# Dr Federica Dragoni

Reader (Associate Professor)

- dragonif@cardiff.ac.uk
- +44 (0)29 2087 5529
- Maths and Education Building , Senghennydd Road, Cardiff, CF24 4AG

## Overview

I am Senior Lecturer at Cardiff University since 2016.

I am a member of the Analysis Group and of the Analysis, Probablity and Stochastic Processes Group.

My research interests are mainly in the area of **nonlinear PDEs,** using techniques crossing analysis, geometry and stochastic analysis.

### Present administrative duties

- MAGIC Consortium Cardiff Co-ordinator
- Work-Life Balance Coordinator
- Senior Tutor for all Undergraduate Female Students
- Personal Tutor

### Conference, workshop and Research Network organisation

- Grant-Holder of South-West Network in Generalised Solutions for Nonlinear PDEs, Cardiff-Bath-Reading, 2016-2018
- Organiser of 12th LMS Network worhshop, Cardiff, November 2018
- Organiser of 11th LMS Network worhshop, Cardiff, May 2018
- Organiser of 8th LMS Network worhshop, Cardiff, September 2017
- Organiser of New Trends in nonlinear PDEs: from theory to applications, Cardiff, 2016
- Organiser of 2nd LMS Network worhshop, Cardiff, April 2016
- Organiser of Stochastic methods and nonlinear PDEs, Cardiff, 2012
- Extended local Organising Committee for the 7th ISAAC congress, Imperial College London 2009

### External duties and professional memberships

- EPSRC Peer Review College Member (2017-present)
- London Mathematical Society Representative for Cardiff (2012-2018)
- Member of the London Mathematical Society

### Other activities

- International Teaching Placement in Italy for undegradute students
- Maths Games After School Club at Cwrt Rawling Primary School
- Supervision of various mathematical activities in local primary schools

## Biography

### Education and Qualification

- 2013: Fellow of the Higher Education Academy (
**FHEA**), Cardiff University. - 2006:
**PhD in Mathematics**,**Scuola Normale Superiore di Pisa**, Italy. Mark: 70/70 cum Laude. Title: Carnot-Carathéodory metrics and viscosity solutions. Advisor: Prof. Italo Capuzzo Dolcetta. - 2002: Laurea (equivalent of
**Master Degree**) in Mathematics,**University of Florence,**Italy. Mark: 110/110 cum Laude. Title:*Photon transport in an interstellar cloud: direct and inverse problems*. Advisor: Prof. Luigi Barletti

### Employment

- 2016-present: Senior Lecturer at Cardiff School of Mathematics, Cardiff University
- 2011-2016: Lecturer at Cardiff School of Mathematics, (including two breaks of maternity leave in 2011 and 2013)
- 2010: Research associate at University of Padova, Italy and temporary position, University of Bristol
- 2009: Research associate at Imperial College London
- 2008-2009: Research associate at University of Padova, Italy
- 2007-2008: Post-doc position at Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
- 2007: INDAM research position, at University of Pittsburgh, USA

### Honour, prizes and activities for professional bodies

2017-present: EPSRC Peer Review College Member2012-present: LMS Local Representative at Cardiff

2017: Awarded Research Leave from University of Cardiff

2017: Personal Tutor of the year, Cardiff University

2014: Research Leave from School of Mathematics, University of Cardiff

2002: Prize as Best Student in the College of Science, Mathematics and Physics, University of Florence, Italy

### Reviewer

**International Journal:**Journal of London Mathematical Society; Analysis and Geometry in Metric Spaces; Springer INdAM Series, Advances in Calculus of Variation, and many others.**Books:**Springer.**Grants:**EPSRC grants, LMS Summer Research projects for undergraduates.

