Seminars and Colloquia by Series

Inverse scattering and wave-equation tomography - Imaging Earth's deep interior

Series
School of Mathematics Colloquium
Time
Thursday, March 4, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Maarten V. de Hoop – Department of Mathematics, Purdue University
Much research in modern, quantitative seismology is motivated -- on the one hand -- by the need to understand subsurface structures and processes on a wide range of length scales, and -- on the other hand -- by the availability of ever growing volumes of high fidelity digital data from modern seismograph networks or multicomponent acquisition systems developed for hydro-carbon exploration, and access to increasingly powerful computational facilities. We discuss (elastic-wave) inverse scattering of reflection seismic data, wave-equation tomography, and their interconnection using techniques from microlocal analysis and applied harmonic analysis. We introduce a multi-scale approach and present a framework of partial reconstruction in connection with limited boundary acquisition geometry. The formation of caustics leads to one of the complications which will be discussed. We illustrate various aspects of this research program with examples from global seismology and mineral physics coupled to thermo-chemical convection.

For compactly supported measures, universality holds in measure

Series
Analysis Seminar
Time
Wednesday, March 3, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Doron Lubinsky – Georgia Tech
Let mu be a measure with compact support, with orthonormal polynomials {p_{n}} and associated reproducing kernels {K_{n}}. We show that bulk universality holds in measure in {x:mu'(x)>0}. The novelty is that there are no local or global conditions on the measure. Previous results have required regularity as a global condition, and a Szego condition as a local condition.As a consequence, for a subsequence of integers, universality holds for a.e. x. Under additional conditions on the measure, we show universality holds in an L_{p} sense for all finite p>0.

Two weight Inequality for Hilbert transform

Series
Analysis Working Seminar
Time
Wednesday, March 3, 2010 - 13:46 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Michael Lacey – GT
We start the sufficiency proof of arXiv:1001.4043, which characterizes the two weight inequality for the Hilbert transform. This session will be devoted to the martingale methods employed. Joint work with Ignacio Uriate-Tuero, and Eric Sawyer.

Global solutions for the Navier-Stokes equations with some large initial data

Series
PDE Seminar
Time
Tuesday, March 2, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Marius Paicu – Université Paris-Sud
We consider the three dimensional Navier-Stokes equations with a large initial data and we prove the existence of a global smooth solution. The main feature of the initial data is that it varies slowly in the vertical direction and has a norm which blows up as the small parameter goes to zero. Using the language of geometrical optics, this type of initial data can be seen as the ``ill prepared" case. Using analytical-type estimates and the special structure of the nonlinear term of the equation we obtain the existence of a global smooth solution generated by this large initial data. This talk is based on a work in collaboration with J.-Y. Chemin and I. Gallagher and on a joint work with Z. Zhang.

Two weight inequality for the Hilbert transform

Series
Research Horizons Seminar
Time
Tuesday, March 2, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Michael Lacey – School of Math, Georgia Tech

Please Note: Hosted by: Huy Huynh and Yao Li

The Hilbert transform is a foundational transform, with deep connections to electrical charge, and analyticity. The `two weight inequality for the Hilbert transform' concerns the most general setting in which the Hilbert transform admits a (weighted) L^2 inequality. We will give a couple of (surprising?) ways that this question arises. And we will indicate the surprise that is behind the recent description of all setting in which the two weight inequality holds.

How to Partition a Mixed Phase Space - with Applications to Atomic Physics

Series
Other Talks
Time
Monday, March 1, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Howey N110
Speaker
Kevin Mitchell – University of California, Merced
Hamiltonian systems typically exhibit a mixture of chaos and regularity, complicating any scheme to partition phase space and extract a symbolic description of the dynamics. In particular, the dynamics in the vicinity of stable islands can exhibit extremely complicated topology. We present an approach to extracting symbolic dynamics in such systems using networks of nested heteroclinic tangles-- fundamental geometric objects that organize phase space transport. These tangles can be used to progressively approximate the behavior in the vicinity of stable island chains. The net result is a symbolic approximation to the dynamics, and an associated phase-space partition, that includes the influence of stable islands. The utility of this approach is illustrated by examining two applications in atomic physics -- the chaotic escape of ultracold atoms from an atomic trap and the chaotic ionization of atoms in external fields.

Explicit points on the Legendre elliptic curve

Series
Algebra Seminar
Time
Monday, March 1, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Doug Ulmer – Georgia Tech
It turns out to be very easy to write down interesting points on the classical Legendre elliptic curve y^2=x(x-1)(x-t) and show that they generate a group of large rank. I'll give some basic background, explain the construction, and discuss related questions which would make good thesis projects (both MS and PhD).

Large-Scale Inverse Problems in Imaging

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 1, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
James G. Nagy – Mathematics and Computer Science, Emory University
Large-scale inverse problems arise in a variety of importantapplications in image processing, and efficient regularization methodsare needed to compute meaningful solutions. Much progress has beenmade in the field of large-scale inverse problems, but many challengesstill remain for future research. In this talk we describe threecommon mathematical models including a linear, a separable nonlinear,and a general nonlinear model. Techniques for regularization andlarge-scale implementations are considered, with particular focusgiven to algorithms and computations that can exploit structure in theproblem. Examples will illustrate the properties of these algorithms.

Two Weight inequalities for Hilbert Transform

Series
Analysis Working Seminar
Time
Monday, March 1, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Michael Lacey – GT
We start the proof of arXiv:1001.4043, which characterizes the two weight inequality for the Hilbert transform. This session will be devoted to necessity of the Poisson A_2 condition and the Energy Condition. Joint work with Ignacio Uriate-Tuero, and Eric Sawyer.

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