Northern California Symplectic Seminar
Past Events
Abstract: For a graded Liouville domain X, its symplectic cohomology (normally defined over the integers) can be lifted to a module over the complex cobordism ring using Floer homotopy theory. I'll discuss some computational aspects in the rational case, using Chern classes on Floer moduli…
I will give an update on recent progress in the study of Reeb dynamics on 3-dimensional contact manifolds: existence of nice Birkhoff sections, count of periodic orbits and Reeb chords, together with applications. This is joint work with Pierre Dehornoy, Umberto Hryniewicz and Ana Rechtman.
Abstract: I will discuss Floer theoretical invariants of arbitrary open contact manifolds in their relation with invariants of contactomorphisms.
This is a work in progress with Kiran Ajij, Mahan Mg, Dishant Pancholi and Leonid Polterovich.
Abstract: A symplectic homeomorphism is a C^0 limit of symplectic diffeomorphisms; a topological symplectic manifold is a manifold with an atlas whose transition maps are symplectic homeomorphisms. I will explain recent joint work showing that all such manifolds are bi-Lipschitz. As a…
Abstract: Much is known about algebraic K theory of the integers, in particular these groups are finitely generated. There is a secondary (or categorified) K theory of a commutative ring k, replacing finite type k modules by "finite type" A_infty categories over k. I explain how to get elements…
Abstract: Symmetric products of Riemann surfaces play a crucial role in symplectic geometry and low-dimensional topology. They are key to defining Heegaard Floer homology and serve as important examples of Liouville manifolds when the surfaces are open. In this talk, I will present ongoing work…
Abstract: In positive characteristic, on one hand the quantum D-module (from Gromov--Witten theory) carries extra central endomorphisms known as quantum Steenrod operations. On the other hand, in representation theory, the algebra of differential operators also carry a "large center" in positive…
Abstract: The presence of hyperbolic periodic orbits or invariant sets often has an effect on the global behavior of a symplectic dynamical system. In this talk we discuss two theorems along the lines of this phenomenon, extending some properties of Hamiltonian diffeomorphisms to dynamically…
Relying on Morse theory and an Euler class argument of Atiyah and Bott, Frances Kirwan proved two important results about the rational cohomology of compact symplectic manifold X with the Hamiltonian action of a connected, compact group G: equivariant formality, or the triviality of the G-action…
Abstract: We will present some recent results on the existence of special structures on compactnon Kahler manifolds obtained as quotients of Cn ⋉ Cm. More in particular, we will focus on p-Kahler structures and on symplectic structures satisfying the hard Lefschetz condition. Bott-Chern and…