Researcher Summary
If you are a student interested in finding a project (Summer project, a thesis project, or a PhD project), or if you are a researcher interested in scientific collaboration, see my research webpage (link at the very end of this page). Feel free to write me an email or drop by my office if you'd like to discuss options!
I am interested in most mathematical aspects involving "getting information about hidden parameters via indirect and noisy observation". Different communities have different names for that, some of which are "(Nonparametric) Statistics", "Inverse Problems", "Bayesian statistics", "Inference", "Regression", "Data Assimilation", "(semi-)Supervised Learning".
These aspects include
• the question "can this work at all?" (i.e. well-posedness of the inversion process),
• Computational issues, algorithmic advances, and efficient implementation of inversion, which is often related to
• Useful mathematical/conceptual approximations (linearity/Gaussianity assumptions, e.g. within the Ensemble Kalman methodology; or the Laplace approximation as a surrogate measure for use in computational models) which make the problem computationally more feasible and raises the question of "how rough is this approximation?", which is a key question of
• Error analysis, convergence behaviour and stability of inversion schemes; as well as
• difficult mathematical questions related to probability theory, functional analysis (in particular for Banach-space-valued inverse problems)
