Short Course Video Lectures
Short Graduate and Undergraduate Lecture Courses • An Introduction to Topological Fluid Dynamics (7 lectures; 2018) A graduate course held at the Institute for Theoretical Physics, Beijing University of Technology (BJUT). • Knots and Applications: An Elementary Introduction (3 lectures, in Italian; 2017) A short undergraduate course held at the Scuola Normale Superiore (Pisa) under the … Continue reading
Research Presentations
Review Talks (1 hr) and Seminars (30 mins) • Review talks for graduate students and researchers Presentations of new results providing a historical context and a review of the recent progress in the field. • Seminars at international meetings and conferences Short presentations of new results in special thematic sessions. Click on to visit and … Continue reading
New Results
Scientific results categorised by research area and listed in inverse chronological order (numbered item and date in brackets referred to the publication list page). (i) Classical vortex dynamics and fluid knots topological cascade of fluid knots in terms of geodesic flows in polynomial space (75, 2020); influence of winding number on the evolution of vortex … Continue reading
Recent Progress in Topological Fluid Dynamics
Slides from the Ravello School on Mathematical Physics (2017) Topological interpretation of helicity Coherent structures and topological fluid mechanics Diffeomorphisms and topological equivalence Kinetic and magnetic helicity of flux tubes Gauss linking number Călugăreanu invariant and geometric decomposition Vortex knots dynamics and momenta of a tangle Localized Induction Approximation (LIA) and Non-Linear Schroedinger (NLS) equation … Continue reading
Research Interests
My work concerns the following thematic areas: Classical vortex dynamics and fluid knots; Quantum defects in condensates and topological phases; Energy-complexity relations for magnetic fields; Topological transitions of critical energy surfaces; Hydrodynamic analogue models in black hole theory. (i) Classical vortex dynamics and fluid knots Study of dynamical properties of three-dimensional vortex fields, and of … Continue reading
Research Group and Collaborators
Current Collaborators Former Collaborators Sultan AlamriCarlo BarenghiMitchell BergerIrma Cruz-WhiteRay GoldsteinChristian LaingFrancesca MaggioniKeith MoffattBernardo NipotiChiara ObertiAlessandra PesciDavid Samuels Thesis Advisors Massimo GermanoGiuseppe GeymonatMario RasettiTullio Regge PhD Supervisor Keith Moffatt… Continue reading
International Programmes and Advanced Schools
Topological Methods in Mathematical Physics 74th School of Mathematics «Guido Stampacchia» and International Workshop, Majorana Foundation and Centre for Scientific Culture, September 2022 In 2022 I organised and directed the 74th School of Mathematics «Guido Stampacchia» and International Workshop on Topological Methods in Mathematical Physics at the Majorana Foundation and Centre for Scientific Culture in Erice … Continue reading
Mathematical Methods for Modern Physics
Introduction This is an elective course of the Master Degree in Mathematics, and it contributes to the educational training in Mathematical Physics. All lectures are given in English, and they are delivered during the second semester of each academic year, from March to June. It consists of 5 hours per week of front lectures, accounting … Continue reading
Matematica, Statistica e Informatica
Struttura Il corso si suddivide in due parti (13 CFU in totale): Matematica: I semestre, 6 ore di lezioni ed esercitazioni per settimana, 12 settimane di durata, 8 CFU. Statistica e Informatica (svolto dalla Professoressa Daniela Besozzi): II semestre, 5 CFU. Obiettivi dell’insegnamento di Matematica Fornire concetti e tecniche matematiche di base su: calcolo vettoriale, … Continue reading