Current Lectures and Events
17.04.2018 um 16:15 Uhr in 69/125:
Van Duc Trung (University of Genova, Italy)
The initial ideal of generic sequences and Fröberg's Conjecture
Let K be an infinite field and let I = (f1,...,fr) be an ideal in the polynomial ring R = K[x1,...,xn] generated by generic forms of degrees d1,...,dr. In the case r=n, following an effective method by Gao, Guan and Volny, we give a description of the initial ideal of I with respect to the degree reverse lexicographic order. From this description, we prove a conjecture stated by Pardue in 2010 under a suitable condition on d1,..., dn. This holds partial solutions to a longstanding conjecture stated by Fröberg (1985) on the Hilbert series of R/I in the case r ≤ n+2 and over an infinite field of any characteristic.
10.04.2018 um 16:15 Uhr in 69/125:
Arun Kumar (Universität Osnabrück)
We will construct the Grassmannian and the Quaternionic Grassmannian Varieties and see how are they are related to Algebraic and Hermitian K-theory respectively.
24.04.2018 um 16:15 Uhr in 69/125:
Holger Brenner (Universität Osnabrück)
Asymptotic properties of differential operators on a singularity
For a local algebra R over a field, we study the decomposition of the module of principal parts. A free summand of the nth module of principal parts is essentially the same as a differential operator E of order ≤ n with the property that the differential equation E(f) =1 has a solution. The asymptotic behavior of the seize of the free part gives a measure for the singularity represented by R. We compute this invariant for invariant rings, monoid rings, determinantal rings and compare it with the F-signature, which is an invariant in positive characteristic defined by looking at the asymptotic decomposition of the Frobenius. This is joint work with Jack Jeffries and Luis Nuñez Betancourt.
17.04.2018 um 14:15 Uhr in 69/E15:
Lyne Moser (École polytechnique fédérale de Lausanne)
Injective and projective model structures on enriched diagram categories
R. Garner, K. Hess, M. Kedziorek, E. Riehl, and B. Shipley have developed methods to induce model structures from an adjunction. The injective and projective model structures on categories of diagrams in accessible model categories can be induced from specific Kan extension adjunctions using these methods. In this talk, I will explain how to adapt this result to an enriched setting, in order to prove the existence of injective and projective model structures on categories of enriched diagrams in enriched model categories, which satisfy some enriched accessibility and enriched local presentability conditions.