### Research Visists

- 2018: Invited partecipant at
**Oberwalfach**, Germany. Multiple research visits at Paris, Chicago, Florence and Padova - 2017: Multiple research visits at Warwick, Heriot-Watt (Edinburgh), Paris, Florence and Padova
- 2016: Multiple research visits at Florence and Padova
- 2015: Visiting University of Florence, University of Bologna, and University of Padova
- 2014: Semester of Research Visit at University of Florence. In the same year I was also invited for shorter periods at University of Bologna, University of Padova, et al.
- 2008: Research visit at University of Venice
- 2007: Research visists at University of Purdue (USA), University of Arkansas, AR (USA), University of Helsinki (Finland), University of Pittsburgh (USA)
- 2006: Research visit at University of Pittsburgh (USA)

### Former administrative duties

Member of Learning and Teaching Committee, School of Mathematics, Cardiff (2014-2018)

Athena SWAN Panel, School of Mathematics, Cardiff (2014-2018, Bronze Medal awarded)

- Chair of Review Panel for the MMath Programme (2016)

Chair of Review Panel on Tutoring Co-ordinator, School of Mathematics, Cardiff (2015-2016)

Member of a hiring committee for Lecturer position, Cardiff (2014)

Organiser of Analysis Seminars, Cardiff (2012-2014)

Organiser of Mathematical Colloquium, Cardiff (2012)

Co-ordinator of the analysis working group, Imperial College London (2009)

## Publications

### 2020

- Dirr, N.et al. 2020. Gamma-convergence and homogenisation for a class of degenerate functionals. Nonlinear Analysis 190, article number: 111618. (10.1016/j.na.2019.111618)
- Dirr, N., Dragoni, F. and Grande, R. 2020. Asymptotics for optimal controls for horizontal mean curvature flow.. arXiv.org

### 2019

- Dragoni, F. and Filali, D. 2019. Starshaped and convex sets in Carnot groups and in the geometries of vector fields. Journal of Convex Analysis 4(24), pp. -.
- Dragoni, F., Garofalo, N. and Salani, P. 2019. Starshapedeness for fully-nonlinear equations in Carnot groups. Journal of the London Mathematical Society 99(3), pp. 901-918. (10.1112/jlms.12198)

### 2018

- Dirr, N.et al. 2018. Stochastic homogenization for functionals with anisotropic rescaling and non-coercive Hamilton-Jacobi equations. SIAM Journal on Mathematical Analysis 50(5), pp. 5198-5242. (10.1137/17M1144428)
- Dragoni, F. and Feleqi, E. 2018. Ergodic mean field games with Hörmander diffusions. Calculus of Variations and Partial Differential Equations 57, article number: 116. (10.1007/s00526-018-1391-1)

### 2014

- Bardi, M. and Dragoni, F. 2014. Subdifferential and properties of convex functions with respect to vector fields. Journal of Convex Analysis 21(3), pp. 785-810.

### 2013

- Dragoni, F., Manfredi, J. J. and Vittone, D. 2013. Weak Fubini property and infinity harmonic functions in Riemannian and sub-Riemannian manifolds. Transactions of the American Mathematical Society 365, pp. 837-859. (10.1090/S0002-9947-2012-05612-1)

### 2012

- Dragoni, F., Kontis, V. and Zegarliński, B. 2012. Ergodicity of Markov semigroups with Hörmander type generators in infinite dimensions. Potential Analysis 37(3), pp. 199-227. (10.1007/s11118-011-9253-x)

### 2011

- Bardi, M. and Dragoni, F. 2011. Convexity and semiconvexity along vector fields. Calculus of Variations and Partial Differential Equations 42(3-4), pp. 405-427. (10.1007/s00526-011-0392-0)
- Gentil, I.et al. Zegarlinski, B. ed. 2011. Aspects of analysis curvature criterion, isoperimetry, evolution equations. Mathematical Notebooks Vol. 3. Matrix Press.

