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)

A Connection Between Arithmetic and Geometry

Suppose that f(x_1, ..., x_n) is a polynomial with coefficients in ℤ. Different people may ask very different questions about f: Number theorists might consider f as a diophantine equation, i.e., trying to understand the integer solutions of the equation f=0. Since this is intrinsically difficult, one often first tries to understand solutions modulo m, for integers m ≥ 2. Conceretely, one is interested in the number N_m of such solutions, as a function of m.
Geometers, on the other hand, are typically interested in the complex hypersurface X defined by f, i.e., the set of solutions of f=0 in ℂ^n. More conretely, one can ask whether X has singularities, and if yes, one would like to classify how bad those singularities are.
In this talk, I will explain why number theorists and geometers should (and do) talk to each other: It turns out that the singularities of X determine how complicated N_m is, as a function of m. This has already been known at least since the 70s, but I will give a rather new, geometric explanation for this connection.

05.11.2025 um 17:15 Uhr in Raum 69/125

Dr. Kateryna Pozharska (TU Chemnitz and NAS Ukraine)

Some Approaches for Multivariate Function Recovery from Incomplete Data and Related Problems

In the talk, we will discuss different decoders (linear, nonlinear) for function recovery from partial information,
such as function values, and compare the obtained error bounds with other benchmark quantities
to comment on the optimality. In what follows, we will consider concrete examples of relevant function classes
as well as present our findings concerning the related problem of norm discretization.

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.

17.12.2025 um 17:15 Uhr in Raum 69/125

Prof. Dr. Sabrina Pauli  (TU Darmstadt )

Counting Rational Plane Curves Using Tropical Geometry

In enumerative geometry, one asks how many geometric objects satisfy certain given conditions.
A classical example is to count rational plane curves of degree d passing through 3d-1 points in general position.
In the simplest case d=1, this means: how many lines go through two points? The answer is one, but as soon as d increases, the problem becomes surprisingly
difficult and requires modern techniques to solve.
One powerful approach comes from Mikhalkin’s tropical correspondence theorem, whichtranslates this classical counting problem into the tropical world.
There, curves are replaced by certain kinds of graphs and the counting becomes algorithmic. Remarkably, this correspondence completely solves this curve
counting problem for any degree d.
In the talk, I will introduce the idea behind this tropical correspondence theorem, show how the algorithms work in practice, and illustrate everything with many
concrete examples and pictures. If time permits, I will also touch on recent advances that refine these curve counts so that they make sense over arbitrary fields,
and mention a version of the tropical correspondence theorem in this broader setting.

07.01.2026 um 17:15 Uhr in Raum 69/125

Dr. Daniel Valesin (University of Warwick)

The Contact Process on Static and Dynamic Random Graphs

14.01.2025 um 17:15 Uhr in Raum 69/125

Prof. Dr. Stefan Kunis (Universität Osnabrück)

Sign Localized Test Functions in Fourier Analysis

We would like to discuss multivariate Fourier transform pairs where one function has bounded support and the transformed function has a well specified zero crossing. Such functions have widespread applications ranging from analytic number theory, sphere packing, geometry of quadrature points to computational diffraction limits in super-resolution microscopy. We discuss two specific constructions with their applications in deriving a diffraction limit and in estimating covering properties of generalized quadrature methods in detail.

21.01.2026 um 17:15 Uhr in Raum 69/125

Dr. David Krieg (Universität Passau) 

Optimal Sampling for Least Squares Approximation

28.01.2026 um 16:15 Uhr in Raum 69/125

Jun.-Prof. Dr. Marie-Charlotte Brandenburg (Ruhr-Uni Bochum)

TBA

This is an   Osnabrücker Maryam Mirzakhani Lecture