Two Spring Lecture Series in Geometric Analysis

几何分析中的两个春季讲座系列

• 批准号: 0963810
• 负责人: Andrew Raich
• 金额: $ 8.58万
• 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: 2010
• 资助国家: 美国
• 起止时间: 2010-04-01 至 2013-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0963810&HistoricalAwards=false
• 关键词: Two; Spring; Lecture; Series; Geometric

The 35th and 36th Arkansas Spring Lectures Series in the Mathematical Sciences (SLS) will take place in 2010 and 2011 at the University of Arkansas, in Fayetteville, AR. The focus topics are the following. For SLS 2010: "Minimal Surfaces and Mean Curvature Flow." The conference will take place April 15-17, 2010. The principal speaker will be Professor William Minicozzi from Johns Hopkins University. There will be additional one-hour talks by ten invited speakers to be chosen by Professor Minicozzi, and several twenty-minute contributed talks by graduate students and recent Ph.D.'s. Professor Minicozzi will address recent progress on the study of minimal surfaces and mean curvature flow. In particular, he will speak about sharp partial regularity theorems for weak solutions of the mean curvature flow and other instances of the increased understanding of geometric flows that have accompanied recent dramatic progress on Ricci flow. Many of the tools of regularity theory that were originally invented for minimal surfaces have been widely applied to other geometric problems. In the case of mean curvature flow, this includes the monotonicity formula of Huisken, Brian White's parabolic version of Federer's dimension reducing, and Brakke's regularity theorem (which is a parabolic version of Allard's theorem for stationary varifolds). For SLS 2011: "Conformal Differential Geometry and Its Interaction with Representation Theory." The conference will take place April 7-9, 2011, and feature principal speaker Professor Michael Eastwood of the University of Adelaide. There will be additional one-hour talks by ten invited speakers to be chosen by Professor Eastwood, and several twenty-minute contributed talks by graduate students and recent Ph.D.'s. Professor Eastwood's talks will address the interplay between conformal differential geometry and Bernstein-Gelfand-Gelfand (BGG) machinery. The conformal case, important in itself, also acts as an excellent testbed for the more general theory of parabolic geometry. In particular, these talks will set the scene for a conjectured vast extension of the BGG machinery and a properly geometric theory of prolongation. Branson's Q-curvature and its prescription problem will be discussed in this context. Recent work of Oshima finds the symmetry algebras of all conformally invariant differential operators on the flat model. These lectures will discuss the curved cases, which are completely open at present. Finally, the BGG machinery can be used with complex analysis to solve reconstruction problems for integral geometry on suitable homogeneous spaces. The talks will present the current research and outlook in this direction.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 Daniel Rockmore (Dartmouth College) in 2010 and by Professor Eastwood (Adelaide) in 2011 will address audiences of high school students and the public at large.

第35届和第36届阿肯色州春季数学科学系列讲座（SLS）将于2010年和2011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。SLS 2010：“最小曲面和平均曲率流。“会议将于2010年4月15日至17日举行。主讲人是约翰霍普金斯大学的William Minicozzi教授。此外，Minicozzi教授还将挑选10位受邀演讲者进行一小时的演讲，并由研究生和最近获得博士学位的学生进行几次20分钟的演讲。's. Minicozzi教授将介绍最小曲面和平均曲率流研究的最新进展。特别是，他将谈到尖锐的部分正则性定理弱解的平均曲率流和其他情况下，增加了理解的几何流动，伴随着最近的戏剧性进展里奇流。正则性理论的许多工具，最初发明的极小曲面已被广泛应用于其他几何问题。在平均曲率流的情况下，这包括Huisken的单调性公式，Brian白色的Federer降维的抛物线版本，以及Brakke的正则性定理（这是Allard定理的抛物线版本）。SLS 2011：“共形微分几何及其与表示理论的相互作用。“会议将于2011年4月7日至9日举行，主要发言人是阿德莱德大学的迈克尔·伊斯特伍德教授。将有十个特邀演讲者将由伊斯特伍德教授选择额外的一个小时的演讲，并由研究生和最近的博士几个20分钟的贡献会谈。's.教授伊斯特伍德的会谈将解决共形微分几何和伯恩斯坦-Gelfand-Gelfand（BGG）机械之间的相互作用。共形的情况，重要的是本身，也作为一个很好的测试平台，为更一般的理论，抛物几何。特别是，这些会谈将设置现场的一个approximately巨大的延伸的BGG机械和适当的几何理论的延长。布兰森的Q-曲率和它的处方问题将在这方面进行讨论。最近的工作大岛发现对称代数的所有共形不变微分算子的平坦模型。这些讲座将讨论弯曲的情况下，这是完全开放的，目前。最后，BGG机器可以与复分析一起使用，以解决在适当的齐性空间上的积分几何的重建问题。讲座将介绍当前的研究和展望在这一方向。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。丹尼尔洛克莫尔教授（达特茅斯学院）在2010年和伊斯特伍德教授（阿德莱德）在2011年将向高中生和广大公众发表公开演讲。