University of Michigan
Department of Mathematics
 Commutative Algebra Seminar
Fall 2009
Thursdays 3-4pm, 3096 East Hall


The commutative algebra seminar is currently being organized by Karl Schwede.

DateSpeakerTopicAbstract
September 10th Karl Schwede
University of Michigan
Organizational meeting
September 17th Not meeting this week
September 24th Karl Schwede
University of Michigan
Rationality of Hilbert-Kunz multiplicity for 2 dimensional graded rings, part 1 I'll talk about work of Brenner on this topic.
October 1st Karl Schwede
University of Michigan
Rationality of Hilbert-Kunz multiplicity for 2 dimensional graded rings, part 2 I'll talk about work of Brenner on this topic.
October 8th Christine Berkesch
Purdue University
The rank of a hypergeometric system An A-hypergeometric system is a D-module determined by a toric ideal and certain homogeneity parameters. The dimension of its solution space, called its rank, is constant for generic parameters. I will discuss the combinatorial nature of this rank at non-generic parameters and its ties to the local cohomology of the toric algebra with support in the maximal ideal.
October 15th Kevin Tucker
University of Michigan
On the Behavior of Test Ideals Under Generically Etale Finite Morphisms Test ideals are important invariants in positive characteristic commutative algebra arising from the theory of tight closure, and correspond to multiplier ideals under reduction to characteristic p>0. By analyzing the lifting properties of p^e-linear maps using the trace map, we are able to describe the behavior of test ideals under generically etale finite morphisms (joint with Karl Schwede). This generalizes previously known results on the behavior of test ideals under finite morphisms which are etale in codimension one.
October 22nd Wenliang Zhang
University of Michigan
Robust Closure The notion of the robust closure of an ideal in a noetherian ring will be introduced and some properties will be discussed, for example, robust closure agrees with tight closure in positive characteristic; every ideal is robustly closed in a regular ring (of any characteristic). This is a joint work with Professor Melvin Hochster.
October 29th
Special time, 4:00pm
Hans Schoutens
New York City College of Technology
Schemic Grothendieck rings, arc integrals, and motivic rationality Click here
November 5th Mel Hochster
University of Michigan
Tight closure and localization in equal characteristic 0 The talk will discuss instances in which the equal characteristic 0 notion of tight closure is known to commute with localization. A lot of progress has been made recently utilizing the notion of homogeneous tight closure. This is joint work with Neil Epstein.
November 12th Mel Hochster
University of Michigan
Tight closure and localization in equal characteristic 0, part 2 The talk will discuss instances in which the equal characteristic 0 notion of tight closure is known to commute with localization. A lot of progress has been made recently utilizing the notion of homogeneous tight closure. This is joint work with Neil Epstein.
November 17th
Note special day
(But usual time and place)
Tigran Ananyan
Adrian College
On Direct Summands of Modules of Finite Phantom Projective Dimension I will talk about an example of local ring R of finite characteristic and R-modules M and N such that their direct sum has a finite phantom projective dimension, however neither M nor N has finite phantom projective resolution. This result is joint work with Mel Hochster.
November 19th No seminar today No seminar


For more information, or to volunteer to give a talk, contact Karl Schwede