### 2010

- Dirr, N. P., Dragoni, F. and Von Renesse, M. 2010. Evolution by mean curvature flow in sub-Riemannian geometries: a stochastic approach. Communications on Pure and Applied Analysis 9(2), pp. 307-326. (10.3934/cpaa.2010.9.307)
- Bardi, M. and Dragoni, F. 2010. Convexity along vector fields and applications to equations of Monge-Ampére type. In: Ruzhansky, M. and Wirth, J. eds. Progress in Analysis and Its Applications. Proceedings of the 7th international ISAAC Congress.. World Scientific, (10.1142/9789814313179_0059)

### 2009

- Bieske, T., Dragoni, F. and Manfredi, J. J. 2009. The Carnot-Carathéodory Distance and the Infinite Laplacian. Journal of Geometric Analysis 19(4), pp. 737-754. (10.1007/s12220-009-9087-6)

### 2007

- Dragoni, F. 2007. Metric Hopf-Lax formula with semicontinuous data. Discrete and Continuous Dynamical Systems 17(4), pp. 713-729. (10.3934/dcds.2007.17.713)
- Dragoni, F. 2007. Limiting behavior of solutions of subelliptic heat equations. Nonlinear Differential Equations and Application NoDEA 14(3-4), pp. 429-441. (10.1007/s00030-007-6013-0)

### 2006

- Dragoni, F. 2006. Carnot-Carathéodory metrics and viscosity solutions. PhD Thesis, Scuola Normale Superiore, Pisa, Italy.

### 2005

- Barletti, L. and Dragoni, F. 2005. An inverse problem for two-frequency photon transport in a slab. Mathematical Methods in the Applied Sciences 28(14), pp. 1695-1714. (10.1002/mma.633)

## Teaching

I am currently teaching the following modules:

- MA1006 Foundations of Mathematics II (Spring Term)
- MA4013 Advanced topics in Analysis with application to PDEs (Spring Term)
- Foundations Tutorial (Autumn Term and Spring Term)

### Former teaching experience

Further topics in Analysis with applications to PDEs, Postgraduate and MMath course, Cardiff University (2016-present)

Foundation II, year 1, Cardiff (2016-present)

Analysis 2, year 1, Cardiff (2012, 2014, 2015)

Theoretical and computational PDEs, year 3, Cardiff (2012, 2013)

Linear Algebra, year 1, University of Bristol (2010)

Calculus 2, year 1, University of Bristol (2010)

Introduction to viscosity theory for Nonlinear PDEs, Postgraduate and MMath course, Imperial College London (2009)

Calculus I and Geometry and Linear Algebra (teaching assistant), year 1, Department of Engineering, University of Florence (2007)

Preparatory class of Mathematics, University of Florence (2006)

Mathematics and Physics at Secondary Schools, Florence (2006)

### Research interests

My research is motivated by a broad range of interrelated problems in the area of analysis in sub-Riemannian manifolds and degenerate nonlinear PDEs. In this settings I have dealt with very different questions, making use of many interdisciplinary methods and techniques from probability, analysis, differential geometry, Lie algebras, metric spaces, calculus of variations and measure theory. Sub-Riemannian geometries and related PDEs (as subelliptic/ultraparabolic PDEs) turn out to be extremely useful to create mathematical models to describe many different phenomena from applications. An example are the use of the Rototranslation geometry for modelling the first layer of the visual cortex and problems in finance related to pricing so-called Asian options.Unlike Riemannian manifolds (where the structure looks locally always like the Euclidean R^{N}), sub-Riemannian spaces are never, at any scale, isomorphic to the Euclidean space. In particular they are highly anisotropic in the sense that at any point some directions for the motion on the manifold turn out to be forbidden, making the metric and geometric structure much more complicated than in the non-degenerate case (Euclidean space and Riemannian manifolds). The admissible directions for the motion are described by vector fields which do not span at any point the whole tangent space. PDEs on these geometries are defined by replacing the standard partial derivatives by the vector fields.

Some of the topics I am interested in are listed below.

