Algebra and Geometry Meetings in the Midwest

Purdue University, West Lafayette IN

Investigators

Abstract

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.