Commutative Algebra Seminar

Spring 2008




 Seminars will be in  Avery 351,  and will be held twice a week:

 Wednesdays 3:30 - 4:20 pm

 Thursdays  2:30 - 3:20 pm

 There is a mailing list (unlcas) of the participants of the
 Commutative Algebra Seminar: If you want to subscribe or unsubscribe
 visit the unlcas info
 page, and follow the instructions.
 


This week's seminar
16th April (Wednesday) at 3:30pm. Speaker: Sylvia Wiegand, University of Nebraska-Lincoln Title: Abstract:
17th April (Thursday) at 2:30pm. Speaker: Liana Sega Title: Abstract:
9th April (Wednesday) at 3:30pm. Speaker: Title: Abstract:
10th April (Thursday) at 2:30pm. Speaker: , Title: Abstract:
12th March (Wednesday) at 3:30pm. Speaker: Title: Abstract:
12th March (Wednesday) at 3:30pm. Speaker: Samar El Hitti, University of Missouri Title: ALGEBRAIC RESOLUTION OF FORMAL IDEALS ALONG A VALUATION Abstract: Let X be a possibly singular complete algebraic variety, defined over a field k of characteristic zero. X is nonsingular at p ∈ X if OX,p is a regular local ring. The problem of resolution of singu- larities is to show that there exists a nonsingular complete variety X, which birationally dominates X. Resolution of singularities (in characteristic zero) was proven by Hironaka in 1964. Let v be a valuation of the function field of X, v dominates a unique point p, on any complete variety Y , which birationally dominates X. The problem of local uniformization is to show that, given a valuation v of the function field of X, there exists a complete variety Y , which birationally dominates X such that the center of v on Y , is a regular local ring. Zariski proved local uniformization (in character- istic zero) in 1944. His proof gives a very detailed analysis of rank 1 valuations, and produces a resolution which reflects invariants of the valuation. We extend these methods to higher rank in our thesis to give a proof of local uniformization which reflects important properties of the valuation. We simultaneously resolve the centers of all the composite valuations, and resolve certain formal ideals associated to the valuation.
5th March (Wednesday) at 3:30pm. Speaker: Manoj Kummini, University of Kansas Title: Free resolutions of quadratic monomial ideals. Abstract:In this talk, we discuss some properties of free resolutions of quadratic monomial ideals. We will discuss some bounds for regularity, studied by X. Zheng and, later, by M. Katzman. When the ideal is the edge ideal of a bipartite graph, we descrbe a reduction to a Cohen-Macaulay ideal, which preserves the regularity and the multiplicity of the ideal.
4th March (TUESDAY) at 2:30pm. Speaker: Ian Aberbach, University of Missouri Title: Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension Abstract:
20th February (Wednesday) at 3:30pm. Speaker: Title: Abstract:
28th February (Thursday) at 2:30pm. Speaker: Claudia Miller, Syracuse University Title: On rigidity of Frobenius Abstract: We give an example of a ring in positive characteristic such that the Frobenius endomorphism is not rigid. The ring is Gorenstein. This is in stark contrast to complete intersection rings, where rigidity is known to hold. In the process, we also investigate how the questions on rigidity of the Frobenius endomorphism are related to the behavior of the depth of $F^n(M)$ for a module $M$ of infinite projective dimension.
20th February (Wednesday) at 3:30pm. Speaker: Lars Winther Christensen, Texas Tech University Title: Growth of Bass numbers Abstract: Let R be a commutative noetherian local ring with residue field k and depth d; it is Gorenstein if Ext^i(k,R) vanishes for some i>d. Thus, if R is not Gorenstein, then the vector space dimensions of the modules Ext^i(k,R) form an infinite sequence of positive numbers, known as the Bass numbers of the ring. Surprisingly little is known about the behavior of Bass numbers; for example a ring for which the Bass numbers have polynomial growth has not yet been found. For several, quite diverse, classes of rings we prove that the sequence of Bass numbers is strictly increasing with termwise exponential growth. The talk is based on joint work with Janet Striuli and Oana Veliche.
21 February (Thursday) at 2:30pm. (This talk will be part of the colloquium series of the Computer Science and Engineering Department. Speaker: Lars Winther Christensen, Texas Tech University Title: The Ultra Secret Abstract: In August 1945, evidence of the most spectacular contribution of Physics to the war effort came in the form of a mushroom cloud. The grand contribution of Mathematics, however, remained secret well into the 1970s. It was the effort to crack the German Enigma cipher machine. In the talk will give a brief survey of this momentous effort. It is an entertaining story of elementary mathematics with nontrivial implications for world history
13th February (Wednesday) at 3:30pm. Speaker: Title: Abstract:
14th February (Thursday) at 2:30pm. Speaker: Emilie Dufresne, Queen's University Title: Polynomial Separating Algebras Abstract: The idea of separating invariants comes from the desire to distinguish the orbits of a group action on a finite dimensional vector space. This can not be done in general, using just polynomial invariants, but we can still ask for a set of invariants to "separate" as much as the whole ring of invariants. Separating algebras (subalgebras that are separating sets) can be better behaved than the ring of invariants. In this talk we give necessary conditions for the existence of polynomial separating algebras ("best" possible behavior) and complete intersection separating algebras.
6th February (Wednesday) at 3:30pm. Speaker: Title: Abstract:
7th February (Thursday) at 2:30pm. Speaker: Tom Marley, University of Nebraska-Lincoln Title: Abstract:
16th January (Wednesday) at 3:30pm. Speaker: Christina Eubanks-Turner, University of Nebraska-Lincoln Title: Abstract:
17th January (Thursday) at 2:30pm. Speaker: , Title: Abstract: Past Seminars.
Maintained by Janet Striuli Back to the top