Commutative Algebra Meetings in the Southeast
Columbia, SC
September 12 and 13, 2009.
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Commutative Algebra Meetings in the Southeast
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The meeting will take place in room 310 LeConte.
LeConte is on the corner of Greene Street and Pickens Street.
Map, Hotels, and Parking.
The Schedule
- Saturday 1:45 PM -- 2:00 PM: Refreshments.
- Saturday 2:00 PM -- 3:00 PM: Florian Enescu, Georgia State University, "The lower semicontinuity of the Frobenius splitting numbers".
- Saturday 3:30 PM -- 4:30 PM: Yongwei Yao, Georgia State University, "Some extensions of Hilbert-Kunz multiplicity".
- Saturday Evening: Dinner. Delhi Palace Restaurant, 7:00 PM. Here are directions to the restaurant from the Math Department. (We had dinner here in November 2008.)
- Sunday 9:15 AM -- 9:45 AM, Refreshments.
- Sunday 9:45 AM -- 10:45 AM, Alina Iacob, Georgia Southern University, "Homological dimensions and regular rings".
- Sunday 11:00 AM -- 12:00 noon, Joseph Brennan, University of Central Florida, "Alexander duality".
Organizers
Other participants include:
- Brett Barwick, University of South Carolina
- Jong-Wook Kim, Georgia State University
- Sara Malec, Georgia State University
- John Webb, University of South Carolina
Abstracts
- Joseph Brennan, "Alexander duality". The notion of Alexander duality has proven to be a useful tool in investigating properties of monomial subrings associated to simplicial complexes. This is an expository talk on the extension of the notion of Alexander duality to arbitrary monomial subrings with particular emphasis on applications to cut ideals. The current status of several conjectures regarding cut ideals will also be discussed.
- Florian Enescu, "The lower semicontinuity of the Frobenius splitting numbers". The Frobenius splitting numbers can be used to define the F-signature of a local ring of prime positive characteristic. The talk will investigate the lower semicontinuity of these numbers for an excellent locally equidimensional ring. This is joint work with Yongwei Yao.
- Alina Iacob, "Homological dimensions and regular rings". A question of Avramov and Foxby concerning injective dimension of complexes is settled in the affirmative for the class of noetherian rings.
This is joint work with Srikanth Iyengar.
- Yongwei Yao, "Some extensions of Hilbert-Kunz multiplicity". In this talk, we define some numerical characterizations related to a nested pair of ideals in a Noetherian ring of prime characteristic p. They could be thought of as extensions of Hilbert-Kunz multiplicity, and are closely related to whether the nested pair of ideals shares the same tight closure. This is joint work with Neil Epstein.