From random matrices to algebraic geometry


Bertrand Eynard

CEA Saclay

Northeastern University

Thursday, October 7, 2010


Talk at 4:30 p.m. in 509 Lake Hall

Tea at 4:00 p.m. in 544 Nightingale Hall


Abstract:   Random matrices have many applications in physics, mathematics, and technology. One of the main questions is to understand the asymptotic large size (N) behavior of the eigenvalues of random matrices. I will show a method to compute all terms in the large N expansion of correlation functions. This method uses algebro-geometric properties of a certain plane curve, which in this case is the Stieljes transform of the leading large N density of eigenvalues. That plane curve is the sole ingredient needed to compute all the large N expansion. Thus, random matrices can also teach us something about algebraic geometry, by associating to any plane curve, a series. The terms of that series are symplectic invariants of the plane curve, and have many fascinating properties. Beside, it was conjectured [BKMP 2008], that if one chooses the plane curve mirror to a toric Calabi-Yau threefold, the associated series is nothing but the generating series of Gromov-Witten invariants. So far, this conjecture was proved only in a handful of examples.

Here are some directions to Northeastern University. Lake Hall and Nightingale Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street. The two halls are connected, with no well-defined boundary in between. In particular, 509 Lake Hall is on the same corridor as 544 Nightingale Hall.

There is free parking available for people coming to the Colloquium at Northeastern's visitor parking (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from Andrei Zelevinsky.

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Posted:: September 22, 2010    URL: