GSU-USC Commutative Algebra Seminar
Columbia, SC
April 4-5, 2009

The Schedule

• 3:30 Saturday, Refreshments, Room 310 LeConte.
• 3:45 -- 4:45 Saturday, Room 310 LeConte, Janet Vassilev, University of New Mexico, "Prime and Semiprime operations over 1-dimensional domains".
• 5:00 -- 6:00 Saturday, Room 310 LeConte, Yongwei Yao, Georgia State University, "The linear growth property on Tor modules".
  
  
• 7:00 Saturday, dinner at Golden Chopstix.
  
  
• 9:00 Sunday, Refreshments, Room 310 LeConte.
• 9:30 -- 10:30 Sunday, Room 310 LeConte, Florian Enescu, Georgia State University, "Finite dimensional vector spaces with Frobenius action".
• 11:00 -- 12:00 Sunday, Room 310 LeConte, Hannah Robbins, Wake Forest University, "Associated primes of local cohomology modules over small dimensional rings".

Organizers

• Andy Kustin (University of South Carolina) kustin@math.sc.edu
  
  
• Adela Vraciu (University of South Carolina) vraciu@math.sc.edu
  

Other participants include:

• Brett Barwick, University of South Carolina
• Joe Brennan, University of Central Florida
• Louiza Fouli, University of Texas
• Sara Malec, Georgia State University
• Bart Snapp, Coastal Carolina University
• John Webb, University of South Carolina

Abstracts

• Florian Enescu, Georgia State University, "Finite dimensional vector spaces with Frobenius action". I will discuss the structure theory of finite dimensional vector spaces that admit a Frobenius action and give a criterion to determine which such vector spaces are antinilpotent.
  
  
• Hannah Robbins, Wake Forest University, "Associated primes of local cohomology modules over small dimensional rings". We will look at when the set of associated primes of local cohomology modules is finite. If the dimension of the base ring is small enough we give some conditions so that the local cohomology of every module is finite - even when the ring is not local.
  
  
• Janet Vassilev, University of New Mexico. "Prime and Semiprime operations over 1-dimensional domains". We view the set of closure operations in the monoid of maps from the set of ideals of a ring to itself. Although the closure operations do not form a submonoid of this monoid, we can determine an algebraic structure on the set of semiprime and prime operations for Dedekind domains and the complete cuspidal cubic. In fact, in both cases, the only prime operation is the identity map. However, we can exhibit there are 1-dimensional domains which have non-identity prime operations. We will also discuss how the structure of the semiprime operations changes if we consider them as a subset of the monoid of maps from the set of fractional ideals of a domain to itself.
  
  
• Yongwei Yao, Georgia State University, "The linear growth property on Tor modules". Let R be a Noetherian ring, I and J be ideals, and M and N be finitely generated R-modules. The linear growth property about the primary decomposition has been proved for M/I^nM, Tor_c(N, M/I^nM) and Ext^c(N, M/I^nM), in which c is fixed. In this talk, I will speak on the linear growth of Tor_c(M/I^mM, N/J^nN) with c fixed.

This seminar is supported in part by the National Security Agency.

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Previous seminars

• Spring 2009, Atlanta.
• Fall 2008, Columbia.
• Fall 2008, Atlanta.
• Spring 2008, Atlanta.
• Spring 2008, Columbia.
• Fall 2007, Columbia.
• Fall 2007, Atlanta.
• Spring 2007, Columbia.
• Spring 2007, Atlanta.
• Fall 2006, Columbia.
• Fall 2006, Atlanta.