Geometric figures in the square grid
Maths circle meeting on 14 June 2025
Room and time: virtual/online with the video conferencing software Zoom (Paderborn University campus licence) from 10:00 to 13:00
Leader of the workshop: Dr Kerstin Hesse
Description: We consider a rectangular square grid in which all points of the grid have a distance of 1 to the direct link to the neighbouring points. The grid points are therefore (m,n), where m, n…
Abstract: In this talk I would like to discuss error estimates for anisotropic mean curvature flow of closed surfaces. We will first derive the evolution equations for the anisotropic flow, which formally resemble to those for the mean curvature flow (isotropic case), yet have substantially more complicated proofs. The discretisation in space uses evolving surface finite elements. Thanks to this formal resemblance, stability and consistency…
Abstract: For every prime p, a construction by Eichler-Shimura and Deligne attaches to a modular eigenform of weight k>1 a p-adic representation rho of the absolute Galois group of the rationals. The restriction of rho to a decomposition group at p is determined by k, by the Hecke eigenvalue a_p, and if the form is new at p, by its so-called L-invariant. When the weight is allowed to vary p-adically and a_p is nonzero, the theory of the…
Abstract: We study the existence versus blow-up for solutions to semilinear heat equations both on certain classes of Riemannian manifolds and on infinite graphs. On the manifold side, we show that when the bottom $\Lambda$ of the $L^2$ spectrum of the Laplace-Beltrami operator is strictly positive, as is the case for hyperbolic space $\mathbb{H}^N$, a Fujita-type phenomenon re-emerges for nonlinearities different from the classical power-type…
The Spin-Boson model describes the interaction between a quantum-mechanical two-state system, a spin, and a Bosonic field. Its Hamiltonian is said to have a ground state if the infimum of its spectrum is an eigenvalue. Using the Feynman-Kac formula, one can express matrix elements of the semigroup generated by the Hamiltonian in terms of a self-attractive jump process. We will discuss how one can apply this representation in order to derive…
Title: Dual complex of genus one mapping spaces
Abstract: The dual complex of a smooth variety encodes the combinatorial structure that underlies all its possible normal crossings compactifications. We prove that the dual complexes of genus zero and genus one mapping spaces are contractible (in degrees > 0 and > 1 respectively) via an explicit deformation retraction. In genus one, the key…
The Faculty of Electrical Engineering, Computer Science and Mathematics cordially invites you to the inaugural lectures of Jun. Prof. Dr. Simone Jablonski (Didactics of Mathematics) and Prof. Dr.-Ing. Nils Gerhardt (Semiconductor and Optoelectronic Devices) on Monday, June 23, starting at 4:15 pm.Simone Jablonski:“How much water do all schools in Paderborn use in one day?” So-called Fermi problems are a special form of modelling task: They…
Abstract:
Für Kindergartenkinder sind eigene mathematische Erfahrungen zentral für das mathematische Lernen (Hasemann & Gasteiger, 2014). Häufig besteht beim Sammeln von Erfahrungen im Kindergarten jedoch die Gefahr, dass die Kinder nur kindgemäße, aber kaum sachgerechte und fachlich anschlussfähige Erfahrungen sammeln können (vgl. Gasteiger, 2017). Im Vortrag wird das neu entwickelte Modell der «Mathematische Basiserfahrungen» vorgestellt. Mit…
On June 27th, the Colloquium of the CRC-TRR 358 will take place at the Department of Mathematics, Paderborn. The speakers are Prof. Ulrich Derenthal (Hannover) and Prof. Christian Lehn (Bochum).
In this talk I describe a novel Law of Dynamics for non-relativistic Quantum Mechanics (QM). The time evolution of individual physical systems consisting of charged matter interacting with the quantized electromagnetic field, e.g., electrons in the shell of an atom coupled to the radiation field, is non-linear, dissipative and stochastic, featuring isolated random events, called “quantum jumps." – We must search for the equations describing it!…
