UW-PIMS Mathematics Colloquium

Sponsored by the UW Department of Mathematics and the Pacific Institute for the Mathematical Sciences.

October 17, 2014 at 2:30pm
SIG 225
Marianna Csörnyei
The University of Chicago
Geometry of Null Sets

We show how product decompositions of measures can detect directionality in sets. In order to show this we prove that sets of small measure are always contained in a "small" number of Lipschitz surfaces. We also discuss the higher co-dimensional versions of our statements. This is a joint work with Peter Jones.

October 31, 2014 at 2:30pm
SIG 225
Christopher D. Hacon
The University of Utah
Which Powers Of A Holomorphic Function Are Integrable?

Let f = f(z1, . . . , zn) be a holomorphic function defined on an open subset P ∈ U ⊂ Cn. The log canonical threshold of f at P is the largest s ∈ R such that |f|s is locally integrable at P. This invariant gives a sophisticated measure of the singularities of the set defined by the zero locus of f which is of importance in a variety of contexts (such as the minimal model program and the existence of Kähler-Einstein metrics in the negatively curved case). In this talk we will discuss recent results on the remarkable structure enjoyed by these invariants.

November 21, 2014 at 2:30pm
SIG 225
Andrea R. Nahmod
University of Massachusetts Amherst
Randomization and long time dynamics in nonlinear evolution PDE

In the last two decades, there has been substantial progress in the study of nonlinear dispersive PDE thanks to the influx of ideas and tools from nonlinear Fourier and harmonic analysis, geometry and analytic number theory, to the existing functional analytic methods. This body of work has primarily focused on deterministic aspects of wave phenomena and answered important questions related to existence and long time behavior of solutions in various regimes. Yet there remain important obstacles and open questions.

A natural approach to tackle some of them, and one which has recently seen a growing interest, is to consider certain evolution equations from a non-deterministic point of view (e.g. the random data Cauchy problem, invariant measures, etc) and incorporate to the deterministic toolbox, powerful but still classical tools from probability as well. Such approach goes back to seminal work by Bourgain in the mid 90's where global well-posedness of certain periodic Hamiltonian PDEs was studied in the almost sure sense via the existence and invariance of their associated Gibbs measures.

In this talk we will explain these ideas, describe some recent work and future directions. with an emphasis on the interplay of deterministic and probabilistic approaches.

February 20, 2015 at 2:30pm
MEB 246
Mark Rudelson
University of Michigan, Ann Arbor
Non-asymptotic approach in random matrix theory

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 matrices of a large fixed size, especially of their singular values.

We will discuss several recent results in this area concerning matrices with independent entries, as well as random unitary and orthogonal perturbations of a fixed matrix. We will also show an application of the non-asymptotic random matrix theory to estimating the permanent of a deterministic matrix.

March 6, 2015 at 2:30pm
MEB 246
Lauren Williams
University of California, Berkeley
The positive Grassmannian

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 Grassmannian, focusing on a few intriguing aspects: what it "looks like," and its connection to shallow water waves (via the KP hierarchy).

May 1, 2015 at 3:30pm
LOW 101
Michelle Wachs
University of Miami
Eulerian polynomials and beyond

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 the Eulerian polynomials have been introduced. I will discuss some of these generalizations and describe intriguing connections with algebraic geometry, representation theory, symmetric functions and chromatic polynomials.

May 8, 2015 at 2:30pm
LOW 101
Catherine Williams
Chief Data Scientist at AppNexus
The Mathematical Monetization of the Internet:
How Theory + Data Ads Up

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 and general relativity at UW (PhD '08), I'll give an overview of the online advertising ecosystem, including both Class 1 and RTB (real-time bidding) mechanisms, and sketch a few of the interesting "data science" problems we encounter at AppNexus, including buy-side and sell-side optimizations, fraud detection, and marketplace design. The theoretically optimal bidding strategy for the direct-response advertising in a second-price auction setting is particularly elegant; I'll discuss some details of how AppNexus implements it in practice as well as a recent mathematical innovation to help solve the "boiling the ocean" problem.

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Colloquium Video Archive


Archives from Previous Years

Archive of 2013-2014 colloquia         Archive of 2012-2013 colloquia
Archive of 2011-2012 colloquia         Archive of 2010-2011 colloquia
Archive of 2009-2010 colloquia         Archive of 2008-2009 colloquia
Archive of 2007-2008 colloquia         Archive of 2006-2007 colloquia
Archive of 2005-2006 colloquia         Archive of 2004-2005 colloquia
Archive of 2003-2004 colloquia         Archive of 2002-2003 colloquia
Archive of 2001-2002 colloquia         Archive of 2000-2001 colloquia
Archive of 1999-2000 colloquia         Archive of 1998-1999 colloquia


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