Veranstaltungen

Dienstag, 21.01.2025, 17:00 Uhr (Online Event)

Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Francesca Primavera, Universität Wien:
Functional Ito-formula and Taylor expansions for non-anticipative maps of Càdlàg rough path (online talk)
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Online Event

Abstrakt
We rely on the approximation properties of the signature of Càdlàg rough paths to derive a functional Ito-formula for non-anticipative maps of rough paths. This leads to a functional extension of the Ito-formula for Càdlàg rough paths (by Friz and Zhang (2018)) which coincides with the change of variable formula formulated by Dupire (2009) whenever the functionals representations, the notions of the regularity of the functionals and the integration concepts can be matched. In contrast to these works, by using the concept of vertical Lie derivatives, we can also incorporate path functionals where the second order vertical derivatives do not commute as it is the case for typical signature functionals. As a byproduct, we show that sufficiently regular non-anticipative maps admit a functional Taylor expansion, leading to a far reaching generalization of the recently established results by Dupire and Tissot-Daguette (2022). The talk is based on an ongoing joint work with Chrsta Cuchiero and Xin Guo.

Weitere Informationen
Link to the seminar room: https://zoom.us/j/492088715

Veranstalter
WIAS Berlin

Mittwoch, 22.01.2025, 10:00 Uhr (WIAS-HVP-3.13)

Forschungsseminar Mathematische Statistik
Prof. Dr. Vincent Rivoirard, Université Paris Daupine, Frankreich:
PCA for point processes
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Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13

Abstrakt
We introduce a novel statistical framework for the analysis of replicated point processes that allows for the study of point pattern variability at a population level. By treating point process realizations as random measures, we adopt a functional analysis perspective and propose a form of functional Principal Component Analysis (fPCA) for point processes. The originality of our method is to base our analysis on the cumulative mass functions of the random measures which gives us a direct and interpretable analysis. Key theoretical contributions include establishing a Karhunen-Lo`eve expansion for the random measures and a Mercer Theorem for covariance measures. We establish convergence in a strong sense, and introduce the concept of principal measures, which can be seen as latent processes governing the dynamics of the observed point patterns. We propose an easy-to-implement estimation strategy of eigenelements for which parametric rates are achieved. We fully characterize the solutions of our approach to Poisson and Hawkes processes and validate our methodology via simulations and diverse applications in seismology, single-cell biology and neurosiences, demonstrating its versatility and effectiveness. Joint work with Victor Panaretos (EPFL), Franck Picard (ENS de Lyon) and Angelina Roche (Université Paris Cité).

Weitere Informationen
Dieser Vortrag findet hybrid statt. Die Teilnahme per Zoom ist über den (neuen!) Link: https://hu-berlin.zoom-x.de/j/62476510180?pwd=1bws9DORlDM2Iub3ANrb7zzDNANvsJ.1

Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin

Mittwoch, 22.01.2025, 14:00 Uhr (WIAS-405-406)

Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Jan-Frederik Pietschmann, Universität Augsburg:
Gradient flows on metric graphs with reservoirs
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
We study an evolution equation on metric graphs with reservoirs, that is graphs where a one-dimensional interval is associated to each edge and, in addition, the vertices are able to store mass. We focus on the case then the dynamics is driven by an entropy functional, defined both on edges and vertices. We provide a rigorous understanding of such equations as a gradient flow (in continuity equation format) with respect to metric that allows for a coupling between edge and vertex dynamics. By approximating the edges by a sequence of vertices, resulting in a fully discrete system, we are able to establish existence of solutions in this formalism. Next, we study several scaling limits and using in the framework of EDP convergence with embedding we are able to rigorously show convergence to again gradient flows on reduced graphs. Finally, numerical studies confirm our theoretical findings.

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Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin

29. – 31. Januar 2025 (WIAS-405-406)

Workshop/Konferenz: Critical behaviour in spatial particle systems
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Veranstalter
WIAS Berlin

Mittwoch, 29.01.2025, 10:30 Uhr (WIAS-405-406)

Seminar Interacting Random Systems
Anh Duc Vu, WIAS Berlin:
Basics on random walks and electrical networks
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
The talk aims to give a low-level introduction to random walks on certain graphs and how they are intricately linked to physical quantities in electrical networks. Edges in the graph are assigned conductances which govern the rate at which the random walk traverses said edge. We will see that this model has nice intuitive interpretations in the framework of electrical networks and explore some milestone results, e.g. Solomon's "random walks in random environment" from 1975.

Veranstalter
WIAS Berlin

Mittwoch, 05.02.2025, 15:15 Uhr (WIAS-405-406)

Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Ass. Prof. Sebastian Schwarzacher, Uppsala University, Schweden:
Time-periodic solutions for fluid-solid interactions
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
I will discuss several recent analytic discoveries and numerical experiments about the appearance of time-periodic motions when fluids interact with solids. On one hand, I will present abstract results on the existence and uniqueness of solutions when a parabolic PDE interacts with a hyperbolic PDE. In this setting, geometric conditions will be explored that allow for unique solutions and, as such, exclude hyperbolic resonances. Additionally, I will discuss some results for deformable shells interacting with fluids. On the other hand, I will show numerical experiments related to the appearance of bifurcations in the Navier-Stokes equations, known as the von Karman vortex street. The work presented was established in collaboration with J. Cach, C. Midnrila, S. Mosny, B. Muha, K. Tuma, and J. Webster.

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Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin

Mittwoch, 12.02.2025, 11:30 Uhr (WIAS-405-406)

Seminar Interacting Random Systems
Benedikt Jahnel, WIAS Berlin and TU Braunschweig:
tba
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Veranstalter
WIAS Berlin

Mittwoch, 12.02.2025, 15:15 Uhr (WIAS-Library)

Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. André Schlichting, Universität Ulm:
Breakdown of the mean-field description of interacting systems: Phase transitions, metastability and coarsening
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Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Abstrakt
We present results concerning the qualitative and quantitative description of interacting systems, with particular emphasis on those possessing a phase transition under the change of relevant system parameters. For this, we first discuss and identify continuous and discontinuous phase for mean-field limits of interacting particle systems on the torus and spheres. Since phase transitions are intimately related to the metastability of the stochastic particle system, we show how a suitable mountain pass theorem in the space of probability measures can describe the metastable behaviour of the underlying finite particle system. We also argue that the mean-field description of the particle system in the regime of strong local interaction has to break down. In this regime, coarsening is observed, where smaller clusters grow through coagulation events. We provide numerical experiments with a positivity preserving numerical scheme for a SPDE of Dean-Kawasaki type, consisting of the McKean-Vlasov equation and conservative noise. Joint works with Nicolai Gerber (U Ulm), Rishabh Gvalani (ETH Zürich), Greg Pavliotis (Imperial London) and Anna Shalova (TU Eindhoven).

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Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin

Donnerstag, 20.02.2025, 10:15 Uhr (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
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
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.

Veranstalter
WIAS Berlin

Donnerstag, 27.02.2025, 14:00 Uhr (WIAS-405-406)

Seminar Numerische Mathematik
Dr. El-Houssaine Quenjel, La Rochelle Université:
Stable finite volume methods for transient convection-diffusion systems with anisotropy
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Veranstalter
WIAS Berlin

Donnerstag, 27.03.2025, 14:00 Uhr (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
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
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.

Veranstalter
WIAS Berlin