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Series: Other Talks

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.

YouTube link.

Series: Analysis Seminar

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.

Series: Analysis Working Seminar

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.

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

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.

Series: Research Horizons Seminar

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.

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

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.

Series: Algebra Seminar

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).

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 ,
James G. Nagy ,
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.

Series: Analysis Working Seminar

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.

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.

Series: Combinatorics Seminar

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.

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.