An afternoon of geometric analysis in honor of Sergei Novikov
Titles and Abstracts
Gennadi Kasparov (Vanderbilt University), On the Novikov higher signature conjecture: history and development
(This talk is part of the Lie Groups and Representation Theory Seminar)
Abstract: The Novikov higher signature conjecture played and continues to play an important role in the development of several areas of mathematics: topology, geometric group theory, K-theory of C*-algebras. I will give a brief exposition of the history and progress in research related with the Novikov conjecture up to the most recent results.
Igor Krichever (Columbia University), A discrete analog of the Novikov-Veselov hierarchy and its applications
(This talk is part of the Mathematics Colloquium)
Abstract: The spectral theory of the 2D Schrödinger operator on one energy level, pioneered by Novikov and Veselov, has developed over the years is still full of open problems. In the talk I will present recent progress in this area and its application to a wide range of problems including characterization of Prym varieties in algebraic geometry and solution of a sigma SO(N) model in mathematical physics.
Anton Zorich (Institut de Mathématiques Paris-Jussieu), Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes
(This talk is part of the Dynamics Seminar)
Abstract: We show how recent equidistribution results allow one to compute
approximate values of Masur-Veech volumes of the strata in the moduli spaces
of Abelian and quadratic differentials, by a Monte Carlo method.
We also show how a similar approach allows one to count the asymptotical number of
meanders of fixed combinatorial type in various settings in all
genera. Our formulae are particularly efficient for classical
meanders in genus zero.
This is joint work with V. Delecroix, E. Goujard, and P. Zograf.