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Monday, 15.07.2024, 10:00 (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” .
more ... Location
Berlin Mitte

Abstract
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

Host
WIAS Berlin
Einstein Foundation Berlin
Tuesday, 16.07.2024, 10:00 (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” .
more ... Location
Berlin Mitte

Abstract
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

Host
WIAS Berlin
Einstein Foundation Berlin
Tuesday, 16.07.2024, 13:30 (WIAS-ESH)
Seminar Numerische Mathematik
Nishant Ranwan, Indian Institute of Science Education and Research Thiruvananthapuram, Kerala, Indien:
Existence of a weak solution to the fluid-structure interaction problem of blood flow in coronary artery
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
This work is dedicated to proving the existence of a weak solution to the nonlinear coupled fluid-structure interaction (FSI) problem arising in modeling the blood flow through the coronary artery. Considering blood as a homogeneous, incompressible, Newtonian fluid, the $3D$ Navier--Stokes equations model the flow. We adopt the St. Venant--Kirchhoff elasticity model for the arterial wall. With the help of dynamic and kinematic boundary conditions, we define the fluid-structure coupling (two-way) at the interface. Using the operator splitting approach, we split the coupled problem into two parts: the structure sub-problem (SSP) in the Galerkin framework and the piece-wise stationary fluid sub-problem (FSP). In order to establish the existence of a weak solution, the initial step is to tackle the SSP. Following this, the fluid domain is updated through the Harmonic Extension of the structural displacement. Subsequently, the focus shifts to solving the coupled Navier--Stokes equations within the updated fluid domain.

Further Informations
Seminar Numerische Mathematik

Host
WIAS Berlin
Tuesday, 16.07.2024, 15:15 (FU-140)
Oberseminar Nonlinear Dynamics
Dr. Sören von der Gracht, Universität Paderborn:
Exploring exotic symmetries to explain exotic behavior of network dynamical systems (hybrid talk)
more ... Location
Freie Universität Berlin, Arnimallee 7, 14195 Berlin, Hinterhaus, Raum: 140

Abstract
Many dynamical systems models of real world processes exhibit the structure of a network consisting of nodes with connections between them. The specific interaction structure of a network can produce remarkable dynamics beyond that of the individual nodes. Prominent examples include synchronization and highly complex branching behavior in bifurcations, phenomena that are not found in dynamical systems without the structure of a network. Network dynamical systems are not well understood mathematically, which makes it hard to quantify and control their behavior. The reason is that most of the established machinery of dynamical systems theory fails to distinguish between networks and general dynamical systems. Several mathematical tools that are tailor-made for network problems have been proposed recently. Strikingly, they have one thing in common: they exploit the algebraic nature of networks. In this talk, I will give an overview over some recent results regarding the question which dynamical behavior and generic bifurcations are dictated by the network structure of a system. In particular, I will illustrate how structural and algebraic properties culminate in symmetries of the governing equations and how these can be exploited for (partial) answers. This includes classical symmetries but also more exotic concepts such as monoid and quiver representations.

Further Informations
Oberseminar Nonlinear Dynamics

Host
Freie Universität Berlin
WIAS Berlin
Tuesday, 16.07.2024, 16:30 (FU-140)
Oberseminar Nonlinear Dynamics
Prof. Hans Engler, Georgetown University, USA:
The Lorenz System of 1996 (hybrid talk)
more ... Location
Freie Universität Berlin, Arnimallee 7, 14195 Berlin, Hinterhaus, Raum: 140

Abstract
The meteorologist and applied mathematician Edward Lorenz is famous for discovering chaotic behavior in dynamical systems in 1963. In 1996, Lorenz introduced a dynamical system that describes very simple "weather" on a cartoon planet: a scalar quantity evolves on a circular array of N sites, undergoing radiative forcing, dissipation, and nonlinear advection. Lorenz proposed this system as a test bed for numerical weather prediction. Since then, it has found much use as a test case in data assimilation. Related systems have been studied by other authors earlier. Mathematically, this is an nonlinear N-dimensional dynamical system that is invariant under rotating the sites. There is a single parameter, namely forcing strength. For small forcing strength, there is no "weather": the only possible stable solutions are constant in space and time. As the strength of the forcing increases, periodic wave patterns appear that move around the circle of sites. These periodic patterns are not unique - the same forcing strength may be associated with stable patterns that are qualitatively different, depending on the system's initial state. For even larger forcing, the motion becomes chaotic. Regular wave patterns are replaced by moving irregular wave trains that are short-lived, similar to changing weather systems that move across a landscape. The talk will introduce the main properties of this and of related systems. The appearance of periodic solutions can be explained with bifurcation theory for all these versions. By using the discrete Fourier transform and explicit computation of normal form coefficients, the stability of bifurcating periodic solutions and the coexistence of multiple such solutions for the same radiative forcing can be understood. The system also shows delayed transition to instability as the forcing parameter increases slowly.
This is joint work with John Kerin, a former Georgetown University undergraduate student.