- Nonlinear PDEs, in particular degenerate ellipitc and parabolic PDEs.
- PDEs in the Heisenberg groups and Carnot groups
- PDEs in sub-Riemannian manifolds and in general related to Hoermander vector fields
- Geometrical properties for PDEs
- Convexity and starshapedness in non Euclidean spaces
- Stochastic methods for deterministc PDEs
- Stochastic Homogenization
- Hamilton-Jacobi equations and Hopf-Lax formulas
- Absolutely Minimizing Lipschitz extensions
- Infinite-Laplacian
- Mean Field Games
- Tug-of-war, more in general deterministic and stochastic differential games

### Research group

### External funding and grants

- 2017-2018: Cardiff University Research Leave Grant £3000, LMS Scheme 3 £1500; LMS Educational Grant £400
- 2016-2017: LMS Grant Scheme 4 £1200; LMS Grant Scheme 3 £1200
- 2015-2016:
**EPSRC First Grant**£99,896; LMS Grant Scheme 3 £1979 - 2012-2013: LMS grant Scheme 1 £5000; OxPDE grant for conference £3500; WIMCS grant for conference £2000
- 2010: LMS collaborative small grant £600
- 2007: INDAM research grant Euro 6000 (Italian grant)

### Selected talks since 2016

I have been invited to give 57 talks in seminars, colloquia and international conferences in various universities across the UK, Europe, USA and China. I here list just a selection of the talks given during the last 3 years.

- 06/2019: (upcoming) Invited speakers at Workshop on Nonlinear Averaging PDEs (in honor of the 60's birthday of Professor Juan J. Manfedi), Levico, Italy
- 10/2018: Joint Firenze-Tohoku Research Workshop on Nonlinear PDEs, Florence, Italy
- 09/2018: LMS Analysis and Probability Workshop, Cardiff, UK
- 09/2018: UMI-SIMAI-PTM Joint Meeting, Wroclaw, Poland
- 09/2018: LMS Prospects Meeting, Warwick, UK
- 08/2018: Durham Symposium, Durham, UK
- 07/2018: Stochastic Systems: their analysis, geometry and perturbation, Beijing, China
- 10/2018: LMS Newtork on Generalised Solution for Nonlinear PDEs, Reading, UK
- 12/2017: Seminars of Calculus of Variations, Florence, Italy
- 09/2017: Analysis seminar, University of Edinburgh, UK
- 04/2017: Seminar, University of Chicago, USA
- 12/2016: LMS Regional Meeting, Bath, UK
- 11/2016: Stochastics seminar, Warwick, UK
- 11/2016: Seminar at Heriot-Watt University, UK
- 07/2016: 11th AIMS Conference on Dynamical Systems, Differential Equatios and Applications, Orlando, Florida, USA
- 05/2016: Young Applied Analysts in UK, Bath, UK
- 02/2016: Analysis seminars, Bristol, UK

## Supervision

- Nonlinear PDEs degenerate elliptic and parabolic.
- PDEs in Carnot groups, subRiemannian manifolds and related to Hoermander vector fields.
- Geometrical properties for PDEs.
- Convexity in non Euclidean spaces.
- Periodic Homogenization
- Stochastic Homogenizitaion
- Mean Field Games

### Current supervision

## Raffaele Grande

Research student

### Past projects

### Formwe Research Associate

**Ermal Feleqi**2016-2017

### Former Research Students

**Doaa Filali**2013-2018**Ahmed Jama**2014-2018

### MMath (equivalent of Master) Students

**Matthew Tandy**2018-2019**Liam M. Rosser**2016-2017**Ahmed Jama**2013-2014

### Undergraduates Students

**Ruth Cresswell**(50%) 2016-2017**Cordula Mayerhofer**2012-2013**James Evans**2011-2012**Jordan P. Thomas**2011-2012

### PhD External Examiner

PhD Thesis of B. Franceschiello (joint PhD from University of Bologna and EHESS Paris).