About

I am a Von Karman Postdoctoral Instructor in Applied and Computational Mathematics at the Department of Computing and Mathematical Sciences, California Institute of Technology (Caltech) in Pasadena, USA.

In July 2017, I completed my PhD at the Cambridge Centre for Analysis (CCA) Doctoral Training Centre, University of Cambridge and Imperial College London, under the supervision of Prof. José A. Carrillo and Prof. Clément Mouhot. A copy of my thesis can be downloaded here. I’m honoured to have received the 2016 Imperial College Outstanding Student Achievement Award.

Have a look here for a short video about some of my research to a non-mathematical audience, presented at the finals of the 3-Minute-Thesis Competition 2016, Imperial College London. For a one hour seminar about my PhD research, click here.

My research interests lie at the interface of model-driven and data-driven approaches.

      • Mathematical Tools for PDE Analysis: This part of my research focuses on partial differential equations and their applications. My current interests are among others non-linear drift-diffusion equations, kinetic theory, many particle systems, gradient flows, entropy methods, optimal transport, functional inequalities, parabolic and hyperbolic scaling techniques, hypocoercivity and diffusive models in mathematical biology.

      • Mathematical Tools for Data Analysis: I am interested in developing rigorous mathematical tools for data analysis in the context of  inverse problems, Bayesian inference and machine learning, unsupervised and semi-supervised learning, focusing on data clustering and classification, graph Laplacians and their continuum counterparts, spectral analysis, uncertainty quantification and consistency analysis.

I believe that it is not just about what mathematical analysis can do for applications, but also what applications can do for mathematics. Applications that benefit from a PDE approach often generate new questions giving rise to novel mathematical theories, and thus providing insights not just for the application at hand, but also enabling to push boundaries in seemingly unrelated fields. I am interested in how PDE techniques can be employed to answer modeling questions across different scales, disciplines and applications. For more details about my research, have a look here.

Updates

20170901_134822

Caltech Campus, picture taken on my day of arrival at this beautiful place.

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