Two Spring Lecture Series in Analysis and PDE

第33届和第34届阿肯色州数学科学(ASL)春季讲座将于2008年和2009年在阿肯色州费耶特维尔的阿肯色大学举行。重点主题如下。ASL 2008：“共形几何中的偏微分方程式”。会议将于2008年4月10日至12日举行。主讲嘉宾为普林斯顿大学张善荣教授。由张教授挑选的十位受邀演讲者将另外进行一小时的演讲，以及研究生和最近的博士们20分钟的演讲。张教授的演讲将涉及以下问题的几何和偏微分方程方面的相互作用：(A)研究完全非线性偏微分方程组，以研究黎曼流形上Ricci张量的特征值；(B)渐近双曲流形上的散射理论与共形不变量和共形协变算子的Fefferman-Graham构造之间的联系；(C)对维度大于2的流形上的Paneitz-Branson q-曲率的研究。对于ASL 2009：“差异功能的新发展，以及相关结果。”会议将于2009年4月16日至18日举行。主讲人是佐治亚理工学院的迈克尔·莱西教授。由莱西教授挑选的十位受邀演讲者将另外进行一小时的演讲，研究生和最近的博士将发表几篇20分钟的演讲。莱西教授将讲解关于点相对于单位立方体中矩形的不规则分布的研究。特别是，他将基于几个领域的相互作用描述关于差异函数的最新结果：调和分析(端点Littlewood-Paley估计)、概率理论(小球概率)和逼近理论(立方体公式；函数类的复杂性)。莱西教授的讲座将解释技术问题，以及这些学科领域之间的相互联系。数学会议对该领域的发展至关重要。它们为来自不同分领域的科学家提供了独特的会面机会，以便(A)总结这些领域的最新进展及其相互作用，(B)以足够详细的方式提出新的研究方向，以制定和制定未决问题清单，以及(C)提供机会，促进新的合作和交流意见，以解决重要的未决问题。按照阿肯色州春季讲座的传统，这些会议将为年轻的研究人员和研究生提供与各自研究领域的知名专家互动的独特机会。弗兰克·摩根教授(威廉姆斯学院)08年和莱西教授(佐治亚理工学院)09年的公开演讲将面向高中生和广大公众听众。

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.