Dr Emilio Ferrucci
Research Member of Common Room
Postdoctoral Research Associate
I am a postdoctoral research associate at the Mathematical Institute, University of Oxford, in the DataSıg research group The focus of my current postdoc is the applications rough path theory – a technique of probability theory that is used to give meaning to certain differential equations driven by irregular inputs – to data science and machine learning. I am also interested in many theoretical questions about rough paths, both deterministic and stochastic, and their applications to other areas of pure mathematics, such as differential geometry and algebraic combinatorics.
More specifically, my research interests are:
- Machine learning techniques that use path signatures and neural differential equations. In this context, I am particularly interested in applications to data science for mental health.
- The behaviour of rough integration theories on smooth manifolds.
- Malliavin calculus for gaussian processes, and other theories of stochastic integration for non-semimartingales.
- Applications of algebraic combinatorics to rough analysis (e.g. Hopf algebras and branched rough paths).