37th, 38th, and 39th Arkansas Spring Lecture Series in the Mathematical Sciences

数学科学(SLS)第37、38和39届阿肯色州春季系列讲座将于2012年、2013年和2014年在阿肯色州费耶特维尔的阿肯色大学举行。每个SLS包括主讲人的5场演讲，由主讲人选择的特邀演讲者的10场45分钟的演讲，以及研究生和新近的博士S贡献的几场20分钟的演讲。2012年的主题是“高维椭圆型边值问题”。会议将于2012年4月12日至14日举行。主要演讲人将是斯坦福大学的Rafe Mazzeo教授。Mazzeo教授将专注于几何微局部方法，该方法源于梅尔罗斯和他的学校的工作。这包含了各种各样的问题，包括对具有圆锥点和边的空间上的算子的详细分析，以及关于一般分层空间的一些不太详细的结果。除了这些一般的分析方法，讲座还将着眼于将这些工具应用于具体的几何问题，涉及线性和非线性算子。2013年的主题将是“扩展和内插”。会议将于2013年4月4日至6日举行。主要演讲人将是普林斯顿大学的查尔斯·费弗曼教授。费弗曼教授的演讲将解决以下问题：假设我们被定义在欧几里德空间的一个有限子集上的函数f，由N个数据点组成。我们如何在所有欧氏空间上计算一个m次可微函数F，使其在数据点与f一致(精确或近似)，并且对前m个导数具有最小可能的范数？它需要多少次计算机操作？如果我们被允许丢弃一些数据点会怎么样？应该丢弃哪些点才能在插补中实现最佳改进？2014年的主题是“多参数几何与分析”。会议将于2014年4月10日至12日举行。主要演讲人将是威斯康星大学的亚历山大·内格尔教授。复分析和调和分析中的许多结果建立了线性或次线性算子的有界性，这些结果可以用几何和齐次型空间的分析来表示。这一概念为经典的Calderon-Zygmund极大函数理论以及奇异积分和分数次积分的基本概念提供了一个一般的抽象设置。在一个重要意义上，以齐型空间为范型的理论是单参数理论。Nagel教授的讲座将集中在复数和调和分析中的一些初步观察和结果，这些不属于标准的单参数理论。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。按照阿肯色州春季系列讲座的传统，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。2012年洛伦佐·萨登教授、2013年阿利·彼得斯教授和2014年科林·亚当斯教授的公开演讲将向广大公众发表讲话。其他活动包括非正式午餐讨论，讨论与数学领域女性相关的问题(由阿肯色州统计和数学领域的女性主办)，以及为阿肯色州研究生和外部研究生举办的招待会，让他们见面并比较他们的职业生涯。

The 37th, 38th, and 39th Arkansas Spring Lecture Series in the Mathematical Sciences (SLS) will take place in 2012, 2013, and 2014 at the University of Arkansas, in Fayetteville, AR. Each SLS will consist of five lectures by the principal speaker, ten 45-minute talks by invited speakers chosen by the principal speaker, and several twenty-minute contributed talks by graduate students and recent Ph.D.'s. The topic in 2012 will be "Higher Codimensional Elliptic Boundary Value Problems." The conference will take place April 12-14, 2012. The principal speaker will be Professor Rafe Mazzeo from Stanford University. Professor Mazzeo will focus on the geometric microlocal method, stemming from the work of Melrose and his school. That encompasses a wide variety of problems, and includes detailed analyses of operators on spaces with conic points and edges, as well as somewhat less detailed results on general stratified spaces. Beyond these general analytic approaches, talks will look at applying these tools to specific geometric problems, involving both linear and nonlinear operators. The topic in 2013 will be "Extension and Interpolation." The conference will take place April 4-6, 2013. The principal speaker will be Professor Charles Fefferman of Princeton University. Professor Fefferman's talks will address the following questions: suppose we are given a function f defined on a finite subset of Euclidean space, consisting of N data points. How can we compute an m-times differentiable function F on all of Euclidean space that agrees (exactly or approximately) with f at the data points, and has the least possible norm for the first m derivatives? How many computer operations does it take? What if we are allowed to discard a few of the data points? Which points should be discarded to achieve the best improvement in the interpolation? The topic in 2014 will be ''Multi-parameter Geometry and Analysis.'' The conference will take place April 10-12, 2014. The principal speaker will be Professor Alexander Nagel of the University of Wisconsin. Many results in complex and harmonic analysis in which one establishes the boundedness of some linear or sub-linear operator can be formulated in terms of geometry and analysis on spaces of 'homogeneous type'. This concept provides a general abstract setting for the concepts underlying classical Calderon-Zygmund theory of maximal functions and singular and fractional integrals. In an important sense, a theory which uses spaces of homogeneous type as a paradigm is a one-parameter theory. Professor Nagel's lectures will focus on some preliminary observations and results in complex and harmonic analysis which fall outside this standard one parameter theory.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 Series, 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 Lorenzo Sadun in 2012, by Professor Arlie Petters in 2013, and by Professor Colin Adams in 2014 will address audiences of the public at large. Other events include an informal lunch discussion where issues related to being women in mathematics are discussed (hosted by Arkansas Women in Statistics and Mathematics) and a reception for Arkansas graduate students and external graduate students to meet and compare their careers.