The Department of Applied Mathematics is pleased to host this series of colloquium lectures, funded in part by a generous gift from the Boeing Company. This series will bring to campus prominent applied mathematicians from around the world.

The talks should be of general interest to researchers and students in the mathematical sciences and related fields. All are welcome to attend.

There will be three talks in this series each quarter, on Thursday afternoons at 4:00pm. Each talk will be followed by a reception. Boeing seminars are currently held in Smith Hall 205. Below is a list of the Boeing seminars in the autumn, winter, and spring quarters of the 2013-2014 academic year.

# Autumn Quarter 2013

## October 17, 2013.

## Tamara Kolda, Sandia National Labs

### Analytical and Algorithmic Challenges in Network Analysis

**Abstract:**

## October 24, 2013.

## Bard Ermentrout, University of Pittsburgh

### All the way with Gaston Floquet:

A theory for flicker hallucinations

**Abstract:**

When the human visual system is subjected to diffuse flickering light in the range of 5-25 Hz, many subjects report beautiful swirling colorful geometric patterns.In the years since Jan Purkinje first described them, there have been many qualitative and quantitative analyses of the conditions in which they occur.

Here, we use a simple excitatory-inhibitory neural network to explain the dynamics of these fascinating patterns. We employ a combination of computational and mathematical methods to show why these patterns arise. We demonstrate that the geometric forms of the patterns are intimately tied to the frequency of the flickering stimulus. We combine a Turing-type stability analysis with Floquet stability theory to find parameters regimes where there are flicker-induced hallucinations. We close with some general comments on what symmetric bifurcation theory says about the patterns

## December 5, 2013

## Anna-Karin Tornberg, KTH-Stockholm

**Abstract:**

# Winter Quarter 2014

## February 27, 2014

## David Donoho, Stanford University

**Abstract:**

#### Optimal Shrinkage of Singular Values and Eigenvalues in the Spiked Covariance model

In the 1950′s Charles Stein had the revolutionary insight that in estimating high-dimensional covariance matrices, the empirical eigenvalues ought to be dramatically outperformed by nonlinear shrinkage of the eigenvalues. This insight inspired dozens of papers in mathematical statistics over the next 6 decades. In the last decade, mathematical analysts working in Random Matrix Theory made a great deal of progress on the so-called ‘spiked covariance model’ introduced by Johnstone (2001). This talk will show how this recent progress makes it now possible to elegantly derive the unique asymptotically admissible shrinkage rules in many problems of matrix de-noising and covariance matrix estimation. The new rules are very concrete and simple, and they dramatically outperform heuristics such as scree plot truncation and bulk edge truncation which have been around for decades and are used in thousands of papers across all of science. Joint Work with Matan Gavish and Iain Johnstone

## March 13, 2014

## Mary Wheeler, University of Texas, Austin

**Abstract: **Modeling of Coupled Flow and Mechanics in Fractured Porous Media

The coupling of flow and geomechanics in porous media is a major research topic in energy and environmental modeling. Of specific interest is induced hydraulic fracturing. Here fracking creates fractures from a wellbore drilled into reservoir rock formations. In 2012, more than one million fracturing jobs were performed on oil and gas wells in the United States and this number continues to increase. Clearly there are economic benefits of extracting vast amounts of formerly inaccessible hydrocarbons. In addition, there are environmental benefits in producing natural gas. Opponents to fracking point to environmental impacts such as contamination of ground water, risks to air quality, migration of fracturing chemical and surface contamination from spills to name a few. For this reason, hydraulic fracturing is being heavily scrutinized resulting in the need for accurate and robust mathematical and computational models for treating fluid filled fractures surrounded by a poroelastic medium.

Even in the most basic formulation, hydraulic fracturing is complicated to model since it involves the coupling of (1) mechanical deformation; (ii) the flow of fluids within the fracture and in the reservoir; (iii) fracture propagation. In this presentation we first discuss the modeling of coupled flow and mechanics in a fixed fracture system. We then present an incremental formulation of a phase field model for modeling crack propagation with a fluid filled crack in a poroelastic medium that was recently developed by Andro Mikelić, Mary F. Wheeler, and Thomas Wick. This mathematical model represents a linear elasticity with fading elastic moduli as the crack grows, which is coupled with an elliptic variational inequality for the phase field variable. Computational results of benchmark problems are provided that demonstrate the effectiveness of this approach in treating fracture propagation.

# Spring Quarter 2014

## April 24, 2014

## Richard Murray, Caltech

**Abstract:**

## May 8, 2014

## Peter Olver, University of Minnesota

**Abstract: Dispersion of Rough Data on Periodic Domains**

The evolution, through spatially periodic linear dispersion, of piecewise constant initial data leads to surprising quantized structures at rational times, and fractal, non-differentiable profiles at irrational times. Similar phenomena have been observed in optics and quantum mechanics, and lead to intriguing connections with exponential sums arising in number theory. Ramifications of these observations for numerics, and extensions to more general dispersive linear and nonlinear wave models will be presented and copiously illustrated with movies.