Seminars and Colloquia by Series

Wednesday, September 8, 2010 - 14:00 , Location: Skiles 269 , Manwah Wong , Georgia Tech , Organizer:
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.
Wednesday, September 1, 2010 - 14:00 , Location: Skiles 114 , Yen Do , Georgia Tech , Organizer:
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.
Wednesday, April 28, 2010 - 14:00 , Location: Skiles 269 , Alfredo Deaño , Universidad Carlos III de Madrid (Spain) , Organizer: Plamen Iliev
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).
Wednesday, April 21, 2010 - 14:00 , Location: Skiles 269 , Dolores Barrios , Polytechnical University of Madrid , Organizer: Plamen Iliev
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.
Wednesday, April 14, 2010 - 14:00 , Location: Skiles 269 , Mohammad Ghomi , Georgia Tech , Organizer: Plamen Iliev
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.
Monday, April 5, 2010 - 13:00 , Location: Skiles 269 , Steven Hofmann , University of Missouri , Organizer: Michael Lacey
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.
Wednesday, March 31, 2010 - 14:00 , Location: Skiles 269 , Paul Terwilliger , University of Wisconsin - Madison , Organizer: Plamen Iliev
Wednesday, March 17, 2010 - 14:00 , Location: Skiles 269 , Brett Wick , Georgia Tech , Organizer: Plamen Iliev
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.
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, February 24, 2010 - 14:00 , Location: Skiles 269 , Craig Sloane , Georgia Tech , Organizer: Plamen Iliev
We prove a sharp Hardy inequality for fractional integrals for functions that are supported in a convex domain. The constant is the same as the one for the half-space and hence our result settles a recent conjecture of Bogdan and Dyda.  Further, the Hardy term in this inequality is stronger than the one in the classical case.  The result can be extended as well to more general domains

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