Idisplays

[MM Connect] Julia Schleuss "After 12.5 Years - Now What? A Personal Case Study in Leaving Academia and Applying Elsewhere" + MM Arrival Talks by Bastián Arturo Mora García, Thorger Geiß, Tara Trauthwein, Edoardo Tolotti

5 sessions on professional competences. You can pick and choose: either one, several, or all sessions.
Open to all! All sessions are open to all MM researchers of Mathematics Münster, regardless of their experience level, as all input and exercises are designed for individual needs.
Register via: mm.careers@uni-muenster.de

5 sessions on professional competences. You can pick and choose: either one, several, or all sessions.
Open to all! All sessions are open to all MM researchers of Mathematics Münster, regardless of their experience level, as all input and exercises are designed for individual needs.
Register via: mm.careers@uni-muenster.de

5 sessions on professional competences. You can pick and choose: either one, several, or all sessions.
Open to all! All sessions are open to all MM researchers of Mathematics Münster, regardless of their experience level, as all input and exercises are designed for individual needs.
Register via: mm.careers@uni-muenster.de

Learning dynamical systems from data has become a vital interdisciplinary research area, uniting concepts from mathematics, engineering, and data science. These systems, which describe how states evolve over time according to underlying mathematical laws, are essential for modeling a wide array of time-dependent phenomena. For practical applications, achieving high accuracy, interpretability, and explainability are crucial properties that are inherently connected to the mathematical structure of the dynamical systems. For instance, in modeling mechanical or electro-mechanical processes, systems with second-order time derivatives typically arise, with data available in the frequency domain as samples of transfer functions. To effectively learn such structured systems from frequency domain data, we introduce a data-driven second-order balanced truncation method. This approach enables the construction of low-dimensional second-order models with generalized proportional damping by assembling appropriate Loewner-like matrices. Numerical experiments illustrate the effectiveness and potential of the proposed methodology.

Further information

Get an insight into the research of five new postdoctoral researchers of Mathematics Münster. In short scientific presentations they will introduce their topics.
After the talks, there will be the opportunity to exchange ideas while enjoying tea, coffee and cake in the Common Room.

• Catrin Mair, Homotopy theory in a condensed world
• Stefan Schrott, Optimal transport of stochastic processes
• Mathias Sonnleitner, Connecting and separating dots
• Ferdinand Wagner, Habiro Cohomology & Refined THH
• Alexander Van Werde, On the spectral determinacy of random graphs

A smooth curve $\gamma: [0,1] \to \Ss^2$ is locally convex if its geodesic curvature is positive at every point. J.~A.~Little showed that the space of all locally positive curves $\gamma$ with $\gamma(0) = \gamma(1) = e_1$ and $\gamma'(0) = \gamma'(1) = e_2$ has three connected components $\cL_{-1,c}$, $\cL_{+1}$, $\cL_{-1,n}$. These spaces and variants have been discussed, among others, by B.~Shapiro, M.~Shapiro and B.~Khesin. Our first aim is to describe the homotopy type of these spaces. The connected component $\cL_{-1,c}$ is known to be contractible. We construct maps from $\cL_{+1}$ and $\cL_{-1,n}$ to $\Omega\Ss^3 \vee \Ss^2 \vee \Ss^6 \vee \Ss^{10} \vee \cdots$ and $\Omega\Ss^3 \vee \Ss^4 \vee \Ss^8 \vee \Ss^{12} \vee \cdots$, respectively, and show that they are (weak) homotopy equivalences. More generally, a smooth curve $\gamma: [0,1] \to \Ss^n \subset \RR^{n+1}$ is locally convex if $\det(\gamma(t),\ldots,\gamma^{n}(t)) > 0$ (for all $t$). We would like to understand the homotopy type of the space $\cL$ of locally convex curves with $\gamma^{(j)}(0) = \gamma^{(j)}(1) = e_{j+1}$ (for all $j \ne n$). We describe a CW complex with the same homotopy type. The homotopy type of $\cL$ is described for $n = 3$.