Séminaires : Séminaire Groupes, Représentations et Géométrie

Equipe(s) : gr,
Responsables :A. Brochier, O. Brunat, J.-Y. Charbonnel, O. Dudas, E. Letellier, D. Juteau, M. Varagnolo, E. Vasserot
Email des responsables : Adrien Brochier <adrien.brochier@imj-prg.fr>, Olivier Brunat <olivier.brunat@imj-prg.fr>, Jean-Yves Charbonnel <jean-yves.charbonnel@imj-prg.fr>, Olivier Dudas <olivier.dudas@imj-prg.fr>, Emmanuel Letellier <emmanuel.letellier@imj-prg.fr>, Daniel Juteau <daniel.juteau@imj-prg.fr>, Michela Varagnolo <varagnol@math.u-cergy.fr>, Eric Vasserot <eric.vasserot@imj-prg.fr>
Salle : salle 2015, 2em étage,
Adresse :Sophie Germain

Orateur(s) Peter SAMUELSON - University of Edinburgh,
Titre Hall algebras and the Fukaya category
Horaire10:30 à 11:30
RésumeThe Hall algebra of an abelian (or triangulated) category A has a basis given by isomorphism classes of objects, and multiplication given by ``counting extensions.'' The Fukaya category of a (real) symplectic manifold M has objects given by Lagrangians in M, and morphism spaces given by intersections of Lagrangians. In the first half of the talk we give a brief overview of some recent results about Hall algebras of categories of coherent sheaves over (algebraic) curves, and then recall a concrete description of the Fukaya category of a surface due to Haiden, Katzarkov, and Kontsevich. In the second half of the talk we use work of Hernandez and Leclerc to give a precise description of the (derived) Hall algebra of the Fukaya category of a disk, and give a conjectural description of the Hall algebra for ``most'' surfaces. (This is joint work with Ben Cooper.)
Sallesalle 2015, 2em étage,
AdresseSophie Germain