Professor Federica Dragoni

Publication

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Research

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

• Mathematical Analysis Research Group
• Analysis, Probablity and Stochastic Process 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

Teaching

I am currently teaching the following modules:

• MA20006 Real Analysis (Spring Term)
• MA4013 Advanced topics in Analysis with application to PDEs (Spring Term)
• Foundations Tutorial (Autumn Term and Spring Term)

Former teaching experience

• Real Analysis. year 2, Cardiff (2021-present)
• Further topics in Analysis with applications to PDEs, Postgraduate and MMath course, Cardiff University (2016-present)

• Foundation II, year 1, Cardiff (2016-2020)

• 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: 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

• 2021-present: Chain in Mathematics at  Cardiff School of Mathematics, Cardiff University
• 2016-2021: Senior Lecturer and the Reader 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)

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

Research student