FB 6 Mathematik/Informatik

Institut für Mathematik


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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)

TBA

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.