Franca Karoline Olga (Franca) Hoffmann
Visiting Associate in Computing and Mathematical Sciences
Franca Hoffmann's research is focused on the interface between applied mathematics and data analysis, driven by the need to provide rigorous mathematical foundations for modeling tools used in applications. Franca Hoffmann is interested in (1) the theory of nonlinear and nonlocal partial differential equations, making use of gradient flows, entropy methods, functional inequalities, optimal transport techniques, kinetic theory, particle methods and relationships between different scales; and (2) the development of novel tools for data analysis and mathematical approaches to machine learning, involving graph based methods for unsupervised and semi-supervised learning, focusing on data clustering and classification, graph Laplacians and their continuum counterparts, spectral analysis, uncertainty quantification and consistency analysis. It is the intersection of these topics that allow for novel interesting mathematical frameworks, such as recently developed sampling algorithms combining ideas from (1) and (2) to create approximate samples from a posterior distribution solving general classes of inverse problems.