00:00:00 / 00:00:00
26 31

Wall-crossing and geometry at infinity of Betti moduli spaces

By Maxim Kontsevich

Also appears in collection : 3e Séminaire Itzykson: Wall crossing in Hitchin integrable systems

Linear algebraic differential equation (in one variable) depending on a small parameter produces a spectral curve, which is a point in the base of a Hitchin integrable system. Gaiotto, Moore and Neitzke discovered a remarkable structure on the Hitchin base, consisting in certain integer numbers (BPS counting) associated with cycles on the spectral curves, and satisfying universal wall-crossing constraint at hypersurfaces of discontinuity. For a generic spectral curve the wall-crossing structure leads to a preferred coordinate system on the Betti moduli space (a.k.a. the character variety, or the moduli space of monodromy data). I'll speak about interpretation of BPS counting as trees on the Hitchin base, about generalized Strebel differentials and associated quivers, and how one can effectively calculate BPS counting using algebraic curves in Betti moduli spaces

Information about the video

  • Date of recording 11/7/13
  • Date of publication 11/20/13
  • Institution IHES
  • Format MP4

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback