Recent Developments in Positive Characteristic Methods in Commutative Algebra: Frobenius Operators and Cartier Algebras

Georgia State University Research Foundation, Inc., Atlanta GA

Investigators

Abstract

This award supports participation in the conference Recent Developments in Positive Characteristic Methods in Commutative Algebra, held during March 13-15, 2015, at Georgia State University, Atlanta, Georgia. The motivation behind the conference is to bring together researchers, including postdoctoral researchers and graduate students, in commutative algebra and related areas, in order to exchange ideas and discuss recent developments in positive characteristic methods. Top researchers in the field as well as postdocs and graduate students will be invited to speak at the conference. To make the conference accessible to all participants, introductory talks are scheduled. The conference will provide a platform for the participants to start exploring research aspects related to the highlighted topics, and it is anticipated that they will contribute research progress in these areas within a few years. More information can be found on the conference web site: http://www2.gsu.edu/~matfxe/gsu-usc/foca.html The conference will focus on recent developments in positive characteristic methods. Research on positive characteristic methods has seen tremendous developments in recent years via using concepts related to the Frobenius homomorphisms. This includes the tight closure theory in characteristic p, singularities derived via tight closure theory, as well as the corresponding singularities in characteristic zero (via reduction to characteristic p) in algebraic geometry. The highlights of the conference, Frobenius operators and Cartier algebras, also involve the Frobenius homomorphisms in very fundamental ways. Both of them have intricate connections with the tight closure theory, birational geometry, F-modules, F-stability, test ideals, jumping numbers, anti-canonical covers, etcetera. Very recent research also includes the invariant "Frobenius complexity" being defined in order to measure whether a ring Frobenius operators is finitely generated. This conference will provide an opportunity for the participants to get exposed to the topics, exchange ideas, forge collaborations, and contribute to these research areas.