Seminars and Colloquia by Series

Non-homogeneous Harmonic Analysis and randomized Beylkin--Coifman--Rokhlin algorithm (BCR): an application for the solutions of A2 conjecture.

Series
Analysis Seminar
Time
Wednesday, September 15, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Alexander VolbergMichigan State
A2 conjecture asked to have a linear estimate for simplest weighted singular operators in terms of the measure of goodness of the weight in question.We will show how the paradigm of non-homogeneous Harmonic Analysis (and especially its brainchild, the randomized BCR) was used to eventually solve this conjecture.

The Point Mass Problem on the Real Line

Series
Analysis Seminar
Time
Wednesday, September 8, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Manwah WongGeorgia Tech
In this talk, I will talk about recent developments on the point mass problem on the real line. Starting from the point mass formula for orthogonal polynomials on the real line, I will present new methods employed to compute the asymptotic formulae for the orthogonal polynomials and how these formulae can be applied to solve the point mass problem when the recurrence coefficients are asymptotically identical. The technical difficulties involved in the computation will also be discussed.

A Variational Estimate for Paraproducts

Series
Analysis Seminar
Time
Wednesday, September 1, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Yen DoGeorgia Tech
We show variational estimates for paraproducts, which can be viewed as bilinear generalizations of L\'epingle’s variational estimates for martingale averages or scaled families of convolution operators. The heart of the matter is the case of low variation exponents. Joint work with Camil Muscalu and Christoph Thiele.

On complex orthogonal polynomials related with Gaussian quadrature of oscillatory integrals

Series
Analysis Seminar
Time
Wednesday, April 28, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Alfredo DeañoUniversidad Carlos III de Madrid (Spain)
We present results on the asymptotic behavior of a family of polynomials which are orthogonal with respect to an exponential weight on certain contours of the complex plane. Our motivation comes from the fact that the zeros of these polynomials are the nodes for complex Gaussian quadrature of an oscillatory integral defined on the real axis and having a high order stationary point. The limit distribution of these zeros is also analyzed, and we show that they accumulate along a contour in the complex plane that has the S-property in the presence of an external field. Additionally, the strong asymptotics of the orthogonal polynomials is obtained by applying the nonlinear Deift--Zhou steepest descent method to the corresponding Riemann--Hilbert problem. This is joint work with D. Huybrechs and A. Kuijlaars, Katholieke Universiteit Leuven (Belgium).

Interpretation of some integrable systems via multiple orthogonal polynomials

Series
Analysis Seminar
Time
Wednesday, April 21, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Dolores BarriosPolytechnical University of Madrid
Some discrete dynamical systems defined by a Lax pair are considered. The method of investigation is based on the analysis of the matrical moments for the main operator of the pair. The solutions of these systems are studied in terms of properties of this operator, giving, under some conditions, explicit expressions for the resolvent function.

Tangent cones and regularity of real hypersurfaces

Series
Analysis Seminar
Time
Wednesday, April 14, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Mohammad GhomiGeorgia Tech
The tangent cone of a set X in R^n at a point p of X is the limit of all rays which emanate from p and pass through sequences of points p_i of X as p_i converges to p. In this talk we discuss how C^1 regular hypersurfaces of R^n may be characterized in terms of their tangent cones. Further using the real nullstellensatz we prove that convex real analytic hypersurfaces are C^1, and will also discuss some applications to real algebraic geometry.

Extrapolation of Carleson measures

Series
Analysis Seminar
Time
Monday, April 5, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Steven HofmannUniversity of Missouri
We discuss joint work with J.-M. Martell, in which werevisit the ``extrapolation method" for Carleson measures, originallyintroduced by John Lewis to proveA_\infty estimates for certain caloric measures, and we present a purely real variable version of the method. Our main result is a general criterion fordeducing that a weight satisfies a ReverseHolder estimate, given appropriate control by a Carleson measure.To illustrate the useof this technique,we reprove a well known theorem of R. Fefferman, Kenig and Pipherconcerning the solvability of the Dirichlet problem with data in some L^p space.

Interpolation in the Drury-Arveson Space

Series
Analysis Seminar
Time
Wednesday, March 17, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Brett WickGeorgia Tech
The Drury-Arveson space of functions on the unit ball in C^n has recently been intensively studied from the point of view function theory and operator theory. While much is known about this space of functions, a characterization of the interpolating sequences for the space has still remained elusive. In this talk, we will discuss the relevant background of the problem, and then I will discuss some work in progress and discuss a variant of the question for which we know the answer completely.

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.

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