I will introduce two basic problems in random geometry. A
self-avoiding walk is a sequence of steps in a d-dimensional
lattice with no self-intersections. If branching is allowed, it is
called a branched polymer. Using supersymmetry, one can map...
We show a (3/2-\epsilon)-approximation algorithm for the
graphical traveling salesman problem where the goal is to find a
shortest tour in an unweighted graph G. This is a special case of
the metric traveling salesman problem when the underlying...
In the early 80's, Shimura made a precise conjecture relating
Petersson inner products of arithmetic automorphic forms on
quaternion algebras over totally real fields, up to algebraic
factors. This conjecture (which is a consequence of the Tate...
Let G be a connected reductive group over Q such that G(R) has
discrete series representations. I will report on some statistical
results on the Satake parameters (w.r.t. Sato-Tate distributions)
and low-lying zeros of L-functions for families of...