Symplectic Geometry
Organizers: Mohammed Abouzaid, Eleny Ionel, and Jae Hee Lee
There is tea prior to the talk in the 4th floor lounge.
The Northern California Symplectic Geometry Seminar usually meets on the first Monday of each month, and alternates between Stanford and Berkeley.
Past Events
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.
Some years ago, joint with Xu, we resolved the integral version of the Arnold conjecture. Expanding the ad hoc constructions used there, we have developed a package of integral Hamiltonian Floer theory and their mod p reduction, including defining quantum Steenrod…
Symplectically self-polar convex bodies arise in convex geometry and dynamical systems. In this talk I will discuss these two perspectives.
On the convex-geometric side, Mahler’s conjecture on the volume product of a centrally symmetric convex body and its Euclidean polar is equivalent to…
I will describe a new constraint on the topology of smooth Lefschetz fibrations with 4-dimensional fibers, arising from Seiberg--Witten theory. I will explain how it yields smooth isotopy obstructions for products of Dehn twists on self-intersection -2 spheres in 4-manifolds. As an application,…
We adapt the construction of global Kuranishi charts to the moduli space of genus 0 SFT buildings. Using these charts, we associate a flow category with any non-degenerate contact manifold where the objects are collections of Reeb orbits and morphisms are moduli of buildings. This is joint…
The concept of $p$-curvature originated in Grothendieck's unpublished work from the 1960s and was subsequently developed further by V. Katz. The $p$-curvature plays an important role in the theory of ordinary differential equations (ODEs) as well as holonomic PDEs, establishing a connection…
Abstract
Sabloff duality is an analogue of Poincaré duality for Legendrian contact homology, which is a Floer-theoretic invariant of Legendrian knots. In this talk, I will tell you about an A-infinity enhancement of Sabloff duality. If time permits, I will also mention higher homotopies for this enhanced…
Pseudo-Anosov flows, originally introduced by Thurston, are a broad class of hyperbolic flows on 3-manifolds that are Anosov except along a finite link of singular closed orbits. A longstanding conjecture states that any 3-manifold carries only finitely many transitive pseudo-Anosov flows, up to…
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.