Seminars and Colloquia by Series

Introduction to the AJ Conjecture, Part II

Series
Geometry Topology Working Seminar
Time
Friday, March 5, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Anh TranGeorgia Tech
I will explain another approach to the conjecture and in particular, study it for 2-bridge knots. I will give the proof of the conjecture for a very large class of 2-bridge knots which includes twist knots and many more (due to Le). Finally, I will mention a little bit about the weak version of the conjecture as well as some relating problems.

The geometry of dissipative evolution equation

Series
SIAM Student Seminar
Time
Friday, March 5, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Yao LiGeorgia Tech
Last semester, I reviewed the relation between dynamical system, Fokker-Planck equation and thermodynamics (free energy and Gibbs distribution). This time let's go further. I will review the geometric properties of a kind of dissipative evolution equations. I will explain why this kind of evolutionary equations (Fokker-Planck equation, nonlinear Fokker-Planck equation, Porous medium equation) are the gradient flow of some energy function on a Riemannian manifold -- 2-Wasserstein metric space.

Segmentation with hidden Markov model

Series
Stochastics Seminar
Time
Thursday, March 4, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Dr Juri LemberTartu University, Estonia
Abstract: We consider the hidden Markov model, where the dynamic of theprocess is modelled by a latent Markov chain Y and the observations X aresuch that: 1) given the realization of Y, the observations areindependent; 2) the distribution of the i-th observations (X_i) depends onthe i-th element of the Y (Y_i), only.The segmentation problem consists of estimating the underlying realization(path) of Y given the n observation. Usually the realization with maximumlikelihood, the so called Viterbi alignment is used. On the other hand, itis easy to see that the Viterbi alignment does not minimize the expectednumber of misclassification errors.We consider the segmentation problem in the framework of statisticallearning. This unified risk-based approach helps to analyse many existingalignments as well as defining many new ones. We also study theasymptotics of the risks and infinite alignments.

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 HoopDepartment 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 LubinskyGeorgia 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 LaceyGT
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 PaicuUniversité 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 LaceySchool 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 MitchellUniversity 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.

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