Further Informations
Oberseminar Nonlinear Dynamics

Host
Freie Universität Berlin
WIAS Berlin
Wednesday, 17.07.2024, 14:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Daniel Matthes, Technische Universität München:
Covariance modulated optimal transport: Geometry and gradient flows
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
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.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Thursday, 18.07.2024, 10:00 (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” .
more ... Location
Berlin Mitte

Abstract
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


Host
WIAS Berlin
Einstein Foundation Berlin
Thursday, 18.07.2024, 15:00 (WIAS-406)
Seminar Materialmodellierung
Prof. Dr. Jan Giesselmann, Technische Universität Darmstadt:
A posteriori error estimates for systems of hyperbolic conservation laws modeling compressible flows
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
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.

Further Informations
Seminar Materialmodellierung

Host
WIAS Berlin
Friday, 19.07.2024, 10:00 (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” .
more ... Location
Berlin Mitte

Abstract
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

Host
WIAS Berlin
Einstein Foundation Berlin
Tuesday, 23.07.2024, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Yuanyuan Li, Fudan University, China, Volksrepublik:
Function and derivative approximation by shallow neural networks
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We investigate a Tikhonov regularization scheme specifically tailored for shallow neural networks within the context of solving a classic inverse problem: approximating an unknown function and its derivatives within a bounded domain based on noisy measurements. The proposed Tikhonov regularization scheme incorporates a penalty term that takes three distinct yet intricately related network (semi)norms: the extended Barron norm, the variation norm, and the Radon-BV seminorm. These choices of the penalty term are contingent upon the specific architecture of the neural network being utilized. We establish the connection between various network norms and particularly trace the dependence of the dimensionality index, aiming to deepen our understanding of how these norms interplay with each other. We revisit the universality of function approximation through various norms, establish rigorous error-bound analysis for the Tikhonov regularization scheme, and explicitly elucidate the dependency of the dimensionality index, providing a clearer understanding of how the dimensionality affects the approximation performance.

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

Host
WIAS Berlin
Wednesday, 24.07.2024, 14:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Emil Wiedemann, Friedrich-Alexander-Universität Erlangen-Nürnberg:
Measure-valued solutions in fluid dynamics
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
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.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 30.07.2024, 15:00 (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Egor Gladin, Humboldt Universität zu Berlin:
Cutting plane methods and dual problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
The present talk examines cutting plane methods, which are a group of iterative algorithms for minimizing a (possibly nonsmooth) convex function over a compact convex set. We consider two prominent examples, namely, the ellipsoid method and Vaidya's method, and show that their convergence rate is preserved even when an inexact oracle is used. Furthermore, we demonstrate that it is possible to use these methods in the context of stochastic optimization efficiently. Another direction where cutting plane methods can be useful is Lagrange dual problems. Commonly, the objective and its derivatives can only be computed approximately in such problems. Thus, the methods' insensitivity to error in subgradients comes in handy. As an application example, we propose a linearly converging dual method for a constrained Markov decision process (CMDP) based on Vaidya's algorithm with an inexact oracle. The talk also discusses the concept of accuracy certificates for convex minimization problems. Certificates allow for online verification of the accuracy of approximate solutions and provide a theoretically valid online stopping criterion. We generalize the notion of accuracy certificates for the setting of an inexact first-order oracle. In particular, this includes the setting of a dual problem where the dual function and its derivatives don't necessarily have closed-form representations. Furthermore, we propose an explicit way to construct accuracy certificates for a large class of cutting plane methods that use polytopes as localizers.

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

Host
WIAS Berlin
Thursday, 08.08.2024, 13:30 (WIAS-406)
Seminar Materialmodellierung
Dr. Ferran Brosa Planella, University of Warwick, GB:
Asymptotic methods for lithium-ion battery models
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
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.

Host
WIAS Berlin
Wednesday, 04.09.2024, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Martijn Gösgens, TU Eindhoven:
tba
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
tba

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 18.09.2024, 10:00 (WIAS-405-406)
Seminar Numerische Mathematik
Albert Pool, DLR:
Nonlinear dynamics as a ground-state solution on quantum computers
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Host
WIAS Berlin
Wednesday, 18.09.2024, 10:00 (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
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
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.

Host
WIAS Berlin