Usted está aquí: Inicio / Seminarios / Seminario de Representaciones de Álgebras / Actividades del Seminario de Representaciones de Álgebras / Homological mirror symmetry for not-so-simple singularities

Homological mirror symmetry for not-so-simple singularities

Ponente: Yanki Lekili
Institución: King’s College London
Tipo de Evento: Investigación, Formación de Recursos Humanos
Cuándo 21/10/2020
de 10:15 a 11:15
Dónde https://www.him.uni-bonn.de/programs/current-trimester-program/new-trends-in-representation-theory/new-trends-in-representation-theory-school/
Agregar evento al calendario vCal
iCal

Homological mirror symmetry for not-so-simple singularities 

 

In a joint work with Ueda, we outlined a set of explicit conjectures that precisely explain how homological mirror symmetry should work for Milnor fibers of invertible polynomials. We can prove these conjectures in a number of interesting cases such as the case of simple singularities (in any dimension), when the corresponding categories turns out to be equivalent to the derived category of the Calabi-Yau completion of the path algebra of Dynkin quivers. In general, one has to consider global deformations, but we can show that the possible deformations are parametrized by a moduli space ofA∞ structures which we identify with a certain moduli space of polarized Calabi-Yau varieties. I will explain the case of the Milnor fiber of xyz(and its higher dimensional generalizations) which is among the cases of not-so-simple singularities for which we can fully rigorously prove homological mirror symmetry.

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.