University of Washington

The continual increase in the human population and our demands on the Earth's limited resources, raises the urgent mandate of understanding the degree to which our actions are sustainable. This is an enormous scientific challenge and mathematics...

The Cascade Topology Seminar is a bi-annual gathering of topologists from the Pacific Northwest and Southwestern Canada.

Quantum computers are hypothetical devices based on quantum physics that can out-perform classical computers. A famous algorithm by Peter Shor shows that quantum computers can factor an n-digit integer in n³ steps, exponentially better than the...

The study of nonnegative polynomials is a basic problem in real algebraic geometry. Truncated moment problem is a classical question in real analysis. Symmetric tensor decompositions are of interest in many areas of applied mathematics. The main goal...

The origins of "arithmetic invariant theory" come from the work of Gauss, who used integer binary quadratic forms to study ideal class groups of quadratic fields. The underlying philosophy---parametrizing arithmetic and geometric objects by orbits of...

Let X be a connected smooth projective variety over Q. If X has a Q point, then X must have local points, i.e. points over the reals and over the p-adic completions Q_p. However, local solubility is often not sufficient. Manin showed that quadratic...

I will describe some scary moments that have occurred in the history of elliptic curve cryptography almost from its inception; talk about some of the ironies of controversies in cryptography -- such as RSA's role as defender of strong encryption; and...

Cryptography is the mathematical science of keeping secrets and maintaining trust. Once an arcane study of primarily military significance, over the past several decades the advent of the internet has invigorated this science. There are now results...

Representation theory of finite groups seeks to understand functions on the group known as irreducible characters. A group like GL(n,F_q), the group of invertible square matrices with entries in a finite field F_q, originates in algebraic geometry...