Northern California Symplectic Seminar
Past Events
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…
Abstract: I will discuss the asymptotic growth of autonomous Hamiltonian flows with respect to the Hofer metric. This includes a dichotomy on the two-sphere: the Hofer norm either grows linearly or remains bounded in time by a universal constant. I will also touch on some connections to dynamics…
In this talk, based on a joint work with Erman Cineli and Basak Gurel, we discuss the multiplicity problem for prime closed orbits of dynamically convex Reeb flows on the boundary of a star-shaped domain. The first of our two main results asserts that such a flow has at least n prime closed Reeb…
The ellipsoid embedding function generalizes symplectic ball packing problems. For a symplectic manifold, this function determines the minimum scaling factor required for a standard ellipsoid with a given eccentricity to embed symplectically into the manifold. If the function has infinitely many…
Given a smooth closed n-manifold M and a k-tuple of basepoints in M, we define a Morse-type A∞-algebra called the based multiloop A∞-algebra and show the equivalence with the higher-dimensional Heegaard Floer A∞-algebra of k disjoint cotangent fibers of T*M.