School of Mathematics Seminars and Lectures
Nodal Lines of Maass Forms and Critical Percolation
by Prof. Peter Sarnak (Princeton University and Institute for Advanced Study)
Thursday, May 24, 2012
from
to
(Asia/Kolkata)
at Colaba Campus ( AG-66 )
at Colaba Campus ( AG-66 )
Description |
We describe some results concerning the number of connected components of nodal lines of high frequency Maass forms on the modular surface. Based on heuristics connecting these to an exactly solvable critical percolation model, Bogomolny and Schmit have conjectured, and numerics confirm, that this number follows an asymptotic law. While proving this appears to be very difficult, some approximations to it can be proved by developing number theoretic and analytic methods (Joint with A. Ghosh and A. Reznikov). |