University of Washington

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 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...

Random matrix theory studies the asymptotics of the spectral distributions of families of random matrices, as the sizes of the matrices tend to infinity. Derivation such asymptotics frequently requires analyzing the spectral properties of random...

The positive Grassmannian is a remarkable subset of the real Grassmannian which has recently arisen in diverse contexts such as integrable systems, scattering amplitudes, and free probability. I will provide an elementary introduction to the positive...

Ran­dom matri­ces now play a role in many areas of the­o­ret­i­cal, applied, and com­pu­ta­tional math­e­mat­ics. There­fore, it is desir­able to have tools for study­ing ran­dom matri­ces that are flex­i­ble, easy to use, and pow­er­ful. Over the...

The Eulerian polynomials, which were introduced by Euler over 200 years ago, are pervasive throughout discrete mathematics and arise in a variety of surprising ways. Over the years generalizations and q-analogs possessing fundamental properties of...

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...

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...

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...