Technion Mathematics Colloquium Speaker: Igor Wigman (Cardiff) Title: Nodal length fluctuations for arithmetic random waves Time: Monday, January 9, 3:30 pm Place: Amado 233, Technion *Note unusual room, due to conference Colloquium Homepage: <http://www.technion.ac.il/~yehuday/colloquium/colloq.html> Abstract: This work is joint with Manjunath Krishnapur and Par Kurlberg. Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspaces with Gaussian probability measures. This induces a notion of random Gaussian eigenfunctions on the torus ("arithmetic random waves''.) We study the distribution of the nodal length of random Laplace eigenfunctions for high 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. --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Amir Yehudayoff <amir.yehudayoff@gmail.com>