Dyson-Schwinger equations, topological expansions, and random matrices



August 28 to September 1, 2017



Practical Information

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

Overview and Program

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:

This school is intended for graduate students and postdocs who are starting to learn random matrix theory and have some background in probability. Lecture notes will be distributed in advance for preparation and tutorials and problem sessions will be run throughout the school.

Lecture Description
Lectures 1 + 2Law of large numbers in random matrices (light / heavy tailed entries), and concentration of measure.
Lectures 3 + 4Central limit theorem in the one cut case (light / heavy tailed entries).
Lectures 5 + 6Generalization to the discrete setting of tiling models.
Lectures 7 + 8 Topological expansions for large N asymptotics of partition functions.
Lectures 9 + 10Generalization to several cut models.

Daily Schedule

Time Description Location
09:30 am - 10:00 amBreakfastRoom 508
10:00 am - 11:00 amAM Lecture (Guionnet)Room 520
11:00 am - 11:30 amBreakRoom 508
11:30 am - 12:30 pmTutorialRoom 520
12:30 pm - 02:00 pmLunchRoom 508
02:00 pm - 03:00 pmPM Lecture (Guionnet)Room 520
03:00 pm - 04:00 pmProblem SessionRoom 520
04:00 pm - 04:30 pmBreakRoom 508
04:30 pm - 05:30 pmSupplemental Lecture / Additional DiscussionRoom 520
05:30 pm - 06:30 pmDinnerRoom 508

Application

To apply as a funded participant, please email dysonschwinger@gmail.com by the deadline of March 1, 2017 with the following:

Funded participants will have their local accommodations covered, meals provided at Columbia, and partial travel support (we ask that you inquire with your department for some support as well). Funds are limited, and preference will be given to those who apply before the application deadline of March 1, 2017. Late applications will be considered if there is remaining funding.
To apply as an unfunded participant, email dysonschwinger@gmail.com and provide your name, university, and present position.