26.04.2023 um 17:15 Uhr in Raum 69/125
Prof. Dr. Wolfgang Hackbusch (Max-Planck-Institut für Mathematik Leipzig)
On Nonclosed Tensor Formats
Usually, the dimension of tensor spaces is too large for storing tensors by their entries. Instead, other formats are used which on the other hand represent only a subset F of tensors. A representation if called [non]closed if F is [non]closed.
In the case of nonclosed formats F, there exist 'border tensors' in the closure of F outside of F. Approximating such border tensors causes a numerical instability corresponding to the cancellation error of numerical differentiation. We prove a uniform minimal strength of this unstable behaviour.
In a second part we discuss the case of infinite dimensional tensor spaces. Here the weak [non-]closedness of a format is of interest. We prove for the k-term format that weak closedness and standard closedness coincide and that even in infinite dimensions the instability is the same as for finite dimensional tensor spaces up to constants which are explicitly known.
Finally, we give explicit results for the instability of the 2-term format (for border tensors of border rank 2).
03.05.2023 um 17:15 Uhr in Raum 69/125
Prof. Dr. Hanna Döring und Prof. Dr. Alexander Salle
10.05.2023 um 17:15 Uhr in Raum 69/125
Dr. Alexey Ananyevskiy (LMU München)
Non-Vanishing Sections of Algebraic Vector Bundles and Trivial Chern Classes
24.05.2023 um 17:15 Uhr in Raum 69/125
Prof. Dr. Katharina Jochemko (KTH Stockholm)
Weighted Ehrhart Theory
07.06.2023 um 17:15 Uhr in Raum 69/125
Prof. Dr. Michael Gnewuch (U Osnabrück)
High-Dimensional Integration and Approximation: Randomized Algorithms and
14.06.2023 um 16:15 Uhr in Raum 69/125
Prof. Dr. Kathlén Kohn (KTH Stockholm)
3D-Rekonstruktion aus Bildern und Algebraische Geometrie
This is an Osnabrücker Maryam Mirzakhani Lecture
21.06.2023 um 17:15 Uhr in Raum 69/125
Prof. Mihyun Kang, Ph.D. (TU Graz)
Supercritical Percolation on the Hypercube
We consider a random subgraph obtained by bond percolation on the hypercube in the supercritical regime and derive expansion properties of its giant component. As a consequence we obtain upper bounds on the diameter of the giant component and the mixing time of the lazy simple random walk on the giant component. We also extend the results to random subgraphs of high-dimensional product graphs. This talk is based on joint work with Sahar Diskin, Joshua Erde, and Michael Krivelevich.