Veranstaltungen

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Mittwoch, 03.07.2024, 10:00 Uhr (WIAS-ESH)

Forschungsseminar Mathematische Statistik
Prof. Céline Duval, Université de Lille, Frankreich:
Geometry of excursion sets: Computing the surface area from discretized points
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
The excursion sets of a smooth random field carries relevant information in its various geometric measures. After an introduction of these geometrical quantities showing how they are related to the parameters of the field, we focus on the problem of discretization. From a computational viewpoint, one never has access to the continuous observation of the excursion set, but rather to observations at discrete points in space. It has been reported that for specific regular lattices of points in dimensions 2 and 3, the usual estimate of the surface area of the excursions remains biased even when the lattice becomes dense in the domain of observation. We show that this limiting bias is invariant to the locations of the observation points and that it only depends on the ambient dimension. (based on joint works with H. Biermé, R. Cotsakis, E. Di Bernardino and A. Estrade).

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Der Vortrag findet auch via Zoom statt: https://hu-berlin.zoom-x.de/j/69268586742?pwd=bDZJQTk5TGdnUkVCUk9RWGdsWC9vdz09 Meeting-ID: 692 6858 6742, Passwort: 021844

Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin

Mittwoch, 03.07.2024, 14:14 Uhr (WIAS-ESH)

Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Andreas Vikelis, Universität Wien, Österreich:
Measure-valued solutions for non-associative finite plasticity
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
The variational treatment of evolutionary nonassociative elasto-plasticity at finite strains remains unexplored. In this direction, following the concept of energetic solutions, we present an existence result for measure-valued solutions of the quasistatic evolution problem which are stable and balance the energy. In particular, we apply a modification of the standard timediscretization scheme, considering Young measures generated by piecewise constant interpolants of time-discrete solutions of a properly defined minimization problem. A key point in our analysis is the limit passage in the dissipation. The later calls for time-continuity properties of the stresses which are not expected in the quasistatic framework. To overcome this obstacle we introduce a regularization of the generalized stress in the definitionof our energetic solutions. Joint work with Ulisse Stefanelli.

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Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin

Donnerstag, 04.07.2024, 10:00 Uhr (WIAS-406)

Seminar Materialmodellierung
Dr. Jörg Weber, Universität Wien, Österreich:
Axisymmetric capillary water waves with vorticity and swirl
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
While the research on axisymmetric capillary water waves has a long history, surprisingly little has been done when one wants to allow for vorticity (local spinning) and swirl (angular momentum). After introducing the problem and presenting a well-known formulation in terms of the Stokes stream function, we will explain the main analytical ingredients in order to rigorously construct travelling wave solutions with a free boundary. Then, two solution curves are constructed: First, we start at perfectly cylindrical jets, where we derive the dispersion relation and investigate it in detail in certain cases. Also, we will point out inherent connections to the famous Rayleigh instability observed in everyday life, e.g. when a tap drips. Second, we start at static configurations with constant mean curvature surfaces, so-called unduloids. There, as an interesting interplay between water waves, geometry, and elliptic integrals, we show rigorously that to any such configuration there connects a curve of non-static configurations, which confirms previous numerical observations. The talk is based on joint work with André Erhardt (WIAS), Anna-Mariya Otsetova (Aalto), and Erik Wahlén (Lund).

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Seminar “Materialmodellierung”

Veranstalter
WIAS Berlin

Mittwoch, 10.07.2024, 14:15 Uhr (WIAS-ESH)

Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Caroline Lasser, Technische Universität München:
Variational Gaussian approximation for quantum dynamics
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
The talk considers the time-dependent Schrödinger equation with smooth magnetic and electric potentials in semiclassical scaling. We analyse nonlinearly parametrized approximations by single Gaussian wave packets via the Dirac--Frenkel variational principle. We derive ordinary differential equations of motion for the parameters of the variational solution. We present L²-error bounds and unexpectedly accurate observable error bounds. This is joint work with S. Burkhard, B. Dörich, and M. Hochbruck.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin

Mittwoch, 10.07.2024, 16:15 Uhr (WIAS-ESH)

Berliner Kolloquium Wahrscheinlichkeitstheorie
Dan Crisan, Imperial College London:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Veranstalter
Humboldt-Universität zu Berlin
Technische Universität Berlin
WIAS Berlin

Mittwoch, 10.07.2024, 17:15 Uhr (WIAS-ESH)

Berliner Kolloquium Wahrscheinlichkeitstheorie
Jiniao Qiu, U of Calgary:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Veranstalter
Humboldt-Universität zu Berlin
Technische Universität Berlin
WIAS Berlin

