Brown University home page Math Department Home Page Sergei Treil home page Brown University Department of Mathematics Analysis seminar, Fall 2003 Wednesdays 4:00-5:00 pm Kassar House 105 Hit "reload" often for the latest version Date  Speaker Title of the talk       9/10 Janine Wittwer, Williams College, visiting Brown Title: A fun lemma Abstract: In this talk, we will see how to use Bellman Functions to disprove a bound for a mixed type square function.  9/17 Sergei Treil, Brown University  Title: The Operator Corona Theorem and Geometry of Holomorphic Vector Bundles Abstract: In this talk we will discuss the connection between the operator corona problem and geometry of holomorphic vector bundles. This will lead to some new results in the operator corona problem, as well as to new open problems related to the corona problem in planar domains or in several complex variables.  9/24 Jill Pipher, Brown University          10/1 Alex Izzo, Bowling Green University, visiting Brown Title: Algebras containing bounded holomorphic functions 10/8 Alex Izzo, Bowling Green University, visiting Brown Title: Algebras containing bounded holomorphic functions, II 10/15 Svetlana Roudenko,  Duke University  Title: Level Set Operators vs. Oscillatory Integral Operators Abstract: Both oscillatory integral operators and level set operators appear naturally in the study of properties of degenerate Fourier integral operators (for example, generalized Radon transforms). The properties of oscillatory integral operators have a longer history and are better understood. On the other hand, level set operators, while sharing many common characteristics with oscillatory integral operators, seem easier to handle. We study L2 estimates on level set operators and compare them with what is known about oscillatory integral operators. The cases we consider include operators in one dimension with arbitrary smooth phase functions, operators in 2 dimensions with "non-degenerate" and certain cases of the "degenerate" phase functions. In particular, we discuss the level set version of the Radon transform of Melrose and Taylor. Operators in higher dimensions are considered as well. The estimates are formulated in terms of the Newton polyhedra and the singularity types of the projections from the canonical relation defined by the phase. (join work with Andrew Comech) 10/22 Brian Cole,  Brown University  Title: Interpolation bodies for general domains  Abstract: Clearly, if two domains are biholomorphically equivalent, then they have equivalent sets of interpolation bodies. We are interested in conditions under which the converse implication holds. This is joint work with John Wermer. 10/29 Alexander Kheifets,   U. Mass, Lowell Title: Abstract Interpolation in Scattering Setting click here to see the abstract (pdf format)       11/5 John Wermer,  Brown University  Title: The Argument Principle and Analytic Continuation. Abstract: Let S be the unit circle and let f be a continuous function defined on S. When does f admit an analytic continuation to the unit disk? The classical condition is : the integral of  f times z^{n} dz, over S, = 0 for n = 0,1,2,... Recently J. Globevnik gave a different criterion for the existence of an analytic extension, related to the argument principle. We shall discuss his result, and give an application to function spaces on a Riemann surface. 11/12 Martin Dindos,  Cornell University Title: Large solutions for Yamabe and similar problems on domains in Riemannian manifolds  click here to see the abstract (pdf format) 11/19 Gilad Lerman NYU Title: Multiscale Geometric Analysis via the Multistrip Method 11/26           12/3 Irina Mitrea,  Cornell University Title: On the global regularity of conformal maps Abstract: We study the Besov regularity of conformal mappings for  domains with rough boundary. Our analysis is based on well-posedness results of the Dirichlet problem for  the Laplacian with Besov data. 12/10 Stas Kupin Brown