Organized by: Nikita Nekrasov, Alexander Turbiner and Alexander Abanov.

Timing: Spring 2015/Fall 2015

Abstract: Calogero-Moser-Sutherland many-body systems arose originally in the 1970’s simultaneously in Nuclear Physics, Mathematical Physics and Solid State Physics. Since then they were found in some incarnations in diverse branches of physics and mathematics such as the theory of quantum Hall effect, Yang-Mills and Chern-Simons gauge theories in various dimensions with various amounts of supersymmetry, noncommutative geometry, topology of Hilbert schemes, geometric representation theory, Gromov-Witten invariants, theory of symmetric functions, SLE, Random Matrix theory, collective field theory and random geometries.

The aim of the seminar series is to review and explore these connections.

Fall 2015 Lectures:

Date | Title | Speaker | Location |

9/10 | Applied gauge origami | Nikita Nekrasov | Rm 313 |

9/23 | Soliton solutions of a Calogero model in a harmonic potential | Alexander Abanov | Rm 313 |

9/30 | Benjamin-Ono equation and collective behavior of Calogero particles | Alexander Abanov | Rm 313 |

10/7 | CANCELLED: Solving quantum elliptic Calogero-Moser system using classical relativistic CM system (Ruijsenaars-Schneider model) | Nikita Nekrasov | Rm 313 |

10/14 | Comments on Disordered Conformal Field Theories | Z. Komargodski | Rm 313 |

10/23 | Integrability of limit shape equations for the 6-vertex model | Nicolai Reshetikhin | Rm 313 |

10/28 | Heun operator | Alexander Turbiner | Rm 313 |

11/11 | TBD | Fabio Franchini | Rm 313 |

11/18 | 3-body elliptic Calogero model (2D-Lame operator): a solution | Alexander Turbiner | Rm 313 |

11/25 | On the construction of higher quantum integrals of elliptic Calogero-Moser system from gauge theory | Nikita Nekrasov | Rm 313 |

12/2 | The Bannai-ito Algebra and Exactly Solvable Mode | Luc Vinet | Rm 313 |

12/9 | BPZ equation and Riemann-Hilbert correspondence from gauge theory | Nikita Nekrasov | Rm 313 |

12/16 | BPZ equation and Riemann-Hilbert correspondence from gauge theory – Part 2 | Nikita Nekrasov | Rm 313 |

12/23 | |||

Spring 2015 Lectures:

Date and Time | Title | Presenters |

4/15 at 2:30pm – Room 313 | Mathematics and Physics of Calogero Moser-Sutherland systems | Nikita Nekrasov |

4/22 at 2:30pm – Room 313 | Quantum Integrability and Schubert Calculus | Vassily Gorbounov |

4/29 at 2:00pm – Room 313 | From crossed instantons to Calogero-Moser system | Nikita Nekrasov |