Professor Federica Dragoni
(she/her)
Personal Chair
 DragoniF@cardiff.ac.uk
 +44 29208 75529
 Abacws, Room 2.19, Senghennydd Road, Cathays, Cardiff, CF24 4AG
Overview
I am Chair in Mathematics at Cardiff University since August 2021.
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. In particular I work on geometric PDEs, associated to the Heisenberg group, Carnot groups and general subRiemannian geometries.
School Roles
 Senior Tutor
Other Roles
 Welsh Node Leader for the EPSRC Generalised and LowRegularity Solutions of Nonlinear PDEs Network

EPSRC panel member

LSM Undergraduate Research Bursary Board
Conference, workshop and Research Network organisation
 Summer School in nonlinear PDEs, Swansea, July 2024
 Variational methods for nonlinear PDEs, Cardiff, July 2023
 Workshop on Nonlinear Equations: from theory to modelling, Cardiff, November 2022
 Workshop on Calculus of Variation and Nonlinear PDEs, Cardiff, April 2022
 12th LMS Network worhshop, Cardiff, November 2018
 11th LMS Network worhshop, Cardiff, May 2018
 8th LMS Network worhshop, Cardiff, September 2017
 New Trends in nonlinear PDEs: from theory to applications, Cardiff, March 2016
 2nd LMS Network worhshop, Cardiff, April 2016
 Stochastic methods and nonlinear PDEs, Cardiff, 2012
Outreach activities
 Maths Games Clubs at Caerphilly Library and Bargoed Library in collaboration with CTG  Caerphilly TableTop & Gamers Society
External Links
Publication
2020
 Dirr, N., Dragoni, F., Mannucci, P. and Marchi, C. 2020. Gammaconvergence 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.. [Online]. arXiv. Available at: https://arxiv.org/abs/2005.10599
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. 901918. (10.1112/jlms.12198)
2018
 Dirr, N., Dragoni, F., Mannucci, P. and Marchi, C. 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, 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., Qian, Z., Roberto, C., Dragoni, F., Inglis, J. and Kontis, V. 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 subRiemannian geometries: a stochastic approach. Communications on Pure and Applied Analysis 9(2), pp. 307326. (10.3934/cpaa.2010.9.307)
 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
 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)
Articles
 Dirr, N., Dragoni, F., Mannucci, P. and Marchi, C. 2020. Gammaconvergence and homogenisation for a class of degenerate functionals. Nonlinear Analysis 190, article number: 111618. (10.1016/j.na.2019.111618)
 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. 901918. (10.1112/jlms.12198)
 Dirr, N., Dragoni, F., Mannucci, P. and Marchi, C. 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, article number: 116. (10.1007/s0052601813911)
 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.
 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)
 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)
 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)
 Dirr, N. P., Dragoni, F. and Von Renesse, M. 2010. 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)
 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)
 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)
Book sections
 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)
Books
 Gentil, I., Qian, Z., Roberto, C., Dragoni, F., Inglis, J. and Kontis, V. Zegarlinski, B. ed. 2011. Aspects of analysis curvature criterion, isoperimetry, evolution equations. Mathematical Notebooks Vol. 3. Matrix Press.
Thesis
 Dragoni, F. 2006. CarnotCarathéodory metrics and viscosity solutions. PhD Thesis, Scuola Normale Superiore, Pisa, Italy.
Websites
 Dirr, N., Dragoni, F. and Grande, R. 2020. Asymptotics for optimal controls for horizontal mean curvature flow.. [Online]. arXiv. Available at: https://arxiv.org/abs/2005.10599
Research
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
 20232024: LMS Scheme 4; Cardiff University Research Leave
 20202024: Welsh Node for EPSRC Network on Generalised and Lowregularity Solutions for Nonlinear PDEs
 20192020: ERASMUS Mobility Grant; CU Funds to visit Campinas
 20182019: LMS Scheme 5 (Collaborations with developing countries)
 20172018: Cardiff University Research Leave; LMS Scheme 3; LMS Educational Grant
 20162017: LMS Grant Scheme 4; LMS Grant Scheme 3
 20152016: EPSRC First Grant; LMS Grant Scheme 3
 20122013: LMS grant Scheme 1; OxPDE grant for conference; WIMCS grant for conference
 2010: LMS collaborative small grant
 2007: INDAM research grant
Teaching
I am currently teaching the following modules:
 MA20006 Real Analysis (Spring Term)
Former teaching experience
 Real Analysis. year 2, Cardiff (2021present)
 Further topics in Analysis with applications to PDEs, Postgraduate and MMath course, Cardiff University (20162023)

Foundation II, year 1, Cardiff (20162020)

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)
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: 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
 2021present: Chain in Mathematics at Cardiff School of Mathematics, Cardiff University
 20162021: Senior Lecturer and the Reader 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
Supervisions
 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
Prachi Sahjwani
Graduate Tutor