Colloquium on the Occasion of

Alexander Mielke's 65th Birthday


September 6th, 2023
at Festsaal Humboldt Universität zu Berlin


Alexander Mielke is renowned for his fundamental contributions to the field of applied mathematics, and his work has shaped the scientific environment in Berlin, Germany and worldwide. He is not only the leader of the research group Partial Differential Equations at the Weierstrass Institute and Professor for Partial Differential Equations at Humboldt Universität zu Berlin, but also the Chair of the Council of the MATH+ Cluster of Excellence.

In order to celebrate his 65th birthday and to acknowledge his diverse contributions and scientific activities, we organize a scientific colloquium on September 6th, 2023. The event takes place at the

Festsaal Humboldt Universität, Luisenstraße 56, 10117 Berlin

Participation in the colloquium is free. However, we ask all participants to REGISTER ONLINE.

Preliminary Program

2.15 p.m. Welcoming address
2.45 p.m. Rupert Klein (FU Berlin) – Mathematical modelling in geophysical fluid dynamics
Abstract »

Three examples from geophysical fluid dynamics will showcase mathematical modelling as the "art of judicious simplification": The computational prediction of two seasonal to decadal phenomona, the "quasi-biennial oscillation" (QBO) and the "El Niño Southern Oscillation" (ENSO) became possible only after theoreticians had captured their essential causal structures in convincing reduced mathematical models. With our own research, we aim to similarly untangle the mechanisms behind the "rapid intensification" (RI) of tropical storms during their transition to hurricane strength.

3.30 p.m.Coffee break
4.15 p.m.Felix Otto (MPI Leipzig) – Singular stochastic partial differential equations: more geometry and less combinatorics
Abstract »

Singular stochastic PDE are those stochastic PDE in which the noise is so rough that the nonlinearity requires a renormalization. The guiding principle of renormalization is to preserve as many symmetries of the solution manifold as possible. We follow the approach of mathematical physics, and of Hairer's regularity structures, which however we re-interpret as providing an informal parameterization of the infinite-dimensional nonlinear solution manifold.

We systematically follow this more geometric/analytic than combinatorial point-of-view: Instead of appealing to an expansion indexed by trees, we consider all partial derivatives w.r.t. the "constitutive" function defining the nonlinearity. Instead of a Gaussian calculus guided by Feynman diagrams arising from pairing nodes of two trees, we consider derivatives w.r.t. the noise, i.e. Malliavin derivatives. We interpret the Malliavin derivative of the parameterization as an approximate tangent vector to the solution manifold, which yields a sparse representation in terms of the parameterization itself, and paves the way for its stochastic estimate. Ultimately, this gives a characterization of the solution manifold that is oblivious to the divergent counter terms.

This is work with L. Broux, P. Linares, M. Tempelmayr, and P. Tsatsoulis, based on work with J. Sauer, S. Smith, and H. Weber.

5.00 p.m.Riccarda Rossi (U Brescia) – Variational approaches to rate-independent and gradient systems
Abstract »

The mathematical analysis of rate-independent systems has sparked intensive research over the last two decades, both because they are ubiquitous in mechanics, and due to their intrinsic nonsmoothness, which poses several challenges. The work by Alexander Mielke has set a cornerstone in the field, starting with the weak solvability notion of Energetic solution. The Energetic concept has become paradigmatic for rate-independent evolution: one of its fingerprints is its variational character, which paves the way for the usage of the wide toolbox of Calculus of Variations in the analysis of specific systems. And, again, the interplay between rate-independent systems and the variational theory for gradient flows has inspired yet another concept, that of Balanced Viscosity solutions. A twitch upon the thread leads to Alexander's work on discrete systems, to EDP convergence... and to several intriguing open perspectives.

5.45 p.m. Closing

Organizing Committee

Andrea Eismann   |   Thomas Eiter   |   Matthias Liero   |   Artur Stephan   |   Barbara Zwicknagl

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