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WS 2014/2015
28.10.2014 um 16:15 Uhr in 69/125:
Dr. Lukas Katthän (Universität Osnabrück)
Stanley conjecture
11.11.2014 um 16:15 Uhr in 69/125:
Alessio Caminata (Universität Osnabrück)
Symmetric signature
25.11.2014 um 16:15 Uhr in 69/125:
Bayarjargal Batsukh (Universität Osnabrück)
Hilbert-Kunz-functions of binoids
13.01.2015 um 16:15 Uhr in 69/125:
Dr. Thomas Kahle (Otto-von-Guericke-Universität Magdeburg)
Irreducible decomposition of binomial ideals
An ideal is irreducible if it can not be written as the intersection of two strictly larger ideals. Irreducible decompositions underly primary decompositions and are a fundamental tool in Noetherian rings. While generally these decompositions are quite hard to access explicitly, for monomial and binomial ideals, the situation is much better. We discuss combinatorial irreducible decompositions of binomial ideals. Our constructions allow us to answer a conjecture of Eisenbud and Sturmfels. Joint work with Chris O'Neill and Ezra Miller.
27.01.2015 um 16:15 Uhr in 69/125:
Mario Kummer (Universität Konstanz)
Determinantal Representations of Determinantal Varieties
A closed hypersurface in projective space has a determinantal representation if its defining polynomial is the determinant of a matrix with linear entries. The talk will be about different ways of generalizing this concept to projective varieties of higher codimension: Taking maximal minors of a non-square matrix, representing the homogeneous coordinate ring as an algebra generated by commuting matrices with linear entries in some unknowns and the notion of Livšic-type determinantal representations introduced by Shamovich and Vinnikov very recently. I will present a work in progress about how these concepts relate to each other.
10.02.2015 um 16:15 Uhr in 69/125:
Prof. Dr. Matthias Franz (University of Western Ontario)
Cohen-Macaulay modules and syzygies in equivariant cohomology
Let G be a compact, connected Lie group and X a compact G-manifold. Then the (real) cohomology of the classifying space BG is a polynomial algebra, and the G-equivariant cohomology of X is a finitely generated module over it. The filtration of X by the rank of the isotropy subgroups leads to relative equivariant cohomology modules which are Cohen-Macaulay. This fact turns out to be crucial in the study of syzygies (higher versions of torsion-freeness) in equivariant cohomology, which was initiated by Allday, Franz and Puppe in recent years.
In this talk I will survey these results, with an emphasis on the more algebraic aspects. Familiarity with equivariant cohomology is not a prerequisite.
24.02.2015 um 16:15 Uhr in 69/125:
Yusuke Nakajima (University of Nagoya)
Ulrich modules over cyclic quotient surface singularities
Abstract: Let R be a Cohen-Macaulay local ring. An Ulrich module is defined as a maximal Cohen-Macaulay R-module which has the maximum number of generators. In this talk, I will consider such a module for the case where cyclic quotient surface singularities. Especially, I will determine which maximal Cohen-Macaulay R-module is an Ulrich module. If there is time, I will also consider related topics. This is a joint work with Ken-ichi Yoshida.
