Upcoming Events

Tuesday, 18.02.2025, 15:00 (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Anna Shalova, Eindhoven University of Technology:
Solutions of stationary McKean-Vlasov equation on a sphere
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
We study stationary solutions of McKean-Vlasov equation on a high-dimensional sphere. We extend the equivalence of the energetic problem formulation to the manifold setting and characterise critical points of the corresponding free energy functional. Under additional assumptions on the interaction kernel we prove optimality of unimodal (synchronised) solutions. Employing the properties of spherical convolution we study the bifurcation branches around the uniform state. We also give a sufficient condition for an existence of a discontinuous transition point in terms of the interaction kernel and compare it to the Euclidean setting. The talk is mostly based on the joint work with André Schlichting: Solutions of stationary McKean-Vlasov equation on a high-dimensional sphere and other Riemannian manifolds, arXiv:2412.14813 (2024).

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Thursday, 20.02.2025, 10:15 (WIAS-405-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Giulio Schimperna, Università degli Studi di Pavia, Italien:
Some results on a modified Cahn-Hilliard model with chemotaxis
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We will present some mathematical results for a new model coupling the Cahn-Hilllard system with an evolutionary equation describing the active (chemotactic) transport of a chemical species influencing the phase separation process. Specifically, the model may arise in connection with tumor growth processes; mathematically speaking, it may be interesting in itself as it provides a new coupling between a Keller-Segel-like relation (the equation describing the evolution of the concentration of the chemical substance) and a fourth order (rather than a second order as in most models for chemotaxis) evolutionary system. Our main result will be devoted to proving existence of weak solutions in the case when the chemotaxis sensitivity function has a controlled growth at infinity; a particular emphasis will be given to discussing the occurrence of critical exponents and to presenting a regularization scheme compatible with the a-priori estimates. Moreover, we will discuss an extension of the model where the effects of a macroscopic velocity flow of Brinkman type are taken into account and analyze the Darcy limit regime. Finally, referring to the (more difficult) case of linear chemotactic sensitivity we will shortly present some work in progress, in collaboration with Elisabetta Rocca (Pavia) and Robert Lasarzik (WIAS), related to the existence of very weak solutions as well as weak-strong uniqueness.

Host
WIAS Berlin
Wednesday, 26.02.2025, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Renato Soares dos Santos, Universidade Federal de Minas Gerais (UFMG), Brasilien:
Interacting Poissonian trajectories and clonal interference
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We consider a Moran model with mutation and selection in the limit of large population. Mutation occurs in the so-called Gerrish-Lenski regime where mutations are neither too frequent nor too rare, giving rise to clonal interference. Focusing on the case of strong selection, we show distributional convergence of the rescaled process to a system of interacting Poissonian lines. Joint work with Adrian Gonzalez-Casanova, Felix Hermann, Andras Tobias and Anton Wakolbinger.

Further Informations
Seminar Interacting Random Systems

Host
WIAS Berlin
Thursday, 27.02.2025, 14:00 (WIAS-405-406)
Seminar Numerische Mathematik
Dr. El-Houssaine Quenjel, La Rochelle Université:
Stable finite volume methods for transient convection-diffusion systems with anisotropy
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Host
WIAS Berlin
Thursday, 13.03.2025, 14:00 (WIAS-405-406)
Seminar Numerische Mathematik
Dr. John Papadopoulos, WIAS Berlin:
Hierarchical proximal Galerkin: a fast hp-FEM solver for variational problems with pointwise inequality constraints
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Numerical mathematics seminars

Host
WIAS Berlin
Thursday, 27.03.2025, 14:00 (WIAS-405-406)
Seminar Numerische Mathematik
Prof. Cornelis Vuik, Delft University of Technology:
Resolving divergence: the first multigrid scheme for the highly indefinite Helmholtz equation using classical components
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this talk, we (V. Dwarka and C. Vuik) present the first stand-alone classical multigrid solver for the highly in- definite 2D Helmholtz equation with constant costs per iteration, addressing a longstanding open problem in numerical analysis [1]. Our work covers both large constant and non- constant wavenumbers up to k = 500 in 2D. We obtain a full V - and W -cycle without any level-dependent restrictions. Another powerful feature is that it can be combined with the computationally cheap weighted Jacobi smoother. The key novelty lies in the use of higher-order inter-grid transfer operators [2]. When combined with coarsening on the Complex Shifted Laplacian, rather than the original Helmholtz operator, our solver is h-independent and scales linearly with the wavenumber k. If we use GMRES(3) smoothing we obtain k- independent convergence, and can coarsen on the original Helmholtz operator, as long as the higher-order transfer operators are used. This work opens doors to study robustness of contemporary solvers, such as machine learning solvers inspired by multigrid components, without adding to the black-box complexity.

Host
WIAS Berlin