Special Algebra Meetings in the Midwest

摘要 DMS 中西部特别代数会议 - 0753127 这项资助支持的活动的目标是在普渡大学、伊利诺伊大学芝加哥分校、伊利诺伊大学厄巴纳-香槟分校、肯塔基大学和圣母大学的代数几何和交换代数中心之间建立强有力的科学互动。这些机构的各个研究小组有着共同的兴趣，但同时也具有互补的专业知识，并且合作已经在进行中。主要通过促进一系列每两年一次的轮流会议以及支持研究生、初级教员和访客的流动来实现这一目标。这些类型的举措将帮助研究生、博士后和年轻教师拓宽他们的数学背景并开始新的合作。代数几何和交换代数在过去几年中取得了很大的进步，最引人注目的是最近在最小模型程序方面的突破。这两个领域之间的互动尤其富有成效，这也将成为本次赠款支持的活动的重点。此外，高速计算机的出现和算法的发展催生了一系列贴近应用的代数和几何研究。 普渡大学、伊利诺伊大学芝加哥分校、肯塔基大学和圣母大学的小组共同感兴趣的领域是乘数理想、积分闭包和核心的主题。普渡大学、UIC 和 UIUC 的小组共同感兴趣的其他领域是交叉重数和相关问题，以及同调猜想。我们的小组从不同的角度研究这些主题，从复杂的解析几何到交换代数和组合学。这使得研究生的思想交流和相互培养变得更加重要。 该系列会议将展示代数和几何各个领域的最新进展，包括希尔伯特函数和重数、格罗布纳基和计算代数、联络理论、同调猜想、正特征和混合特征问题、紧闭包及其与双有理几何的相互作用、奇点的解决、里斯代数、乘子理想、核和布里昂松-斯科达型定理。 为此，这些领域的许多国内和国际专家将聚集在一起，但年轻研究人员也将有充足的机会展示和讨论他们的工作。人们隐含地期望将会出现许多新的富有成效的合作。

ABSTRACT Special Algebra Meetings in the Midwest DMS - 0753127The goal of the activities supported by this grant is to create strong scientific interactions among the centers in Algebraic Geometry and Commutative Algebra that are located at Purdue University, the University of Illinois at Chicago, the University of Illinois at Urbana-Champaign, the University of Kentucky, and the University of Notre Dame. The various research groups at these institutions have compatible interests, but at the same time complementary expertise, and collaborations are already ongoing. Primarily, this goal will be achieved by promoting a series of bi-annual rotating conferences and by supporting the mobility of graduate students, junior faculty members, and visitors. These types of initiatives will help graduate students, postdocs and young faculty broaden their mathematical background and start new collaborations.Algebraic Geometry and Commutative Algebra have seen a great deal of advances in the past years, most notably through a recent breakthrough in the minimal model program. Particularly fruitful has been the interaction between the two fields, which will also be the focus of the activities supported by this grant. In addition, the advent of high-speed computers and the development of algorithms have led to a line of research in Algebra and Geometry that is close to applications. An area of common interest of the groups at Purdue, UI Chicago, Kentucky, and Notre Dame have been the topics of multiplier ideals, integral closures, and cores. The other areas of common interest among the groups at Purdue, UIC, and UIUC are intersection multiplicities and related problems, and the homological conjectures. Our groups approach these subjects from different points of views, ranging from complex analytic geometry to commutative algebra and combinatorics. This makes an exchange of ideas and the mutual training of graduate students even more crucial. The series of conferences will showcase recent progress in various areas of algebra and geometry, including Hilbert functions and multiplicities, Groebner bases and computational algebra, liaison theory, the homological conjectures, problems in positive and mixed characteristic, tight closure and its interaction with birational geometry, resolution of singularities, Rees algebras, multiplier ideals, cores and Briancon-Skoda type theorems. To this end many of the national and international experts in these areas will be brought together, but there will also be ample opportunities for young researchers to present and discuss their work. It is an implicit expectation that many new fruitful collaborations will emerge.