Two Spring Lecture Series in Analysis and PDE

第33届和第34届阿肯色州春季数学科学讲座（ASL）将于2008年和2009年在阿肯色州费耶特维尔的阿肯色州大学举行。 重点议题如下。 2008年美国数学学会（ASL）：“Partial Differential Equations in Conformal Geometry”。 会议将于2008年4月10日至12日举行。 主讲人是普林斯顿大学的张善勇教授。将有额外的1小时的演讲，由张教授选择的10位特邀演讲者，以及研究生和最近的博士的几个20分钟的演讲。 张教授的讲座将探讨以下问题的几何与偏微分方程之间的相互关系：（a）研究黎曼流形上Ricci张量的特征值的完全非线性偏微分方程;（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Fergusman-Graham构造之间的联系;（c）研究维数大于2的流形上的Paneitz-Branson Q-曲率。 对于ASL 2009：“离散函数的新发展和相关结果。“会议将于2009年4月16日至18日举行。 主讲人是格鲁吉亚理工学院的迈克尔·莱西教授。将有额外的1个小时的演讲，由莱西教授选择的10位特邀演讲者，以及研究生和最近的博士学位的几个20分钟的演讲。 教授莱西将解决的不规则性的研究点的分布相对于矩形的单位立方体。 特别是，他将描述最近的结果差异功能，根据相互作用的几个领域：谐波分析（端点Littlewood-Paley估计），概率论（小球概率），和近似理论（立方公式;复杂性的功能类）。 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。它们为来自不同子领域的科学家提供了独特的机会，以便（a）总结这些领域的最新进展及其相互作用，（B）提出新的研究方向，并提供足够的细节来制定和开发一个开放问题清单，以及（c）提供一个机会来促进新的合作和交流思想，以解决重要的开放问题。 在阿肯色州春季讲座的传统，这些会议将提供独特的机会，为年轻的研究人员和研究生与他们的研究领域的著名专家互动。公开讲座教授弗兰克摩根（威廉姆斯学院）'08和教授莱西（格鲁吉亚技术）'09将解决观众的高中生和广大公众。

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.