Computational Workshop on Singularities and Invariants Defined by Frobenius

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

The singularities and numerical invariants defined via the Frobenius endomorphism are important to Commutative Algebra and Algebraic Geometry in prime characteristic. Since the introduction of tight closure theory and the discovery of the connection between singularities in prime characteristic and those arising from the Minimal Model Program, there has been an extensive theoretical study of these invariants; however, explicit computational examples of these invariants are rare. During this workshop, there will be introductory lecture series on tight closure, Hilbert-Kunz multiplicity, and test ideals, given by leading experts. Additionally, there will be a number of research talks on relevant existing computations of these and other topics. There also will be a session on using the computer algebra system Macaulay2 in the computation of these invariants, as well as a moderated open problem session during the conference. This workshop aims at bringing experts together to compute new and interesting classes of examples; identifying new connections between the measures arising in different contexts, especially numerical relations and bounds; and exposing graduate students, young researchers and even some undergraduate students to simple yet fundamentally important research questions that they can easily get their hands on. This workshop will take place at the University of Michigan, Ann Arbor, May 29th--June 1st, 2012. The organizing committee consists of: Karl Schwede (Pennsylvania State University), Kevin Tucker (Princeton University), and Wenliang Zhang (University of Michigan). More information can be found on the conference website: http://sites.google.com/site/computingfinvariantsworkshop/