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...
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.
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...
Peter Sarnak,
Professor, School of Mathematics. Through the works of Fermat,
Gauss, and Lagrange, we understand which positive integers can be
represented as sums of two, three, or four squares. Hilbert's 11th
problem, from 1900, extends this...
