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/
This NSF grant supported a conference "Computational workshop on Frobenius singularities and invariants" held at University of Michigan, Ann Arbor, Michigan, May 29 -- June 1, 2012. The entire grant was spent supporting travel and lodging for the conference speakers and some graduate students and postdoctoral fellows. There were 3 different introductory lecture series (9 lectures in total), aimed at the level of graduate students: 1. Introduction to the log canonical and F-threshold, given by Karen Smith and Daniel Hernandez. 2. An introduction to Hilbert-Kunz multiplicity and F-signature, given by Craig Huneke and Paul Monsky. 3. Computation of tight closure, given by Holger Brenner. Notes for most of these lectures are available on the conference website: https://sites.google.com/site/computingfinvariantsworkshop/schedule There were also 8 research talks given by leading researchers. The conference had a informational session where researchers demonstrated the Macaulay2 code they developed. Undergraduate and graduate students and postdocs presented posters in a poster session during this conference. There was a moderated open questions session, which was well attended and where numerous interesting problems were posed to the conference attendees. The products of the open problems session are posted on the website: https://sites.google.com/site/computingfinvariantsworkshop/open-questions The conference brought together experts in the field and exposed students and young researchers to an active and accessible field of research within commutative algebra and algebraic geometry.
