## Seminars and Colloquia by Series

Series: Other Talks
Wednesday, March 3, 2010 - 19:30 , Location: LeCraw Auditorium, College of Management, Room 100 , Nalini Nadkarni , Evergreen State College , Organizer:

Hosted by Academic Affairs Honors Program in collaboration with the College of Sciences.

To watch a 15-minute presentation by Dr. Nadkarni see the

YouTube
link.
Wednesday, March 3, 2010 - 14:00 , Location: Skiles 269 , Doron Lubinsky , Georgia Tech , Organizer: Plamen Iliev
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.
Wednesday, March 3, 2010 - 13:46 , Location: Skiles 269 , Michael Lacey , GT , Organizer: Michael Lacey
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.
Series: PDE Seminar
Tuesday, March 2, 2010 - 15:05 , Location: Skiles 255 , Marius Paicu , Université Paris-Sud , Organizer: Zhiwu Lin
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.
Tuesday, March 2, 2010 - 12:00 , Location: Skiles 255 , Michael Lacey , School of Math, Georgia Tech , Organizer:

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.
Series: Other Talks
Monday, March 1, 2010 - 15:00 , Location: Howey N110 , Kevin Mitchell , University of California, Merced , Organizer:
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.
Monday, March 1, 2010 - 14:00 , Location: Skiles 171 , Doug Ulmer , Georgia Tech , Organizer: Matt Baker
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).
Monday, March 1, 2010 - 13:00 , Location: Skiles 255 , , Mathematics and Computer Science, Emory University , Organizer: Sung Ha Kang
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.
Monday, March 1, 2010 - 13:00 , Location: Skiles 269 , Michael Lacey , GT , Organizer: Michael Lacey
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.
Friday, February 26, 2010 - 15:05 , Location: Skiles 255 , Rui Xu , Department of Mathematics, University of West Georgia , Organizer: Prasad Tetali
The map coloring problem is one of the major catalysts of the tremendous
development of graph theory. It was observed by Tutte that the problem of
the face-coloring of an planar graph can be formulated in terms of integer
flows of the graph. Since then the topic of integer flow has been one of the
most attractive in graph theory. Tutte had three famous fascinating flow
conjectures: the 3-flow conjecture, the 4-flow conjecture and the 5-flow
conjecture. There are some partial results for these three conjectures. But
in general, all these 3 conjectures are open.

Group connectivity is a generalization of integer flow of graphs. It
provides us with contractible flow configurations which play an important
role in reducing the graph size for integer flow problems, it is also
related to all generalized Tutte orientations of graphs. In this talk, I
will present an introduction and survey on group connectivity of graphs as
well as some open problems in this field.