Montag, 15.07.2024, 10:00 Uhr (Berlin Mitte)

MATH+ Thematic Einstein Semester on “Mathematics for Quantum Technologies”
Prof. Ulf Leonhardt, Weizmann Institute of Science, Israel:
First advanced lecture of the series “Forces of the quantum vacuum” .
mehr ... Veranstaltungsort
Berlin Mitte

Abstrakt
Topic: Setting the scene
Quantization of the electromagnetic field in media and in space-time
Normal modes and harmomic oscillators
Zero-point energy
Casimir's cavity: 1D case, zeta-function renormalization
Casimir's cavity: 3D case, Casimir's renormalization

Veranstalter
WIAS Berlin
Einstein Foundation Berlin

Dienstag, 16.07.2024, 10:00 Uhr (Berlin Mitte)

MATH+ Thematic Einstein Semester on “Mathematics for Quantum Technologies”
Prof. Ulf Leonhardt, Weizmann Institute of Science, Israel:
Second advanced lecture of the series “Forces of the quantum vacuum” .
mehr ... Veranstaltungsort
Berlin Mitte

Abstrakt
Topic: Lifshitz theory
The need for a theory in dispersive and dissipative media
Point-splitting method
Fluctuation-dissipation theorem
Kubo-Martin-Schwinger relation
Lifshitz formula in planar, piece-wise homogenous media

Veranstalter
WIAS Berlin
Einstein Foundation Berlin

Mittwoch, 17.07.2024, 14:15 Uhr (WIAS-ESH)

Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Daniel Matthes, Technische Universität München:
Covariance modulated optimal transport: Geometry and gradient flows
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
This talk is about a novel variant of optimal mass transport in which particles move with a global linear but anisotropic mobility depending on the covariance of the ensemble density. This gives rise to a novel kind of Wasserstein metric that provides a rigorous gradient flow formulation of the mean-field limit for the ensemble Kalman sampling. In combination with the abstract machinery of metric gradient flows, the new metric is an effective tool to study the rate of convergence of these methods. I shall present several analytic results about the modulated Wasserstein metric. The first is the splitting representation, which allows to write the modulated metric as the sum of two simpler metrics, one measuring the distance in terms of first and second moments, the other one measuring in terms of shapes. The second result is about geodesic convexity and the related rates of convergence in gradient flows. Specifically, we prove exponential equilibration in linear Fokker-Planck equations with Gaussian steady states at a rate that does not depend on the covariance of the Gaussian. The third and only partial result is about geodesics, that we prove to exist for sufficiently close densities, or densities with multiple reflection symmetries. We also characterize geodesics in terms of particle trajectories, that are no longer straight line as in the genuine Wasserstein metric, but follow more complicated curves that satisfy second order ordinary differential equations. This is joint work with Andre Schlichting, Matthias Erbar, Franca Hoffmann, and Martin Burger.

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Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin

Donnerstag, 18.07.2024, 10:00 Uhr (Berlin Mitte)

MATH+ Thematic Einstein Semester on “Mathematics for Quantum Technologies”
Prof. Ulf Leonhardt, Weizmann Institute of Science, Israel:
Third advanced lecture of the series “Forces of the quantum vacuum” .
mehr ... Veranstaltungsort
Berlin Mitte

Abstrakt
Topic: Applications
Imaginary frequencies for capturing the broad band of quantum forces
Thermal Casimir effect
Perfectly conducting cavity
Magnetic mirror and Casimir repulsion
Permittivity hierarchy and repulsive Casimir forces
Negative refraction and quantum levitation
Engineering in the imaginary part of the spectrum


Veranstalter
WIAS Berlin
Einstein Foundation Berlin

Donnerstag, 18.07.2024, 15:00 Uhr (WIAS-406)

