posted Sep 16, 2014, 6:21 PM by AWM Web Editor
Irene M. Gamba, University of Texas at Austin
Twelfth Annual AWMSIAM Kovalevsky Lecture July 7, 2014
Chicago, Illinois USAAbstract. Recent developments in statistical transport modeling, ranging from rarefied gas dynamics, collisional plasmas and electron transport in nanostructures, to selforganized or social interacting dynamics, share a common description based in a Markovian framework of birth and death processes. Under the regime of molecular chaos propagation, their evolution is given by kinetic equations of nonlinear collisional (integral) Boltzmann type. We will present an overview of analytical issues and novel numerical methods for these equations that preserve the expected conserved properties of the described phenomena, while enabling rigorous stability, convergence and error analysis. 
posted Apr 5, 2014, 10:33 AM by AWM Web Editor
Margaret Cheney, Colorado State UniversityEleventh Annual AWMSIAM Kovalevsky Lecture July 8, 2013
San Diego, California USAAbstract. Radar
imaging is a technology that has been developed, very successfully,
within the engineering community during the last 50 years. Radar systems
on satellites now make beautiful images of regions of our earth and of other planets such as Venus. One of the key components of this impressive technology is mathematics, and many of the open problems are mathematical ones. This lecture will explain, from first principles, some of the basics of radar and the mathematics involved in producing highresolution radar images. 
posted Jul 8, 2010, 9:18 PM by Glenna Buford
Dianne P. O'Leary
University of Maryland
Sixth Annual AWMSIAM Kovalevsky Lecture
July 711, 2008
San Diego, CA
Abstract. The adiabatic theorem gives conditions that guarantee that a system defined by Schrödinger's equation remains in its ground state when started in its ground state and evolved slowly. Realistically, such systems are subject to perturbations in the initial condition, systematic timedependent perturbations in the Hamiltonian, coupling to lowenergy quantum systems, and decoherent timedependent perturbations in the Hamiltonian. Using Wilkinsonstyle perturbation analysis, we derive bounds on the effects of these perturbations. This is joint work with Michael J. O'Hara. 
posted Jul 8, 2010, 9:17 PM by Glenna Buford
LaiSang Young
Courant Institute
Fifth Annual AWMSIAM Kovalevsky Lecture
May 30, 2007
Snowbird, UT
Abstract. Guided by a geometric understanding developed in earlier works of Wang and Young, we carry out some numerical studies of shearinduced chaos. The settings considered include periodic kicking of limit cycles, random kicks at Poisson times, and continuoustime driving by white noise. The forcing of a quasiperiodic model describing two coupled oscillators is also investigated. In all cases, positive Lyapunov exponents are found in suitable parameter ranges when the forcing is suitably directed. 
posted Jul 8, 2010, 9:15 PM by Glenna Buford
Irene Fonseca
Carnegie Mellon University
Fourth Annual AWMSIAM Kovalevsky Lecture
July 10, 2006
Boston, Massachusetts
Abstract. Many current questions in applied analysis are motivated by issues in the physical sciences or engineering. They require stateoftheart techniques, new ideas, and the introduction of innovative tools in the calculus of variations, differential equations, and geometric measure theory. This talk will focus on the variational approach as it is used to treat problems on foams, imaging, micromagnetics, and thin structures. 
posted Jul 8, 2010, 9:14 PM by Glenna Buford
Ingrid Daubechies
Princeton University
Third Annual AWMSIAM Kovalevsky Lecture
July 11, 2005
New Orleans, Louisiana
Abstract. This is a story that involves many strands and many players, and like all such stories, it can be told in many ways. I will start by picking up a strand involving superfast wavelet transforms. As the story unfolds, other strands and players will be brought in, to discuss superfast as well as other effective ways in which to compute sparse transforms from what might, at first sight, seem incomplete data. It is a story that features many young researchers, and in which the speaker herself plays an incidental role only. 
posted Jul 8, 2010, 9:12 PM by Glenna Buford
Joyce R. McLaughlin
Rensselaer Polytechnic Institute
Second Annual AWMSIAM Kovalevsky Lecture
July 13, 2004
Portland, Oregon
Abstract. The palpation exam, where the doctor presses against the skin to locate abnormal tissue, senses tissue stiffness changes. We create images of shear stiffness changes using data from Mathias Fink's transient elastography experiment. That experiment yields time and space dependent interior displacements of a propagating elastic wave using an ultrafast ultrasound based imaging technique. In this talk, we present wellposedness results, algorithms and images utilizing positions of the propagating front of the wave. 
posted Jul 8, 2010, 9:10 PM by Glenna Buford
Linda R. Petzold
University of California, Santa Barbara
First Annual AWMSIAM Kovalevsky Lecture
June 20, 2003
Montréal, Québec
Abstract. In microscopic systems formed by living cells, small numbers of reactant molecules can result in dynamical behavior that is discrete and stochastic rather than continuous and deterministic. In simulating and analyzing such behavior it is essential to employ methods that directly take into account the underlying discrete stochastic nature of the molecular events. This leads to an accurate description of the system that in many important cases is impossible to obtain through deterministic continuous modeling (e.g. ODEs). Gillespie’s Stochastic Simulation Algorithm (SSA) has been widely used to treat these problems. However as a procedure that simulates every reaction event, it is prohibitively inefficient for most realistic problems.
We report on our progress in developing a multiscale computational framework for the numerical simulation of chemically reacting systems, where each reaction will be treated at the appropriate scale. The framework is based on a sequence of approximations ranging from SSA at the smallest scale, through a ``birthdeath’’ Markov process approximation, Gillespie’s recentlydeveloped tauleaping approximation, a continuous stochastic differential equation (SDE) approximation, and finally to the familiar reaction rate equations (ODEs) at the coarsest scales. 
