Categorical symplectic geometry is the study of a rich collection of invariants of symplectic
manifolds, including the Fukaya $ A_\infty $-category, Floer cohomology, and symplectic …

For a compact subset KK of a closed symplectic manifold (M, ω) (M,ω), we prove that KK is
heavy if and only if its relative symplectic cohomology over the Novikov field is nonzero. As …

Consider a closed monotone symplectic manifold $(M,\omega) $.\cite {Gan2} constructed a
cyclic open-closed map, which goes from the cyclic homology of the Fukaya category of $ M …

For an oriented manifold $ M $ and a compact subanalytic Legendrian $\Lambda\subseteq
S^* M $, we construct a canonical strong smooth relative Calabi--Yau structure on the …

For a monotone symplectic manifold and a smooth anticanonical divisor, there is a formal
deformation of the symplectic cohomology of the divisor complement, defined by allowing …

We prove that under certain conditions, a normal crossings compactification of a Liouville
domain determines a Maurer--Cartan element for the $ L_\infty $ structure on its symplectic …

We extend the Cohen-Jones-Segal construction of stable homotopy types associated to flow
categories of Morse-Smale functions $ f $ to the setting where $ f $ is equivariant under a …

We formulate and prove a chain level descent property of symplectic cohomology for
involutive covers by compact subsets that take into account the natural algebraic structures …

We derive the notions of BV unital infinitesimal bialgebra and BV Frobenius algebra from the
topology of suitable compactifications of moduli spaces of decorated genus 0 curves. We …

In\cite {PS}, for a stably framed Liouville manifold $ X $ we defined a Donaldson-Fukaya
category $\mathcal {F}(X;\mathbb {S}) $ over the sphere spectrum, and developed an …