Special Algebra Meetings in the Midwest

在中西部举行的特别代数会议本基金支持的活动的目标是在位于普渡大学、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。首先，这一目标将通过促进一系列两年一次的轮换会议和支持研究生、初级教员和访客的流动性来实现。这些类型的倡议将帮助研究生、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展，最显著的是最近在最小模型程序方面的突破。特别富有成果的是这两个领域之间的相互作用，这也将是这项赠款所支持的活动的重点。此外，高速计算机的出现和算法的发展导致了代数和几何领域的一系列研究接近应用。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研究小组共同感兴趣的一个领域是乘数理想、整体闭合和核心的主题。普渡大学、伊利诺伊大学和伊利诺伊大学加州分校的研究小组共同感兴趣的其他领域是交叉多样性和相关问题，以及同源性猜想。我们的小组从不同的角度来研究这些课题，从复杂解析几何到交换代数和组合学。这使得思想交流和研究生的相互培养更加重要。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多重性，格罗布纳基和计算代数，联络理论，同调猜想，正和混合特征问题，紧闭及其与两族几何的相互作用，奇点解，Rees代数，乘数理想，核和briancons - skoda型定理。为此目的，这些领域的许多国内和国际专家将聚集在一起，但年轻的研究人员也将有充分的机会介绍和讨论他们的工作。这是一个隐含的期望，许多新的富有成效的合作将出现。

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.