Symplectic Geometry
Organizers: Eleny Ionel, Mohammed Abouzaid, 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.
Upcoming Events
Given two four-dimensional symplectic manifolds, together with knots in their boundaries, we define an ``anchored symplectic embedding'' to be a symplectic embedding, together with a two-dimensional symplectic cobordism between the knots (in the four-dimensional cobordism determined by the…
Past Events
There has been a burst of interest in gauge theoretic invariants of 3- and 4-manifolds equipped with an involution, developed in various contexts by Tian-Wang, Nakamura, Konno-Miyazawa-Taniguchi, and Li. Notably, Miyazawa proved the existence of an infinite family of exotic RP^2-knots using real…
For a Weinstein manifold, I will compare and contrast the properties of admitting a polarization, admitting an arboreal skeleton and admitting Maslov data, giving cohomological obstructions and illustrating their failure with concrete examples. I will also discuss which implications hold between…
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…
I will describe a new lower bound on the number of intersection points of a Lagrangian pair, in the exact setting, using Steenrod squares on Lagrangian Floer cohomology which are defined via a Floer homotopy type.
In this talk, I will construct an S^1-equivariant version of the relative symplectic cohomology developed by Varolgunes. As an application, I will construct a relative version of Gutt-Hutchings capacities and a relative version of symplectic (co)homology capacity. We will see that these relative…
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…
Associated to a star-shaped domain in R^{2n} are two increasing sequences of capacities: the Ekeland-Hofer capacities and the so-called Gutt-Hutchings capacities. I shall recall both constructions and then present the main theorem that they are the same. This is joint work with Vinicius Ramos.…
I will introduce a new structure on (relative) symplectic cohomology defined in terms of a PROP called the “Plumber’s PROP.” This PROP consists of nodal Riemann surfaces, of all genera and with multiple inputs and outputs, satisfying a condition that ensures the existence of positive Floer data…
In this talk, we will discuss the interplay between the wrapped Floer homology barcode and topological entropy. The concept of barcode entropy was introduced by Çineli, Ginzburg, and Gürel and has been shown to be related to the topological entropy of the underlying dynamical system in various…