Commutative Algebra Seminar

Fall 2017, Friday 2:30 - 3:20, LCB 215

Date Speaker Title — click for abstract
September 1 Aaron Bertam
University of Utah
Unstable syzygies
A stability condition gives a measure of the instability of a complex of vector bundles via its Harder-Narasimhan filtration. There is a canonical Euler stability condition on projective space that we can use in this way to measure the instability of free resolutions of Gorenstein rings. This has more information than the Betti tables (and Hilbert functions), and leads to questions about Gorenstein rings with socle in degree 3 that we would love know more about. This is joint work with Brooke Ullery.
September 8 Pham Hung Quy
FTP University, Vietnam
Applications of filter regular sequences to some positive characteristic problems
We use the notion of filter regular sequence to study some singularities and invariant defined by Frobenius action on local cohomology.
September 13
Nonstandard day
JWB 333
Craig Huneke
University of Virginia
TBD
September 15 Roger Wiegand
University of Nebraska
Betti tables over short Gorenstein algebras
Let k be a field and R a short, standard-graded Gorenstein k-algebra with embedding dimension e > 2. (Thus the Hilbert series of R is 1+es+s^2 .) The category of finitely generated graded R-modules has wild representation type, but much of the representation theory of the category is revealed by the Betti tables of modules. The additive semigroup B of all Betti tables of R-modules is atomic but very far from being factorial. We will show how the atoms of B arise as Betti tables of cosyzygies of ideals of R and describe some specific relations among these atoms. This is joint work with Lucho Avramov and Courtney Gibbons.
September 22 Henning Krause
Bielefeld University, Germany
September 29 TBD
October 6 TBD
October 20 TBD
October 27 TBD
November 3 Benjamin Briggs
University of Toronto
November 3
3:30 - 4:20 PM
JWB 333
Vincent Galinas
University of Toronto
November 10 TBD

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