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The symplectic arc algebra is formal
(Duke University PressDuke Mathematical Journal, 2016-01-28)
We prove a formality theorem for the Fukaya categories of the symplectic manifolds underlying symplectic Khovanov cohomology over fields of characteristic zero. The key ingredient is the construction of a degree-one ...
Markov numbers and Lagrangian cell complexes in the complex projective plane
(Mathematical sciences publishersGEOMETRY & TOPOLOGY, 2018)
We study Lagrangian embeddings of a class of two-dimensional cell complexes L_p,q into the complex projective plane. These cell complexes, which we call pinwheels, arise naturally in algebraic geometry as vanishing cycles ...
Exact Lagrangian immersions with a single double point
(American Mathematical Society, 2015-01-09)
We show that if a closed orientable 2k-manifold K, k > 2, with Euler characteristic χ(K) ≠ -2 admits an exact Lagrangian immersion into C2k with one transverse double point and no other self intersections, then K is ...
Quadratic differentials as stability conditions
(SpringerPublications mathématiques de l'IHÉS, 2014)
We prove that moduli spaces of meromorphic quadratic differentials with simple zeroes on compact Riemann surfaces can be identified with spaces of stability conditions on a class of CY3 triangulated categories defined using ...
Quadratic differentials as stability conditions
(SpringerPublications mathématiques de l'IHÉS, 2014)
We prove that moduli spaces of meromorphic quadratic differentials with simple zeroes on compact Riemann surfaces can be identified with spaces of stability conditions on a class of CY3 triangulated categories defined using ...
A Symplectic Prolegomenon
(American Mathematical SocietyBulletin of the American Mathematical Society, 2014)
A symplectic manifold gives rise to a triangulated A∞-category, the derived Fukaya category, which encodes information on Lagrangian submanifolds and dynamics as probed by Floer cohomology. This survey aims to give some ...
The monotone wrapped Fukaya category and the open-closed string map
(SpringerSelecta Mathematica, 2016-08-09)
We build the wrapped Fukaya category $\textit{W}$($\textit{E}$)for any monotone symplectic manifold $\textit{E}$, convex at infinity. We define the open-closed and closed-open string maps, OC : HH$_{*}$($\textit{W}$($\textit{E}$)) ...
Quiver algebras as Fukaya categories
(Mathematical Sciences PublishersGeometry & Topology, 2015-10-20)
We embed triangulated categories defined by quivers with potential arising from ideal triangulations of marked bordered surfaces into Fukaya categories of quasiprojective 3–folds associated to meromorphic quadratic ...