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

第 37 届、第 38 届和第 39 届阿肯色州春季数学科学系列讲座

• 批准号: 1157517
• 负责人: Phillip Harrington
• 金额: $ 9万
• 依托单位: University of Arkansas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-03-01 至 2016-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1157517&HistoricalAwards=false
• 关键词: 37th; 38th; 39th; Arkansas; Spring

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.

第37届、第38届和第39届阿肯色州春季数学科学系列讲座将于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。每次春季系列讲座将由主要演讲者讲授5次，由主要演讲者选择的10次45分钟的演讲，以及由研究生和最近的博士们讲授的几次20分钟的演讲。2012年的主题是“高协维椭圆边值问题”。会议将于2012年4月12日至14日举行。主讲人是斯坦福大学的Rafe Mazzeo教授。Mazzeo教授将专注于几何微局部方法，源于梅尔罗斯和他的学校的工作。它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，以及对一般分层空间的不太详细的结果。除了这些一般的分析方法，讲座将着眼于将这些工具应用于具体的几何问题，包括线性和非线性算子。2013年的主题是“扩展和插值”。会议将于2013年4月4日至6日举行。主要发言人将是普林斯顿大学的查尔斯·费费曼教授。Fefferman教授的讲座将讨论以下问题：假设我们给定一个函数f，它定义在欧几里德空间的有限子集上，由N个数据点组成。我们如何在整个欧几里德空间中计算一个m倍可微函数F，它在数据点上（完全或近似）与F一致，并且前m阶导数的范数最小？这需要多少次电脑操作？如果我们可以丢弃一些数据点呢？哪些点应该被丢弃以达到插值的最佳改进？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。主讲人将是威斯康星大学的亚历山大·内格尔教授。在复谐分析中，许多建立线性或次线性算子有界性的结果可以用齐次型空间上的几何和分析来表述。这个概念为经典Calderon-Zygmund理论的极大函数和奇异积分和分数积分的概念提供了一个一般的抽象设置。在一个重要的意义上，一个以同质型空间为范式的理论是一个单参数理论。Nagel教授的讲座将集中于一些初步的观察和结果，在复谐分析中，它们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。他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，以及他们之间的相互作用，(b)提供新的研究方向，并提供足够的细节来制定和发展一系列开放问题，(c)提供机会来促进新的合作和交流思想，以解决重要的开放问题。在阿肯色春季系列讲座的传统中，这些会议将为年轻的研究人员和研究生提供独特的机会，与他们研究领域的杰出专家进行互动。2012年Lorenzo Sadun教授、2013年Arlie Petters教授和2014年Colin Adams教授的公开演讲将面向广大公众。其他活动包括非正式的午餐讨论，讨论与数学领域女性相关的问题（由阿肯色州统计和数学女性主办），以及阿肯色州研究生和外部研究生见面并比较他们的职业生涯的招待会。