| 2026 |
20. April |
14:30 |
SR 127.11, IDea_Lab |
Dr. Juan Ricardo Muñoz (University of Dubrovnik): Schatten Norm Estimates for Lyapunov Gramians in Operator ScalesAbstract: We analyze the structure of observability Gramians for infinite-dimensional control systems via the Lyapunov equation $AX+XA^* = -BB^*$. Our approach provides explicit eigenvalue decay and Schatten norm estimates that directly relate the Gramian to the spectral properties of the generator and the regularity of the control operator. These abstract results naturally extend existing ones to singular and unbounded controls, and further open the way to generalizations toward anomalous diffusion models. We validate the theory on heat equation benchmarks with both distributed and pointwise actuators, demonstrating how the estimates accurately capture spectral decay and conditioning. |
| 2026 |
19. January |
14:30 |
Open Space, IDea_Lab |
Prof. Leon Bungert (University of Würzburg): Robustness on the interface of geometry and probabilityAbstract: In this talk I will present the latest developments in the analysis of adversarial machine learning. For this I will build on the geometric interpretation of adversarial training as regularization problem for a nonlocal perimeter of the decision boundary. This perspective allows one to use tools from calculus of variations to derive the asymptotics of adversarial training for small adversarial budgets as well as to rigorously connect it to a mean curvature flow of the decision boundary. We also show that adversarial training is embedded in a larger family of probabilistically robust problems. This is joint work with N. García Trillos, R. Murray, K. Stinson, and T. Laux, and others. |
| 2025 |
17. November |
14:30 |
SR 127.11, IDea_Lab |
Sascha Beutler (University of Münster): From Motion Estimation to Active Correction in Intravital Fluorescence MicroscopyAbstract: Physiological motion from respiration and cardiac cycles poses significant challenges for fluorescence microscopy of living tissues. Since even small motions can move the cell out of the focal plane, it is particularly difficult to observe the same single cell over time. In this talk, I will first describe the nature of data produced by fluorescence microscopes, discuss key considerations for in vivo measurements, and explain which system parameters we can control to actively correct for motion during and in between image acquisition. I will then present a motion correction approach that leverages the periodicity of physiological motion, specifically under the assumption that a cylindrical structure, such as a blood vessel, is being observed. Finally, I will provide an overview of our research involving shape spaces, outlining how this infinite-dimensional geometric framework relates to the motion problem in microscopy and how we aim to integrate these methods to improve motion correction in the future. |
