## Dr Federica Dragoni

### Overview

Telephone: +44(0)29 208 75529

Fax: +44(0)29 208 74199

Extension: 75529

Location: M/2.32

#### Research Interests

**Degenerate nonlinear PDEs under the Hörmander condition**

My main research area are nonlinear partial differential equations under the Hoermander condition (also called subellipticity). These kind of equations describe many phenomena in science and economics and are characterized by a condition named after Lars Hoermander, which is a condition on the geometry associated to the equation. In fact, one can introduce a geometric structure associated to a partial differential equation in the following way: Partial derivatives can be interpreted as derivatives along the basis directions of the Euclidean space. In the Hoermander case, the Euclidean basis is replaced by a family of vector fields which span a space with dimension smaller than the dimension of the ambient space (therefore degenerate). Nevertheless these vector fields are such that some differential operations (called commutators) still allow to move in all directions. In other words, the commutators generate a space of full dimension. Hence the partial derivatives are interpreted as derivatives along the vector fields which replace the Euclidean basis.

#### Research Group

#### Teaching

**Autumn Semester**

MA0126 Analysis II

MA3303 Theoretical & Computational PDEs

**Spring Semester**

MA4901 Reading Module

#### Personal Website

### Publications

### Research

#### External Funding

2004: Research grant to at University La Sapienza, Rome.

2007: INDAM (Istituto Nazionale di Alta Matematica) research grant for research abroad. 2010: LMS Grant (Scheme 4)

#### Major Conference Talks

09/2008: "Stochastic representation for evolution by horizontal mean curvature flow", Conference on Viscosity, metric and control theoretic methods in nonlinear PDEs, University La Sapienza, Rome.

07/2009: "Convexity along vector fields and applications to equation of Monge-Ampère type" ISAAC Conference 2009. Imperial College London.

### Biography

#### Academic history

09/2006: PhD in Mathematics, Scuola Normale Superiore di Pisa, Thesis: Carnot-Carathéodory metrics and viscosity solutions. Advisor: Prof. Italo Capuzzo Dolcetta.

09/2002: Laurea (equivalent of Master Degree) in Mathematics, University of Florence, Thesis: : Photon transport in an interstellar cloud: direct and inverse problems. Advisor: Prof. Luigi Barletti.

#### Employment

2011: Lecturer at Cardiff School of Mathematics, Cardiff University.

2010: Research associate at University of Padova, Italy and teaching position, University of Bristol

2009: Research associate at Imperial College London.

11/2008-02/2009: Research associate at University of Padova, Italy.

09/2007-10/2008: Post-doc position at Max Planck Institute for Mathematics in the Sciences, Leipzig.

02-06/2007: INDAM (Istituto Nazionale di Alta Matematica) research position, at University of Pittsburgh.