## IAS Welcome Day 2017 - Faculty Panel Discussion

Robbert Dijkgraaf, Scott Tremaine, Sabine Schmidtke, Peter Sarnak, Didider Fassin

September 25, 2017

Robbert Dijkgraaf, Scott Tremaine, Sabine Schmidtke, Peter Sarnak, Didider Fassin

September 25, 2017

Peter Sarnak

Institute for Advanced Study; Faculty, School of Mathematics

March 3, 2014

We discuss various Gaussian ensembles for real homogeneous polynomials in several variables and the question of the distribution of the topologies of the connected components of the zero sets of a typical such random real hypersurface. For the "real -Fubini -Study ensemble" and at the other end the "monochromatic wave ensemble ", one can show that these have universal laws. Some qualitative features of these laws are also established. Joint work with I. Wigman.

Peter Sarnak

Institute for Advanced Study; Faculty, School of Mathematics

February 4, 2014

We review some of the connections, established and expected between random matrix theory and Zeta functions. We also discuss briefly some recent Universality Conjectures connected with families of L-functions.

Peter Sarnak

Institute for Advanced Study

March 20, 2012

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 a 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. The work report on is joint with A. Ghosh and A. Reznikov.

Peter Sarnak

Professor, School of Mathematics

February 2, 2011

Peter Sarnak

Institute for Advanced Study

April 6, 2010

Peter Sarnak

Institute for Advanced Study

December 3, 2008

Peter Sarnak

Institute for Advanced Study

March 26, 2008

Peter Sarnak

Institute for Advanced Study

March 11, 2005

Peter Sarnak

Institute for Advanced Study

April 7, 2001