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Mirror symmetry for homogeneous spaces

Hot Topics: Cluster algebras and wall-crossing March 28, 2016 - April 01, 2016

April 01, 2016 (11:30 AM PDT - 12:30 PM PDT)
Speaker(s): Clelia Pech (University of Kent at Canterbury)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • algebraic combinatorics

  • homological mirror symmetry

  • quantum cohomology

  • homogeneous space

  • canonical coordinates

  • parabolic subgroup

  • Bruhat decomposition construction of cluster algebras

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14491

Abstract

In this talk I will explain a construction by K. Rietsch of the mirrors of homogeneous spaces. The latter include Grassmannians, quadrics and flag varieties, and their mirrors can be expressed using Lie theory. More precisely the mirrors of homogeneous spaces live on so-called `Richardson varieties', which possess a cluster structure, and the mirror superpotential is defined on these Richardson varieties.

I will start by detailing Rietsch's general construction, then I will present some recent results by Marsh-Rietsch on Grassmannians, as well as joint work with Rietsch (resp. Rietsch and Williams) on Lagrangian Grassmannians (resp. quadrics). In particular I will show how the restriction of the superpotential on each cluster chart is a Laurent polynomial, which changes as we change cluster charts

Supplements
25699?type=thumb Pech Notes 336 KB application/pdf Download
Video/Audio Files

14491

H.264 Video 14491.mp4 356 MB video/mp4 rtsp://videos.msri.org/data/000/025/647/original/14491.mp4 Download
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