University of Washington

Nonabelian multiplicative integration on curves is a classical theory, going back to Volterra in the 19th century. In differential geometry this operation can be interpreted as the holonomy of a connection along a curve. In probability theory this is...

The online advertising industry is a rich environment for novel mathematical problems at the intersection of technology and theory. After introducing myself, AppNexus, and how I came to have my role there after having studied differential geometry...

Flow and cut prob­lems on graphs are among the most fun­da­men­tal and exten­sively stud­ied prob­lems in Oper­a­tions Research and Opti­miza­tion, play­ing a foun­da­tional role in both the the­ory and prac­tice of algo­rithm design. While the clas...

The Birnbaum Lecture in Probability will be delivered by Balint Virag (University of Toronto) in 2015.Northwest Probability Seminars are mini-conferences held at the University of Washington and/or Microsoft Research and organized in collaboration...

In many appli­ca­tions one wishes to min­i­mize an objec­tive func­tion that is not con­vex and is not dif­fer­en­tiable at its min­i­miz­ers. We dis­cuss two algo­rithms for min­i­miza­tion of non­smooth, non­con­vex func­tions. Gra­di­ent Sam­pling...

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...

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...

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...

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...

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...