# Mathematics Colloquium Fall 2015

For further information please contact Professor Torsten Ehrhardt or call the Mathematics Department at 459-2969

**October 6, 2015
**

*"Science from a sheet of paper."*

**Tadashi Tokieda, University of Cambridge** **and Stanford University**

Starting from a sheet of paper, by folding, stacking, crumpling, tearing, we will explore a rich variety of mathematical sciences. Many physical experiments will be conducted in front of the audience.

**October 13, 2015
** The Riemann zeta function is of great interest to number theorists as it encodes much information about the distribution of primes. Related L-functions encode information about diverse arithmetic phenomena, such as rational points on elliptic curves, representation of integers by quadratic forms, distribution of eigenfunctions of the Laplacian on the modular surface, etc. In many such problems, it is of interest to understand the distribution of values of these functions -- sometimes at the edge of the critical strip (where much is known), and sometimes at the center of the critical strip (which is more mysterious).

*"Moments and Distribution of the Riemann Zeta-function and Related L-functions."*Kannan Soundararajan, Stanford University

I will discuss some of the work in this general topic, including connections with random matrix theory. My goal is to give a broad idea of the questions involved, at a level suitable for graduate students.

**October 20, 2015**

**"Stochastic PDEs and Turbulence."
Nathan Glatt-Holtz, MSRI
** I will survey some recent results concerning the ergodic theory of nonlinear stochastic Partial Differential Equations and describe how these results have bearing on various statistical theories of turbulent fluid flow.

**October 27, 2015**

***Special Colloquium***

*"Elementary mathematics behind phenomena like the evolution of life."***David Haussler, University of California, Santa Cruz, Biomolecular Engineering Department**

We look at the some of the simplest mathematical concepts that are relevant to understanding why certain types of physical systems might be expected to evolve life-like structures, including the abstract universe embodied in Conway's Game of Life and others like it. No Ph.D. level mathematical training is assumed for most of the ideas presented.

**November 3, 2015 - CANCELLED
**

*"Phase retrieval, random matrices, and convex optimization."*

**Thomas Strohmer, University of California, Davis**

Phase retrieval is the century-old problem of reconstructing a function, such as a signal or image, from intensity measurements, typically from the modulus of a diffracted wave. Phase retrieval problems - which arise in numerous areas including X-ray crystallography, astronomy, diffraction imaging, and quantum physics - are notoriously difficult to solve numerically. They also pervade many areas of mathematics, such as numerical analysis, harmonic analysis, algebraic geometry, combinatorics, and differential geometry. In a recent breakthrough we have derived a novel framework for phase retrieval, which comprises tools from optimization, random matrix theory, and compressive sensing. In particular, for certain types of random measurements a function, such as a signal or image, can be recovered exactly with high probability by solving a convenient semidefinite program without any assumption about the function whatsoever and under a mild condition on the number of measurements. Our method, known as PhaseLift, is also provably stable in presence of noise. The mathematical tools behind PhaseLift are inspired by Compressive Sensing, a topic that has received enormous attention in recent years. I will conclude with some extensions and open problems. The talk is accessible to a broad audience.

**November 10, 2015
"** I will give an introduction to the shrinking gradient Ricci solitons (GRS), in particular, the noncompact ones, and explain their fundamental importance in the analysis of the singularities of Ricci flow.

*Gradient Shrinking Ricci Solitons."*Peng Lu, University of Oregon

Shrinking GRS is an active field and has been studied by many people. Besides surveying some key results in this field I will also describe some of the results obtained in the joint works with Bennett Chow and Bo Yang.

**November 17, 2015** ***Special Colloquium* ROOM 1240**

**PLEASE NOTE THE ROOM CHANGE
The speaker of this special colloquium is Martin Hairer who was awarded the Fields Medal in 2014 for his contributions to the theory of stochastic partial differential equations, and in particular for the creation of a theory of regularity structures for such equations.
**

**"Taming infinities."**** Martin Hairer, University of Warwick** Some physical and mathematical theories have the unfortunate feature that if one takes them at face value, many quantities of interest appear to be infinite! Various techniques, usually going under the common name of “renormalisation” have been developed over the years to address this, allowing mathematicians and physicists to tame these infinities. We will tip our toes into some of the mathematical aspects of these techniques and we will see how they have recently been used to make precise analytical statements about the solutions of some equations whose meaning was not even clear until now.

**November 24, 2015
** This talk is about a scheme for animating deformable objects and articulated characters based on spacetime optimization. The main feature is that it robustly and quickly generates interesting motion from a sparse set of spacetime constraints. Providing only partial (as opposed to full) keyframes for positions and velocities is sufficient. The computed motion satisfies the constraints and the remaining degrees of freedom are determined by physical principles and the spacetime constraints paradigm.

*"Animations from Spacetime Constraints using Wiggly Splines."*Christian Schulz, Max Planck Institute for Informatics (Saarbruecken) and Research and Development Engineer at PhaseSpace

Our modeling of the spacetime optimization problem combines dimensional reduction, modal coordinates, wiggly splines, and rotation strain warping. This treatment of the optimization problem avoids a time discretization and the resulting method can robustly deal with sparse input and wiggly motion.

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**December 1, 2015**

**"Products of independent random matrices"
**

**Alexander Soshnikov, University of California, Davis**

Consider a large square matrix filled with independent centred entries with unit variance. Then in the limit of large dimension, the eigenvalues of a suitable normalized random matrix uniformly fill the unit disc. This is the celebrated Circular Law proved in its most general form by Tao and Vu in 2010. What happens if one considers a product of several independent random matrices? In my talk I will explain recent joint results with Sean O'Rourke, David Renfrew, and Van Vu on spectral distribution of products of independent elliptic random matrices.