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

第37届，第38届和第39届阿肯色州春季讲座系列在数学科学（SLS）将于2012年，2013年和2014年在阿肯色州，费耶特维尔，AR大学举行。每个SLS将包括主要演讲者的五个讲座，由主要演讲者选择的特邀演讲者的十个45分钟的演讲，以及研究生和最近的博士的几个20分钟的贡献演讲。's. 2012年的主题是“高阶余维椭圆边值问题”。“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。这包含了各种各样的问题，并包括详细的分析运营商的空间与圆锥点和边缘，以及有点不太详细的结果一般分层空间。 除了这些一般的分析方法，会谈将着眼于将这些工具应用到具体的几何问题，涉及线性和非线性算子。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·费曼教授。教授February man的会谈将解决以下问题：假设我们给出了一个函数f定义在有限子集的欧几里得空间，由N个数据点。我们如何计算一个在所有欧几里得空间上的m次可微函数F，它在数据点上与f一致（精确或近似），并且前m阶导数的范数最小？需要多少次计算机操作？如果我们被允许丢弃一些数据点呢？哪些点应该被丢弃，以实现插值的最佳改进？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。主讲人是威斯康星州大学的亚历山大内格尔教授。许多结果在复杂的和调和分析，其中一个建立有界的一些线性或次线性算子可以制定在几何和分析的空间上的“齐型”。这个概念提供了一个一般的抽象设置的概念基础的经典卡尔德龙-齐格蒙德理论的极大函数和奇异和分数积分。 在一个重要的意义上，使用齐型空间作为范式的理论是单参数理论。 教授内格尔的讲座将集中在一些初步的意见和结果复杂和谐波分析属于这个标准的一个参数理论。数学会议是至关重要的发展领域。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系列的传统，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。Lorenzo Sadun教授在2012年、Arlie Petters教授在2013年和Colin亚当斯教授在2014年的公开演讲将面向广大公众。其他活动包括一个非正式的午餐讨论，其中有关妇女在数学的问题进行了讨论（由阿肯色州妇女统计和数学主办）和接待阿肯色州研究生和外部研究生，以满足和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.