Dr Federica Dragoni
Senior Lecturer
 Email:
 dragonif@cardiff.ac.uk
 Telephone:
 +44 (0)29 2087 5529
 Location:
 Maths and Education Building , Senghennydd Road, Cardiff, CF24 4AG
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 Coordinator
 WorkLife Balance Coordinator
 Senior Tutor for all Undergraduate Female Students
 Personal Tutor
Conference, workshop and Research Network organisation
 GrantHolder of SouthWest Network in Generalised Solutions for Nonlinear PDEs, CardiffBathReading, 20162018
 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 (2017present)
 London Mathematical Society Representative for Cardiff (20122018)
 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
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: CarnotCarathéodory 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
 2016present: Senior Lecturer at Cardiff School of Mathematics, Cardiff University
 20112016: 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
 20082009: Research associate at University of Padova, Italy
 20072008: Postdoc 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

2017present: EPSRC Peer Review College Member2012present: 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, HeriotWatt (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 (20142018)

Athena SWAN Panel, School of Mathematics, Cardiff (20142018, Bronze Medal awarded)
 Chair of Review Panel for the MMath Programme (2016)

Chair of Review Panel on Tutoring Coordinator, School of Mathematics, Cardiff (20152016)

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

Organiser of Analysis Seminars, Cardiff (20122014)

Organiser of Mathematical Colloquium, Cardiff (2012)

Coordinator of the analysis working group, Imperial College London (2009)
2018
 Dragoni, F., Garofalo, N. and Salani, P. 2018. Starshapedeness for fullynonlinear equations in Carnot groups. Journal of the London Mathematical Society (10.1112/jlms.12198)
 Dragoni, F. and Filali, D. 2018. Starshaped and convex sets in Carnot groups and in the geometries of vector fields. Submitted Preprint
 Dirr, N.et al. 2018. Stochastic homogenization for functionals with anisotropic rescaling and noncoercive HamiltonJacobi equations. SIAM Journal on Mathematical Analysis 50(5), pp. 51985242. (10.1137/17M1144428)
 Dragoni, F. and Feleqi, E. 2018. Ergodic mean field games with Hörmander diffusions. Calculus of Variations and Partial Differential Equations 57(5), article number: 116. (10.1007/s0052601813911)
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. 785810.
2013
 Dragoni, F., Manfredi, J. J. and Vittone, D. 2013. Weak Fubini property and infinity harmonic functions in Riemannian and subRiemannian manifolds. Transactions of the American Mathematical Society 365, pp. 837859. (10.1090/S000299472012056121)
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. 199227. (10.1007/s111180119253x)
2011
 Bardi, M. and Dragoni, F. 2011. Convexity and semiconvexity along vector fields. Calculus of Variations and Partial Differential Equations 42(34), pp. 405427. (10.1007/s0052601103920)
 Gentil, I.et al. Zegarlinski, B. ed. 2011. Aspects of analysis curvature criterion, isoperimetry, evolution equations.. Mathematical Notebooks Vol. 3.. Matrix Press.
2010
 Bardi, M. and Dragoni, F. 2010. Convexity along vector fields and applications to equations of MongeAmpére 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
 Dirr, N. P. and Dragoni, F. 2009. Evolution by mean curvature flow in subRiemannian geometries: a stochastic approach. Communications on Pure and Applied Analysis 9(2), pp. 307326. (10.3934/cpaa.2010.9.307)
 Bieske, T., Dragoni, F. and Manfredi, J. J. 2009. The CarnotCarathéodory Distance and the Infinite Laplacian. Journal of Geometric Analysis 19(4), pp. 737754. (10.1007/s1222000990876)
2007
 Dragoni, F. 2007. Metric HopfLax formula with semicontinuous data. Discrete and Continuous Dynamical Systems 17(4), pp. 713729. (10.3934/dcds.2007.17.713)
 Dragoni, F. 2007. Limiting behavior of solutions of subelliptic heat equations. Nonlinear Differential Equations and Application NoDEA 14(34), pp. 429441. (10.1007/s0003000760130)
2006
 Dragoni, F. 2006. CarnotCarathéodory metrics and viscosity solutions. PhD Thesis, Scuola Normale Superiore, Pisa, Italy.
2005
 Barletti, L. and Dragoni, F. 2005. An inverse problem for twofrequency photon transport in a slab. Mathematical Methods in the Applied Sciences 28(14), pp. 16951714. (10.1002/mma.633)
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 (2016present)

Foundation II, year 1, Cardiff (2016present)

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 subRiemannian 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. SubRiemannian 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 socalled Asian options.Unlike Riemannian manifolds (where the structure looks locally always like the Euclidean R^{N}), subRiemannian 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 nondegenerate 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 subRiemannian 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
 HamiltonJacobi equations and HopfLax formulas
 Absolutely Minimizing Lipschitz extensions
 InfiniteLaplacian
 Mean Field Games
 Tugofwar, more in general deterministic and stochastic differential games
Research group
External funding and grants
 20172018: Cardiff University Research Leave Grant £3000, LMS Scheme 3 £1500; LMS Educational Grant £400
 20162017: LMS Grant Scheme 4 £1200; LMS Grant Scheme 3 £1200
 20152016: EPSRC First Grant £99,896; LMS Grant Scheme 3 £1979
 20122013: 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 FirenzeTohoku Research Workshop on Nonlinear PDEs, Florence, Italy
 09/2018: LMS Analysis and Probability Workshop, Cardiff, UK
 09/2018: UMISIMAIPTM 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 HeriotWatt 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
 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 20162017
Former Research Students
 Doaa Filali 20132018
 Ahmed Jama 20142018
MMath (equivalent of Master) Students
 Matthew Tandy 20182019
 Liam M. Rosser 20162017
 Ahmed Jama 20132014
Undergraduates Students
 Ruth Cresswell (50%) 20162017
 Cordula Mayerhofer 20122013
 James Evans 20112012
 Jordan P. Thomas 20112012
PhD External Examiner

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