monday, November 19, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ramon Vera – Durham University
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.

Legendrian torus knots in S1XS2

Series
Geometry Topology Seminar
Time
Monday, November 12, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Youlin Li – Shanghai Jiaotong University and Ga Tech
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.

Symplectic topology of rational blowdowns

Series
Geometry Topology Seminar
Time
Monday, October 29, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yankı Lekili – University of Cambridge & Simons Center
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.

Open book foliation from braid foliation point of view

Series
Geometry Topology Seminar
Time
Wednesday, October 24, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tetsuya Ito – UBC
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.

Classification of minimal surfaces in $S^5$ with constant contact angle

Series
Geometry Topology Seminar
Time
Monday, October 8, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rodrigo Montes – Univerity of Curitiba, Brazil –
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.

Open book foliation and fractional Dehn twist coefficient

Series
Geometry Topology Seminar
Time
Monday, October 1, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Keiko Kawamuro – University of Iowa
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.

Towards flexibility for higher-dimensional contact manifolds

Series
Geometry Topology Seminar
Time
Monday, September 24, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Olga Plamenevskaya – SUNY - Stony Brook
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.)

Pages