The series of meetings represents a collaborative effort of commutative
algebraists at
Georgia State University, University of South Carolina and University
of Central Florida to increase exposure
of their research area in the South-East through periodic meetings.
Each term
GSU, USC and UCF organize two regional meetings and one national one.
This Spring, GSU
will organize one regional meeting. A national meeting in Atlanta will
be scheduled in September 2010. A link with past meetings can be found here. For some of the
past seminars, see the following links Fall 2008,
Spring 2008,
Spring 2007, Fall 2007 or Fall 2006 and earlier.
Florian
Enescu (Georgia State University) fenescu@gsu.edu
Yongwei Yao (Georgia State University) yyao@gsu.edu
Schedule (all talks are in Room 796 College Of Educ. Bldg):
Saturday
2:00pm: Refreshments
2:30-3:30pm: Anton Leykin, Georgia Tech
Computing multiplier ideals via Bernstein-Sato polynomials
Abstract: The Bernstein-Sato polynomial is an important invariant in
singularity theory, which can be obtained using symbolic methods in
the theory of D-modules.
Generalized Bernstein-Sato polynomial introduced by
Budur--Mustata--Saito for an arbitrary variety provides a way to
compute the log canonical threshold and some jumping coefficients.
In our joint work with Christine Berkesch using an even further
generalization due to Shibuta we build algorithms for computing
multiplier ideals and all jumping coefficients.
4:00-5:00pm: Sandra Spiroff, University of Mississippi
A discussion of zero divisor graphs associated to a ring
Abstract: Given a commutative ring R, we begin by comparing and contrasting
the different zero divisor graphs that have been associated to R over the
years, starting with the original graph defined by Istvan Beck in 1988 and
proceeding to the graph determined by equivalence classes of zero divisors.
We consider connectivity, diameter, completeness, girth, etc. Secondly, we
study the relationship between the ring and its graph. More specifically,
we demonstrate how information about the associated primes of R can be
determined from its zero divisor graph, and we consider what, if any,
finiteness condition on the graph can be achieved when R is Noetherian.
This talk covers material from two projects, the first with Cameron Wickham
at Missouri State University, and the second with with Jim Coykendall and
Sean Sather-Wagstaff at North Dakota State University, and Laura Sheppardson
at the University of Mississippi.
Sunday
9:00am: Refreshments
9:30-10:30am: Jinjia Li, Middle Tennessee State
Limit Hilbert-Kunz multiplicity
Abstract: We discuss a more direct way to compute the so-called
"limit Hilbert-Kunz multiplicity" over a 2-dimensional graded normal
domain in characteristic zero, the existence of which was first
established by the work of Trivedi. This is joint with Holger Brenner
and Claudia Miller.
11-12pm: Joe Brennan, University of Central Florida
Infrastructures for commutative algebraists
Abstract: We consider a question of how to compute the unit group and class group of a curve
over a field using the concept of an infrastructure.
There will be a dinner on Saturday night at 6pm at a local
restaurant. Please inform the organizers by Thursday March 18 if you
plan to attend.
For those interested in attending the conference, please complete our registration form. We have limited funds for
financial support and plan to answer any funding requests after January 28, 2010 in the order they are received. Per NSA rules,
we can only fund US citizens and permanent residents of the US.
A few lodging recommendations:
Downtown Atlanta Wyndham.
Downtown Altanta Residence Inn.
North-East Atlanta Courtyard by Marriott.
North-East Atlanta Holiday Inn
Downtown hotels tend to be expensive, but they are within walking
distance to GSU. However, we will organize rides between GSU, hotels
and dining destinations. We would appreciate if you let us where you
plan to stay in case you need rides. There are many other hotels in the
downtown area with varying lodging rates. If you plan to stay there and
have questions regarding a hotel, do let us know.
The meeting is partially supported by the National Security Agency.
Return to the
Commutative Algebra Meetings in the Southeast
home page.