I'll talk on work in progress on algebraic and analytic geometry
over the field of one element F_1. This work originates in
non-Archimedean analytic geometry as a result of a search for
appropriate framework for so called skeletons of analytic...
We attach Galois representations to automorphic representations
on unitary groups whose weight (=component at infinity) is a
holomorphic limit of discrete series. The main innovation is a new
construction of congruences, using the Hasse Invariant...
Non-relativization of complexity issues can be interpreted as
giving evidence that these issues cannot be resolved by
“black-box” techniques. We show that the assumption $DistNP
\subseteq AvgP$ does not imply that $NP\subseteq BPP$ by...
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 a talk sponsored by the Einstein Legacy Society, author Linda
Arntzenius discusses her book, Images of America: Institute for
Advanced Study.This latest addition to the Images of
America series celebrates the Institute’s unique character
and...
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...
