Pan American Advanced Studies Institute: Commutative Algebra and Its Interactions with Algebraic Geometry, Representation Theory, and Physics; Guanajuato, Mexico; May 14-25, 2012

1123059艾扬格这个泛美高级研究所（PASI）奖，由美国国家科学基金会和能源部（DOE）联合支持，将于2012年5月14日至25日在墨西哥瓜纳华托的数学研究中心（CIMAT）举行。 由内布拉斯加大学数学系的Srikanth Iyengar博士和德克萨斯A M大学数学系的Sarah J. Witherspoon博士组织，与Ragnar-Olaf Buchweitz博士（加拿大）和José Antonia de la Peña博士（墨西哥）合作，PASI将解决交换代数及其与代数几何，表示论和理论物理的相互作用问题。 具体议题将涵盖：矩阵分解和最大科恩-麦考利模块;集群代数和集群类别;上同调理论的支持品种;和拓扑量子场论和Frobenius代数。 这PASI将熟悉研究生，博士后，和早期的职业教师与交换代数的新兴应用。 它还将为美洲各国研究人员之间建立和促进合作提供机会。 组织者将鼓励参与者在研究所之后的三年期间在美国数学学会（AMS）会议上组织一次特别会议。 此外，他们将继续指导那些参与者和那些谁成为参与计划在数学科学研究所伯克利分校，加州（MSRI）在交换代数在2012-2013年。 一个维基页面将作为一个平台，用于传播讲师的笔记，并讨论与讲座有关的问题。

1123059Iyengar This Pan-American Advanced Studies Institutes (PASI) award, jointly supported by the NSF and the Department of Energy (DOE), will take place May 14-25, 2012 at the Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. Organized by Dr. Srikanth Iyengar of the Department of Mathematics at the University of Nebraska and Dr. Sarah J. Witherspoon of the Department of Mathematics at Texas A & M University, in collaboration with Dr. Ragnar-Olaf Buchweitz (Canada) and Dr. José Antonia de la Peña (Mexico), the PASI will address issues in commutative algebra and its interactions with algebraic geometry, representation theory, and theoretical physics. The specific topics to be covered are: matrix factorizations and maximal Cohen-Macaulay modules; cluster algebras and cluster categories; cohomological theory of support varieties; and topological quantum field theories and Frobenius algebras. This PASI will familiarize graduate students, postdocs, and early career faculty with emerging applications of commutative algebra. It will also provide an opportunity for building and fostering collaborations among researchers from various countries in the Americas. The organizers will encourage participants to organize a special session at an American Mathematical Society (AMS) meeting during the three-year period following the institute. Furthermore, they will continue to mentor those participants and those who become involved in the program at the Mathematical Sciences Research Institute-Berkeley, California (MSRI) in commutative algebra during the year 2012-2013. A wiki page will serve as a platform for dissemination of notes from the lecturers, and for discussions on problems and questions related to the lectures.