Algebra and Geometry Meetings in the Midwest

这项活动的目标是有助于培养研究生，促进广泛分布在中西部的科学家之间的思想交流，并通过普渡大学的一系列会议推进交换代数和代数几何的研究（2015年8月10日至14日），在肯塔基州大学（2016年5月），并在圣母大学（2017年5月）。积极参与这些活动的其他机构是伊利诺伊大学芝加哥分校和伊利诺伊大学厄巴纳-香槟分校。这些机构的各个研究小组有着共同的兴趣，但同时也有互补的专业知识，合作已经在进行中。交换代数和代数几何的许多国家和国际专家将聚集在一起，但也将有足够的机会让年轻的研究人员介绍和讨论他们的工作。此外，每次会议都将包括关于专业问题的小组讨论。这将有助于指导初级研究人员从研究生院到学术就业的关键过渡。交换代数和代数几何是充满活力的领域，它们之间以及与其他数学领域的联系丰富且不断发展：正在探索素数特征和双有理几何中的代数现象之间的有趣相似之处，并且最大科恩-麦考利模已经在物理学中找到了应用。在最小模型程序和通过解决Boij-Soderberg猜想来研究自由解方面都有重要的进展。中部中西部在这些领域有着悠久的优秀传统，交换代数学家和代数几何学家高度集中。我们的团体之间的共同利益领域包括双有理几何，里斯代数，乘子理想，联络理论，同调代数，希尔伯特函数，局部上同调，和组合方法。会议的主题将在普渡大学的最新进展交换代数及其相互作用与代数几何，特别强调乘数理想，特征p方法，和同调代数。在肯塔基州的会议将集中在自由决议和代表理论方法。在圣母大学数学中心的会议的重点将是多重性理论和隐含问题。

The goal of this activity is to contribute to the training of graduate students, to promote the exchange of ideas among scientists broadly located in the Midwest, and to advance research in Commutative Algebra and Algebraic Geometry through a series of conferences at Purdue University (August 10-14, 2015), at the University of Kentucky (May 2016), and at the University of Notre Dame (May 2017). The other institutions that are actively involved in these events are the University of Illinois at Chicago and the University of Illinois at Urbana-Champaign. The various research groups at these institutions have compatible interests, but at the same time complementary expertise, and collaborations are already ongoing. Many of the national and international experts in commutative algebra and algebraic geometry will be brought together, but there will also be ample opportunities for young researchers to present and discuss their work. In addition, every meeting will include a panel discussion about professional issues. This will help guide junior researchers through the critical transition from graduate school to academic employment.Commutative Algebra and Algebraic Geometry are vibrant fields with rich and ever evolving connections among them and to other areas of mathematics: Intriguing parallels between algebraic phenomena in prime characteristic and birational geometry are being explored, and maximal Cohen-Macaulay modules have found applications in physics. There have been important advances in the minimal model program, and in the study of free resolutions through the solution of the Boij-Soderberg conjecture. The central Midwest has a long tradition of excellence in these areas and a high concentration of commutative algebraists and algebraic geometers. Areas of common interests among our groups include birational geometry, Rees algebras, multiplier ideals, liaison theory, the homological conjectures, Hilbert functions, local cohomology, and combinatorial methods. The topic of the conference at Purdue will be Recent Advances in Commutative Algebra and its Interaction with Algebraic Geometry, with particular emphasis on multiplier ideals, characteristic p methods, and the homological conjectures. The meeting in Kentucky will focus on Free Resolutions and Representation Theoretic Methods. The emphasis of the conference at the Center for Mathematics at the University of Notre Dame will be Multiplicity Theory and Implicitization Problems.