Greg Anderson, University of Minnesota, and Ofer Zeitouni, University of Minnesota and Weizmann Institute, are currently organizing the 2012 New Directions Short Course entitled "Advances in Random Matrix Theory," to be held June 18–29, 2012, at the Institute for Mathematics and its Applications (IMA).
The IMA's New Directions Short Course provides opportunities for establishing collaborations, building connections, and possibly shifting one's research focus. Past attendees have cited the IMA's New Directions short course as the impetus for publishing papers and books; beginning new projects; and joining forces with others in the field to form new, inspired partnerships.
The upcoming New Directions Short Course will cover advances in random matrix theory (RMT). As a mathematical discipline, real intensive progress came about in the 1990s, when Tracy and Widom explicitly linked RMT with integrable systems. Shortly after, the theory of the Riemann Hilbert problem was shown by Deift, Zhou, and co-workers to shed light on asymptotics and in particular universality results for classes of random matrices with explicit expressions for their joint distribution of eigenvalues.
Arguably the crowning achievement of these developments was the proof by Baik, Deift, and Johansson of random matrix limits for the asymptotics of the length of the longest increasing subsequence in a random permutation. In another direction, the introduction of free probability by Voiculescu was able to shed light on combinatorial and algebraic aspects of RMT.
In the last decade, much effort has gone into expanding the basic theory in directions where explicit expressions and tools, such as orthogonal polynomials, are not available. This upcoming short course will highlight some of these developments and will cover the following topics: support properties for polynomials in independent matrices (speaker, Greg W. Anderson, University of Minnesota); multimatrix models and expansions (speaker, Alice Guionnet, ENS de Lyon); beta ensembles (speaker, Balint Virag, University of Toronto); and universality in RMT (speaker, Ofer Zeitouni, University of Minnesota/Weizmann Institute). In addition, shorter presentations (1-2 hours each) on material related to the main topics of the courses will be offered by guest lecturers. In order to keep abreast of current developments, the list of speakers in those presentations is yet to be determined.
More information and an online application are available online at www.ima.umn.edu/2011-2012/ND6.18-29.12. This course is intended for researchers at all levels who have had some prior exposure to RMT and who are interested in learning recent techniques and results in RMT. The applications process is now open; applications are due April 15, 2012.
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