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Partially wrapped Fukaya categories of symmetric products of marked disks

Ponente: Gustavo Jasso
Institución: Universität Bonn
Tipo de Evento: Investigación, Formación de Recursos Humanos
Cuándo 19/10/2020
de 09:00 a 10:00
Dónde https://www.him.uni-bonn.de/programs/current-trimester-program/new-trends-in-representation-theory/new-trends-in-representation-theory-school/
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Partially wrapped Fukaya categories of symmetric products of marked disks

 

Partially wrapped Fukaya categories of symmetric products of marked surfaces were introduced by Auroux so as to give a symplecto-geometric intepretation of the bordered Heegaard-Floer homology of Lipshitz, Ozsv\'ath and Thurston. In this talk, I will explain the equivalence between the partially wrapped Fukaya categories of symmetric products of marked disks and the perfect derived categories of a (discrete) family of finite-dimensional algebras introduced by Iyama, the so-called higher Auslander algebras of type A. In particular, I will explain some of the rich structure present among these mathematical objects as they also relate to the higher Waldhausen S-constructions of Dyckerhoff and Poguntke.

This is a report with Tobias Dyckerhoff and Yanki Lekili and also contains work with Dyckerhoff and Walde.

NOTA: Esta charla es parte de la Escuela de Invierno "Connections between representation theory and geometry" que del 5 al 23 de octubre de 2020 tendrá lugar virtualmente en el Hausdorff Research Institute for Mathematics (HIM) de Bonn, Alemania, organizada por Jenny August, Sondre Kvamme, Daniel Labardini-Fragoso y Alexandra Zvonareva. Si quieres asistir, por favor visita la página web de la Escuela de Invierno e inscríbete.