## Research

I am a postdoc in applied analysis with research ambitions located at the intersection of mean-field particle models, network dynamics, mathematics of machine learning and control theory.

Currently, I am a post-doc at the Department of Mathematics at TU Munich in the research group on dynamical systems of Christian Kuehn funded by the Schrödinger program of the Austrian Science Fund. Before I was a post-doc in the Chair of Dynamics, Contorl and Numerics at FAU Erlangen headed by Enrique Zuazua. I received my PhD in 2020 at the Institute of Analysis and Scientific Computing at TU Vienna in the group of Anton Arnold. In 2019, I was an invited guest of Prof. Shi Jin at Shanghai Jiao Tong University.

### Large-time behaviour of mean-field equations

During my PhD, I focused on obtaining explicit large-time estimates for mean-field equations by means of entropy methods and spectral theory. I am currently interested in including long-range particle interactions in these models, which have many fascinating real-world applications, such as synchronisation phenomena and opinion formations.

### Mathematics of machine learning

The achievements of machine learning algorithms backed by huge computing resources are reshaping our lives, but still surprisingly little is understood about the fundamental mechanisms involved. The mathematician's job is now to look inside the black box and extend the vocabulary to describe what at this point seems like magic. I am currently investigating supervised learning procedures of neural networks and their lack of robustness from an optimal control and dynamical system perspective.## Publications

- Generalised Fisher Information Approach to Defective Fokker-Planck Equations, Arnold, A., Einav, A. and Wöhrer, T.; Submitted (2022).
- Sharpening of decay rates in Fourier based hypocoercivity methods, Arnold, A., Dolbeault, J., Schmeiser, C. and Wöhrer, T.; Springer INdAM Series: Recent Advances in Kinetic Equations and Application, 48, (2021).
- Large time convergence of the non-homogeneous Goldstein–Taylor Equation, Arnold, A., Einav, A., Signorello B. and Wöhrer, T.; Journal of Statistical Physics, 182 (41) (2021).
- Sharp decay estimates in local sensitivity analysis for evolution equations with uncertainties: from ODEs to linear kinetic equations, Arnold, A., Jin, S. and Wöhrer, T.; Journal of Differential Equations, 268 (3), 1156–1204,(2020).
- On the rates of decay to equilibrium in degenerate and defective Fokker–Planck equations, Arnold, A., Einav, A. and Wöhrer, T.; Journal of Differential Equations, 264 (11), 6843–6872, (2018).
- Asymptotic behavior of the Weyl m-function for one-dimensional Schrödinger operators with measure-valued potentials , Luger, A., Teschl, G. and Wöhrer, T.; Monatsh. Math. 179, 603–613, (2016).

"The writers who embellish a language, who treat it as an object of art, make of it at the same time a more supple instrument, more apt for rendering shades of thought."

Henri Poincaré.