Browsing Department of Pure Mathematics and Mathematical Statistics (DPMMS) by Author "Smith, Ivan"
Now showing items 1-9 of 9
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A Symplectic Prolegomenon
Smith, Ivan (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 ...
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Exact Lagrangian immersions with a single double point
Ekholm, Tobias; Smith, Ivan (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 ...
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Markov numbers and Lagrangian cell complexes in the complex projective plane
Evans, Jonathan David; Smith, Ivan (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 ...
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Quadratic differentials as stability conditions
Bridgeland, Tom; Smith, Ivan (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 ...
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Quadratic differentials as stability conditions
Bridgeland, Tom; Smith, Ivan (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 ...
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Quiver algebras as Fukaya categories
Smith, Ivan (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 ...
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The Fukaya category, exotic forms and exotic autoequivalences
Harris, Richard (University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2012-04-10)A symplectic manifold is a smooth manifold M together with a choice of a closed non-degenerate two-form. Recent years have seen the importance of associating an A∞-category to M, called its Fukaya category, in helping ...
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The monotone wrapped Fukaya category and the open-closed string map
Ritter, Alexander F; Smith, Ivan (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$_{*}$($\textit{W}$($\textit{E}$)) ...
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The symplectic arc algebra is formal
Abouzaid, Mohammed; Smith, Ivan (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 ...