Irma Cruz-Rodriguez, Florida State University
Spiral Waves in Excitable Media
Algebra Seminar, 3:30 p.m., 101 Love Building
Roger Wiegand, University of Nebraska
Local Rings of Finite Cohen-Macaulay Type: Schreyer's Conjectures
Let R be a local Cohen-Macaulay ring. A maximal Cohen-Macaulay (MCM) module is a finitely generated module whose depth equals the dimension of the ring. (For one-dimensional rings, e.g., coordinate rings of curves or orders in a number field, the MCM modules are just the finitely generated torsion-free modules, often called lattices.) One says that R has finite CM type provided there are only finitely many isomorphism classes of indecomposable MCM R-modules. The one-dimensional rings of finite CM type were completely classified in 1994. In higher dimensions, relatively little was known until recently, except in the following important situation: R is complete and contains an algebraically closed field mapping onto the residue field of R. In particular, Buchweitz, Greuel, Knöorrer and Schreyer obtained in 1987 a beautiful classification of the hypersurface singularities of finite CM type. These are the rings k[[x_0,\dots,x_d]]/(f), where k is an algebraically closed field of characteristic different from 2, 3, 5.
In 1987 Schreyer made two conjectures, which (since they turn out to be true) greatly expand one's understanding of the rings of finite CM type: (I) R has finite CM type if and only if the completion \hat R has finite CM type. (II) Suppose R contains a field k, and K is a separable algebraic extension of k such that S:=K\otimes_kR is local. Then R has finite CM type if and only if S has finite CM type.
Recently I proved (II) in general, and (I) under the additional assumption that R is excellent with an isolated singularity. Recent work of my student Graham Leuschke suggests that the assumption of an isolated singularity can be omitted.
Workshop, 3:35-5:00 p.m., 499 Dirac Science Library
Web in The Teaching of Mathematics
(Real) Analysis Seminar, 2:30 p.m., 102 Love Building
Working through Carlos Kenig's lecture notes on oscillatory integrals and
nonlinear pde.
No Complex/Symbolic Coffee, 3:15 p.m., 105 Love Building
No Complex/Symbolic, 3:35 p.m., 102 Love Building
No Algebra Seminar, 2:00 p.m., 104 Love Building
Topology Tea Time, 3:00 p.m., 204 Love Building
Topology Seminar, 3:35 p.m., 104 Love Building
Hans Boden, Ohio State University at Mansfield
A Gauge-Theoretic Formula for the SU(3) Casson Invariant
Colloquium Coffee, 3:00 p.m., 204 Love Building
Colloquium, 3:30 p.m., 101 Love Building
Hans Boden, Ohio State University at Mansfield
Universal Formulae for the SU(n) Casson Knot Invariants
No Scientific Computing Seminar, 4:30 p.m., 200 Love Building
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This document is maintained by
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Last modified: 16 April 1998