Wintersemester 2025/26
Wintersemester 2025/26
29.10.2025 um 17:15 Uhr in Raum 69/125
Prof. Dr. Immanuel Halupczok (Heinrich-Heine-Universität Düsseldorf)
TBA
26.11.2025 um 17:15 Uhr in Raum 69/125
Prof. Dr. Chinmoy Bhattacharjee (Universität Hamburg)
Quantitative CLT for Number of Extreme Points in Delaunay Tessellations
In this talk, we will consider three examples of Laguerre tessellations, namely, the β, β ′ and Gaussian Delaunay tessellations based on a
Poisson point process in R^d × R. We prove a quantitative central limit theorem with presumably optimal rates for the Gaussian convergence
of number of extreme points (points that form a cell) in the tessellations with their spatial coordinates falling within a growing window.
The proofs rely on the notion of region-stabilization which allows us to deal with some long-range interactions. The talk is based on an
ongoing joint work with Anna Gusakova.
03.12.2025 um 17:15 Uhr in Raum 69/125
Dr. Dirk Frettlöh (Uni Bielefeld)
Aperiodic Tilings with Infinitely Many Prototiles
10.12.2025 um 17:15 Uhr in Raum 69/125
Prof. Dr. André Uschmajew (Universität Augsburg)
Randomized Low-Rank Approximation of Hilbert-Schmidt Operators
Low-rank approximation methods for matrices are based on projecting the columns (or rows) to suitable low-dimensional subspaces. Taking subspaces spanned by individual columns or by random linear combinations of all columns are common alternatives to the computation of optimal subspaces via the SVD, especially for large or implicitly given matrices. Well-known results on volume sampling or randomized SVD show that such approaches indeed achieve quasi-optimal approximation errors in expectation. In this talk, we discuss generalizations of such results to low-rank approximation of Hilbert-Schmidt operators between infinite-dimensional Hilbert spaces. In the first part, we consider the approximation of vector valued L2 functions in subspaces spanned by point samples, and show existence of quasi-optimal sample points based on a continuous version of volume sampling. In the second part, we discuss infinite-dimensional extensions of the randomized SVD as recently proposed by Boullé and Townsend, for which we present an alternative approach. This also includes a novel extension of the Nyström approximation for self-adjoint positive semi-definite trace class operators. Based on joint work with D. Kressner, T. Ni, and D. Persson.