University of Washington

A conjecture of Read predicts that the coefficients of the chromatic polynomial of a graph form a log-concave sequence for any graph. A related conjecture of Welsh predicts that the number of linearly independent subsets of varying sizes form a log...

Let A be an abelian variety of dimension g over a number field K. The Sato-Tate group ST(A) is a compact subgroup of the unitary symplectic group USp(2g) that can be defined in terms of the l-adic Galois representation associated to A. Under the...

In a simple symmetric random walk on Z a particle jumps left or right with 50% chance independently at each time and space location. What if the jump probabilities are taken to be random themselves (e.g. uniformly distributed between 0% and 100%)? In...

The Pacific Northwest Geometry Seminar (PNGS) is a regional meeting for geometers of all kinds. It is held every fall and spring, and every other winter, rotating among the following participating institutions: Oregon State University Portland State...

Igusa class polynomials are the genus 2 analogue of Hilbert class polynomials; their roots are invariants of genus 2 curves that have complex multiplication by a fixed order. The coefficients of Igusa class polynomials are rational, but, unlike in...

The ABC Conjecture, formulated in the mid-1980's by Oesterlé and Masser, is one of the most important conjectures in number theory. It has many deep consequences, but its basic formulation can be given in entirely elementary terms. In September 2012...

Derivative free optimization (DFO) is the field that addresses optimization of black-box functions – that is functions whose value can be computed (possibly approximately) but whose derivatives cannot be approximated directly. The applications of DFO...

I will begin with the familiar Farey sequences: the subdivisions of the real line obtained by recursively taking the mediant (a+c)/(b+d) of fractions a/b and c/d. I will take this starting point as an excuse for an ecclectic tour which may include...

A symplectic structure is a kind of geometric structure that can be put on an even dimensional space. It generalizes the notion of an area form in two dimensions in such a way that many of the special dynamical features of area preserving geometry...