Seminar Materialmodellierung
Prof. Dr. Jan Giesselmann, Technische Universität Darmstadt:
A posteriori error estimates for systems of hyperbolic conservation laws modeling compressible flows
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
Hyperbolic conservation laws are a class of PDEs that have many applications, most notably in compressible fluid flows when viscosity is neglected. While these equations are successfully used by engineers in simulations, there are many open questions regarding their mathematical study. These are mostly driven by to the non-uniqueness of entropy solutions in multiple space dimensions but even in one space dimensions stability of solutions is challenging if one is to go beyond initial data that are small in BV.
The challenges in the mathematical analysis have lead to a situation where a variety of sophisticated numerical schemes exists and is successfully used in practice but the mathematical foundations of these methods are not as substantial as one would hope. This issue has been addressed by several authors in recent years and we plan plan to present what has been achieved in the field of a posteriori error estimates, i.e. explicit bounds for the error of the numerical solution that can be computed from the numerical solution.
A fundamental building block of a posteriori error estimates are stability theories that allow to relate certain norms of residuals, i.e. quantities measuring by how much an approximate solution fails to satisfy the PDE, to certain norms of the error, i.e. the difference between numerical and exact solution. Examples of such stability theories include the classical relative entropy framework, the theory of shifts developed by Vasseur and coworkers and recent results by Bressan and coworkers.
We will describe these stability results and discuss how they have been used to derive a posteriori error estimates for hyperbolic conservation laws.

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Seminar Materialmodellierung

Veranstalter
WIAS Berlin

Freitag, 19.07.2024, 10:00 Uhr (Berlin Mitte)

MATH+ Thematic Einstein Semester on “Mathematics for Quantum Technologies”
Prof. Ulf Leonhardt, Weizmann Institute of Science, Israel:
Fourth advanced lecture of the series “Forces of the quantum vacuum” .
mehr ... Veranstaltungsort
Berlin Mitte

Abstrakt
Topic: Outlook
The quantum vacuum seen by accelerated observers (relativistic acceleration, Rindler coordinates, Unruh effect)
Entanglement in the quantum vacuum
Classical analogue of the Unruh effect
The case for a Casimir cosmology

Veranstalter
WIAS Berlin
Einstein Foundation Berlin

Mittwoch, 24.07.2024, 14:15 Uhr (WIAS-ESH)

Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Emil Wiedemann, Friedrich-Alexander-Universität Erlangen-Nürnberg:
Measure-valued solutions in fluid dynamics
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
As more and more ill-posedness results have been shown for fluid PDEs (not only by convex integration!), the idea to solve the Cauchy problem by some unique weak or entropy solution has become questionable. Instead, non-deterministic solution concepts such as measure-valued or statistical have sparked much recent research interest. They also seem to be more in line with well-known theories of turbulence, which are typically statistical. I will give an overview of measure-valued solution concepts, including their weak-strong stability, their relation to more conventional solutions, and questions of existence. Links to other notions of "very weak" solution (dissipative, subsolutions, energy-variational) will briefly be discussed.

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Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin

Donnerstag, 08.08.2024, 13:30 Uhr (WIAS-406)

Seminar Materialmodellierung
Dr. Ferran Brosa Planella, University of Warwick, GB:
Asymptotic methods for lithium-ion battery models
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
Lithium-ion batteries have become ubiquitous over the past decade, and they are called to play even a more important role with the electrification of vehicles. In order to design better and safer batteries and to manage them more efficiently, we need models than can predict the battery behaviour accurately and fast. However, in many cases these models are still posed in an ad hoc way, which makes them hard to extend and may lead to inconsistencies. In this talk we will see some examples on how asymptotic methods can be applied to obtain simple models that can be used in battery control and parameterisation.

Veranstalter
WIAS Berlin

Mittwoch, 04.09.2024, 11:30 Uhr (WIAS-405-406)

Seminar Interacting Random Systems
Martijn Gösgens, TU Eindhoven:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
tba

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Seminar Interacting Random Systems (Hybrid Event)

Veranstalter
WIAS Berlin

Mittwoch, 18.09.2024, 10:00 Uhr (WIAS-405-406)

Seminar Numerische Mathematik
Albert Pool, DLR:
Nonlinear dynamics as a ground-state solution on quantum computers
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Veranstalter
WIAS Berlin

Mittwoch, 18.09.2024, 10:00 Uhr (WIAS-405-406)

Seminar Numerische Mathematik
Albert J. Pool, Deutsches Zentrum für Luft- und Raumfahrt e.V.:
Nonlinear dynamics as a ground-state solution on quantum computers
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
For the solution of time-dependent nonlinear differential equations, we present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution from a single ground-state computation. We describe a general procedure to construct efficient quantum circuits for the cost function evaluation required by VQAs. To mitigate the barren plateau problem during the optimization, we propose an adaptive multigrid strategy. The approach is illustrated for the nonlinear Burgers equation. We classically optimize quantum circuits to represent the desired ground-state solutions, run them on IBM Q System One and Quantinuum System Model H1, and demonstrate that current quantum computers are capable of accurately reproducing the exact results.

Veranstalter
WIAS Berlin