ICTP Mathematics Seminars (Bogdan GEORGIEV) - Wednesday 14 June 2017, starting at 15:00

[Math Section]

M A T H E M A T I C S   S E M I N A R S  2017



Wednesday 14 June, at 15:00 hrs.



Bogdan Georgiev (MPIM Bonn)


Title:
Some Recent Estimates On Nodal Geometry In The High-Energy Limit


Abstract:
Given a closed manifold, the Laplace operator is known to possess a 
discrete spectrum of eigenvalues converging to infinity. We are 
interested in properties of the corresponding eigenfunctions as the 
eigenvalue becomes large (i.e. the high-energy limit). From a physical 
point of view, the eigenfunctions represent stationary states of a free 
quantum particle - when properly normalized, they may be interpreted as 
the probability density of a particle in the manifold. Various questions 
about the geometry of Laplace-eigenfunctions have been studied 
thoroughly - for example, distribution and measure of the vanishing 
(nodal) set; localization; shape and inner radius of nodal domains, etc. 
We present some recent results along these lines - this also includes 
joint work with M. Mukherjee.



VENUE:  Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first 
floor)