Seminars and Colloquia by Series

Wednesday, June 15, 2011 - 14:00 , Location: Skiles 05 , Dr Anna Maltsev , University of Bonn , Organizer:
We consider ensembles of $N \times N$ Hermitian Wigner matrices, whose entries are (up to the symmetry constraints) independent and identically distributed random variables. Assuming sufficient regularity for the probability density function of the entries, we show that the expectation of the density of states on arbitrarily small intervals converges to the semicircle law, as $N$ tends to infinity.
Wednesday, April 27, 2011 - 14:00 , Location: Skiles 005 , Yuliya Babenko , Kennesaw State University , Organizer:
Wednesday, April 20, 2011 - 14:00 , Location: Skiles 005 , Maria Reguera Rodriguez , Georgia Tech , Organizer:
We consider boundedness of singular integrals in the two weight setting. The problem consists in characterizing non-negative weights v and w for which H: L^{p}(v)\mapsto L^{p}(w) for 1
Wednesday, April 13, 2011 - 14:00 , Location: Skiles 005 , Mishko Mitkovski , School of Mathematics, Georgia Tech , Organizer:
It is well known that, via the Bargmann transform, the completeness problems for both Gabor systems in signal processing and coherent states in quantum mechanics are equivalent to the uniqueness set problem in the Bargmann-Fock space. We introduce an analog of the Beurling-Malliavin density to try to characterize these uniqueness sets and show that all sets with such density strictly less than one cannot be uniqueness sets. This is joint work with Brett Wick.
Wednesday, April 6, 2011 - 14:00 , Location: Skiles 005 , Karl Deckers , Georgia Tech , Organizer:
Consider a positive bounded Borel measure \mu with infinite supporton an interval [a,b], where -oo <= a < b <= +oo, and assume we have m distinctnodes fixed in advance anywhere on [a,b]. We then study the existence andconstruction of n-th rational Gauss-type quadrature formulas (0 <= m <= 2)that approximate int_{[a,b]} f d\mu. These are quadrature formulas with npositive weights and n distinct nodes in [a,b], so that the quadratureformula is exact in a (2n - m)-dimensional space of rational functions witharbitrary complex poles fixed in advance outside [a,b].
Wednesday, March 30, 2011 - 14:00 , Location: Skiles 005 , Sergey Denissov , University of Wisconsin-Madison , denissov@math.wisc.edu , Organizer:
 We consider the 1d wave equation and prove the propagation of the wave provided that the potential is square summable on the  half-line. This result is sharp. 
Wednesday, March 16, 2011 - 14:00 , Location: Skiles 005 , Betsy Stovall , UCLA , Organizer: Michael Lacey
We will discuss a proof that finite energy solutions to the defocusing cubicKlein Gordon equation scatter, and will discuss a related result in thefocusing case.  (Don't worry, we will also explain what it means for asolution to a PDE to scatter.)  This is joint work with Rowan Killip andMonica Visan.
Thursday, March 10, 2011 - 15:00 , Location: Skiles 006 , Ka-Sing Lau , Hong Kong Chinese University , Organizer:
There is a large literature to study the behavior of the image curves f(\partial {\mathbb D}) of analytic functions f on the unit disc {\mathbb D}. Our interest is on the class of analytic functions f for which the image curves f(\partial {\mathbb D}) form infinitely many (fractal) loops. We formulated this as the Cantor boundary behavior (CBB). We develop a general theory of this property in connection with the analytic topology, the distribution of the zeros of f'(z) and the mean growth rate of f'(z) near the boundary. Among the many examples, we showed that the lacunary series such as the complex Weierstrass functions have the CBB, also the Cauchy transform F(z) of the canonical Hausdorff measure on the Sierspinski gasket, which is the original motivation of this investigation raised by Strichartz.
Wednesday, March 9, 2011 - 14:00 , Location: Skiles 005 , Michael Loss , School of Mathematics, Georgia Tech , Organizer: Jeff Geronimo
This talk is about a random Schroedinger operator describing the dynamics of an electron in a randomly deformed lattice. The periodic displacement configurations which minimize the bottom of the spectrum are characterized. This leads to an amusing problem about minimizing eigenvalues of a Neumann Schroedinger operator with respect to the position of the potential. While this configuration is essentially unique for dimension greater than one, there are infinitely many different minimizing configurations in the one-dimensional case. This is joint work with Jeff Baker, Frederic Klopp, Shu Nakamura and Guenter Stolz.
Wednesday, March 2, 2011 - 14:00 , Location: Skiles 005 , Camil Muscalu , Cornell , Organizer: Michael Lacey
 Calderon's algebra can be thought of as a world whichincludes singular integral operators and operators of multiplicationwith functions which grow at most linearly (more precisely, whose firstderivatives are bounded).The goal of the talk is to address and discuss in detail the followingnatural question: "Can one meaningfully extend it to include operatorsof multiplication with functions having polynomial growth as well ?".

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