Undergraduate, Graduate and Advanced School Lecture Courses • Elements of Topological Vortex Dynamics (5 lectures; 2023) An advanced summer school course held at the Institut d’Études Scientifiques de Cargèse. • 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 … Continue reading
(5 lectures; 2023) Lecture 1: Kelvin’s Topological Vortex Dynamics Lecture 2: Helicity and Linking Numbers Lecture 3: From Linking Numbers to Vortex Motion and Torus Knots Lecture 4: On the De-Singularization of the Biot-Savart Law and Vortex Reconnection Lecture 5: On Vortex Reconnection and Topological Cascade of Vortex Knots… Continue reading
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
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
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
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
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
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
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