Two Spring Lecture Series in Analysis and PDE

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The 33-rd and 34-th Arkansas Spring Lectures in the Mathematical Sciences (ASL) will take place in 2008 and 2009 at the University of Arkansas, in Fayetteville, AR. The focus topics are the following. For the ASL 2008: "Partial Differential Equations in Conformal Geometry". The conference will take place on April 10-12, 2008. The principal speaker is Professor Sun-Yung Alice Chang from Princeton University. There will be additional 1 hour talks by ten invited speakers, chosen by professor Chang, and several 20 minute contributed talks by graduate students and recent PhD's. Professor Chang's talks will address the interplay between the geometric and PDE aspects of the following problems: (a) The study of fully non-linear PDE to study the eigenvalues of the Ricci tensor on a Riemannian manifolds; (b) The connection between the scattering theory on asymptotically hyperbolic manifold and the Fefferman-Graham construction of conformal invariants and conformal covariant operators; (c) The study of the Paneitz-Branson Q-curvature on manifolds of dimension greater than two. For the ASL 2009:"New Developments on the Discrepancy Function, and related results." The conference will take place on April 16-18, 2009. The principal speaker is Professor Michael Lacey of the Georgia Institute of Technology. There will be additional 1 hour talks by ten invited speakers, chosen by professor Lacey, and several 20 minute contributed talks by graduate students and recent PhD's. Professor Lacey will address the study of irregularities of distribution of points with respect to rectangles in the unit cube. In particular he will describe recent results on the discrepancy function, based on the interplay of several fields: Harmonic Analysis (endpoint Littlewood-Paley estimates), Probability Theory (Small Ball Probabilities), and Approximation Theory (Cubature Formulas; Complexity of Function Classes). Professor Lacey's lectures will explain the technical issues, and the interconnections between these subject areas. Mathematics conferences are vital to the development of the field. They provide unique opportunity for scientists from different subfields to meet so as to (a) summarize the most recent progress in these fields, and their interactions, (b) present new directions of research with sufficient detail to formulate and develop a list of open problems, and (c) Provide an opportunity to foster new collaborations and exchange ideas toward the solution of important open questions. In the tradition of the Arkansas Spring Lectures, these meetings will provide unique opportunities for young researchers and graduate students to interact with prominent experts in their research areas. Public talks by Professor Frank Morgan (Williams College) '08 and by Professor Lacey (Georgia Tech) '09 will address audiences of high school students and the public at large.