Date: August 28 to September 1, 2017

Main Lecturer: Alice Guionnet (Lyon)

Location: Columbia Mathematics Department

Funding: NSF CBMS conference grant DMS-1642595 and the Minerva Lecture Series

Organizers: Ivan Corwin and Yi Sun

Conference Poster: Poster

Understanding the large dimension asymptotics of random matrices or related models such as random tilings has been a hot topic for the last twenty years within probability, mathematical physics, and statistical mechanics. Because such models are highly correlated, classical methods based on independent variables fail. Special cases have been studied in detail thanks to specific forms of the laws, such as determinantal laws. These lectures will investigate a general class of models using the so called Dyson-Schwinger equations or generalizations such as Nekrasov's equations. The idea is similar to Stein's method in that the observables are approximate solutions of equations that can be solved asymptotically.

Alice Guionnet (Lyon) will give ten main lectures, divided into two per day. Besides these lectures there will be supplementary lectures by other senior researchers attending the school, including:

- Charles Bordenave (Toulouse)
- Gaetan Borot (Bonn, to be confirmed)
- Paul Bourgade (NYU)
- Vadim Gorin (MIT)
- Sylvia Serfaty (NYU)

Lecture | Description |
---|---|

Lectures 1 + 2 | Law of large numbers in random matrices (light / heavy tailed entries), and concentration of measure. |

Lectures 3 + 4 | Central limit theorem in the one cut case (light / heavy tailed entries). |

Lectures 5 + 6 | Generalization to the discrete setting of tiling models. |

Lectures 7 + 8 | Topological expansions for large N asymptotics of partition functions. |

Lectures 9 + 10 | Generalization to several cut models. |

Time | Description | Location |
---|---|---|

09:30 am - 10:00 am | Breakfast | Room 508 |

10:00 am - 11:00 am | AM Lecture (Guionnet) | Room 520 |

11:00 am - 11:30 am | Break | Room 508 |

11:30 am - 12:30 pm | Tutorial | Room 520 |

12:30 pm - 02:00 pm | Lunch | Room 508 |

02:00 pm - 03:00 pm | PM Lecture (Guionnet) | Room 520 |

03:00 pm - 04:00 pm | Problem Session | Room 520 |

04:00 pm - 04:30 pm | Break | Room 508 |

04:30 pm - 05:30 pm | Supplemental Lecture / Additional Discussion | Room 520 |

05:30 pm - 06:30 pm | Dinner | Room 508 |