3pm – Igor Wigman (King’s College)
Title: Nodal length fluctuations for arithmetic random waves
Abstract: Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspaces with Gaussian probability measures. This induces a notion of random Gaussian Laplace eigenfunctions on the torus (“arithmetic random waves”). We study the distribution of the nodal length of random eigenfunctions for large eigenvalues, and our primary result is that the asymptotics for the variance is non-universal, and is intimately related to the arithmetic of lattice points lying on a circle with radius corresponding to the energy. This work is joint with Manjunath Krishnapur and Par Kurlberg.
4.30pm – Alex Iosevich (Rochester)
Title: Multi-linear operators, geometric measure theory and combinatorics.
Abstract: Sobolev bounds for classical Fourier integral operators have been used with great success over the years in partial differential equations, geometry and many other areas. In this talk we shall establish some simple bounds for multi-linear analogs of these operators and we shall deduce some interesting consequences for a diverse set of problems in classical harmonic analysis, Falconer-ErdH os type problems in geometric measure theory and combinatorics, and best constants for Sobolev type inequalities.