Commutative Algebra Seminar
Fall 2007

Wed, 05 Dec 2007: Frank Moore. 

Thu, 29 Nov 2007: *Ovidiu Pasarescu*, Institute of Mathematics of the 

Romanian Academy in Algebraic Geometry, Fulbright scholar at Colorado State University 

Title: *Classification of the degenerate Del Pezzo Surfaces after the Singular Locus * 

ABSTRACT: It is well known that the smooth, non-degenerate, surfaces of degree d in P^d exists only if d is between 3 and 9. These surfaces are called Del Pezzo surfaces, and they are all rational. Gorenstein surfaces of degree d in P^d with isolated singularities also exists only if d is between 3 and 9 (Hidaka-Watanabe). They are either cones or they are rational and have only A-D-E singularities (in this last case they are called degenerate Del Pezzo surfaces). I will present a strategy giving, for any d, all the possible configurations of singularities which appear on the degenerate Del Pezzo surfaces of degree d. For d=3 (resp. d=4) we recover the classical case of cubic surfaces (resp. of complete intersections of type (2,2) from P^4. 

Wed, 28 Nov 2007: Srikanth Iyengar. 

Title: "Modules of finite projective dimension and finite injective dimension". 

Thu Nov 15 2007: Tyler Lemberg 

Title: Numerical Monoids. 

Wed Nov 14 2007: Jeffrey Mermin 

Title: Progress on the Lex-Plus-Powers Conjecture 

Thu Nov 1 2007: Jinjia Li 

Wed Oct 31 2007: Jinjia Li 

Thu Oct 25 200: Bill Arveson (joint with Operator Theory Seminar) 

Wed Oct 24 2007: David Pitts "A tour of Choquet Theory" (joint with Operator Theory Seminar) 

Wed Oct 10 2007: Livia Miller 

Title: A tale of non-Noetherian Rings: Defining non-Noetherian Gorenstein Rings. 

ABSTRACT:Motivated by a question of Glaz, Hamilton and Marley recently introduced a theory of non-Noetherian Cohen-Macaulay rings equivalent to the usual definition of Noetherian Cohen-Macaulay rings. In my talk I will introduce this definition and use it to develop a theory of non-Noetherian Gorenstein rings. I plan to give a global picture of this theory by explaining how non-Noetherian regular, Gorenstein and Cohen-Macaulay rings relate. If time allows, will also discuss additional characterizations and properties of non-Noetherian Gorenstein rings. 

Thu Oct 4 2007: Brian Harbourne 

Title: Comparing powers and symbolic powers of ideals 

ABSTRACT: Craig Huneke has asked: is it true for any radical homogeneous ideal I defining a 0-dimensional subscheme of P2 that I^2 contains I^(3)? More generally, given a homogeneous ideal I in a polynomial ring k[x0,...,xn], for precisely what r and m does I^r contain I^(m)? Recent joint work of Harbourne with C. Bocci has begun to address such problems. 

Wed Oct 3 2007: Frank Moore. 

Title: *Cohomology of connected sums of artinian Gorenstein rings * 

ABSTRACT: We will give the (topologically motivated) definition of a connected sum of artinian Gorenstein rings, as well as give some results on its Ext algebra. Time permitting, we will also discuss some results on its Koszul homology algebra. In order to perform these calculations, we will use the theory of Golod homomorphisms, and so the talk will also contain the relevant definitions and some basic examples. 

Wed Sep 26 2007: Mark Walker 

Title: The K-theory of toric varieties 

ABSTRACT: This is joint work with Chuck Weibel, Christian Haesemeyer, and Willie Cortinas. Our main result is a new and (it is hoped) simpler proof of Gubeladeze's "Nilpotence Conjecture", proven by him a few years ago. Our proof uses the "cdh-topology", Hochschild homology, and Andre-Quillen homology. My goal in these talks is to explain what all these terms mean and to sketch our proof. 

Thu Sep 13 2007: Andrew Crabbe. 

Wed Sep 12 2007: Andrew Crabbe. 

Wed Sep 5 2007: Janet Striuli. 

Wed Aug 29 2007: Peter Symonds, University of Manchester 

Title: Group actions on polynomial rings. 

Wed Aug 8 2007: Tim Roemer.