26.04.2018 um 17:15 Uhr in Raum 69/125
Prof. Dr. Bernd Sturmfels (MPI Leipzig)
Learning Algebraic Varieties from Samples
This lecture discusses the role of algebraic geometry in data science.
We report on recent work with Paul Breiding, Sara Kalisnik and Madeline Weinstein.
We seek to determine a real algebraic variety from a fixed finite subset of points.
Existing methods are studied and new methods are developed. Our focus lies on
topological and algebraic features, such as dimension and defining polynomials.
All algorithms are tested on a range of datasets and made available in a Julia package.
02.05.2018 um 17:15 Uhr in Raum 69/125
Prof. Dr. Yurii Kolomoitsev (Universität zu Lübeck)
On the Growth of Lebesgue Constants for Convex Polyhedra
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.