Skip to main content

Date and location

Saturday 22 April 2017
Malott Hall 532 (Mathematics Lounge)
Cornell University
Ithaca, New York

Schedule

09:00 am–09:30 amCoffee and bagels
09:30 am–10:30 amCatagay Kutluhan, University at Buffalo
Filtering the Heegaard Floer contact invariant
Heegaard Floer homology is a topological invariant of closed oriented 3-manifolds defined by Ozsvath-Szabo. Given a contact structure on a closed orientable 3-manifold, there exists a distinguished element of Heegaard Floer homology (well-defined up to sign) which is an invariant of the contact structure up to isotopy. Using the Heegaard Floer chain complex, we define a refinement of the Heegaard Floer contact invariant which has many desirable properties. After giving some background and explaining the origin of our invariant, I will talk about some of its key properties and present some examples. This is joint work with Gordana Matic, Jeremy Van Horn-Morris, and Andy Wand.
10:30 am–11:00 amCoffee
11:00 am–11:30 amDamien Broka, Pennsylvania State University
Symplectic realizations of holomorphic Poisson manifolds
We present our construction of a holomorphic symplectic realization for an arbitrary holomorphic Poisson manifold $(X,\pi)$. More precisely, we construct a new holomorphic symplectic structure on a neighborhood $Y$ of the zero section of the cotangent bundle $T^*X$ such that the projection map is a holomorphic symplectic realization. By using Poisson sigma models, deceptively simple formulas can then also be obtained for the symplectic form. In that way, we find an extension of a recent result due to Crainic-Marcut to holomorphic Poisson manifolds.
11:30 am–11:45 amCoffee
11:45 am–12:15 pmWai-kit Yeung, Cornell University
Perverse sheaves and knot contact homology
In this talk, I will present an algebraic construction, called homotopy braid closure, that produces invariants of links in $\mathbf{R}^3$ starting with a braid group action on objects of a (model) category $C$. Applying this construction to the natural action of the braid group $B_n$ on the category of perverse sheaves on the two-dimensional disk with singularities at $n$ marked points, we obtain a differential graded (DG) category that gives knot contact homology in the sense of L. Ng, originally defined by counting pseudoholomorphic disks. This is joint work with Yu. Berest and A. Eshmatov.
12:15 pm–02:00 pmLunch
02:00 pm–03:00 pmFrançois Ziegler, Georgia Southern University
Contact Imprimitivity
The symplectic "imprimitivity theorem" characterizes those hamiltonian $G$-spaces that are induced, in the sense of Kazhdan-Kostant-Sternberg, from hamiltonian $H$-spaces for a closed subgroup $H$ of the Lie group $G$. Its main application is to the structure and classification of homogeneous (or more generally "primary") hamiltonian $G$-spaces when $G$ has a normal subgroup. When trying to fully mirror Mackey's representation-theoretic normal subgroup analysis, however, one is soon forced to remember that representations better correspond not to hamiltonian $G$-spaces, but to Kostant and Souriau's "prequantum", contact $G$-spaces over them. In this talk, I will describe the construction of induced objects in that category, and their characterization by an imprimitivity theorem.
03:00 pm–03:30 pmTea
03:30 pm–04:30 pmLuca Vitagliano, Università degli Studi di Salerno
Holomorphic Jacobi Manifolds
After an introduction to Jacobi manifolds and their role in Poisson Geometry, we introduce and study holomorphic Jacobi structures from a real differential geometric point of view. We also discuss the relationship with Generalized Geometry (in odd dimensions). Our analysis parallels a similar one for holomorphic Poisson structures by Laurent-Gengoux, Stiénon and Xu. However, the situation appears more involved in the Jacobi case. This is joint work with Aïssa Wade.
06:30 pmDinner