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
(3 lectures, in Italian; 2017) Lecture 1: An Intuitive Approach Lecture 2: When Topology Meets Geometry Lecture 3: From Gauss coding to Modern Tabulation… Continue reading
(7 lectures; 2018) Lecture 1: Fundamentals of Fluid Flows and Kinematic Transport Theorem Lecture 2: Conservation of Linear Momentum and Decomposition of Fluid Flows Lecture 3: Circulation and Vorticity Transport Equation September 26, 2018 Click on to watch this video Duration: 1:31:26 Summary of the talk Lecture 4: Helmholtz’s Conservation Laws and Kinetic Helicity September … Continue reading
On Quantum Vortex Knots and Links Defect Production by Phase Twist Injection as Aharonov-Bohm Effect Minimal Unlinking Pathways as Geodesics in Polynomial Space Quantum Vortex Dynamics by Seifert Surface Information Vortex knots cascade by HOMFLYPT polynomial On the Energy Spectrum of Magnetic Knots and Links Impulse of Vortex Knots from Diagram Projections On Călugăreanu’s Theorem… Continue reading
The Beautiful Interplay of Topology and Physics Multi-Valued Potentials and Physical Reality Minimal Unlinking Pathways as Geodesics in Knot Polynomial Space Vortex Reconnection in Classical and Quantum Systems Topological Cascade Through Vortex Reconnection Geometric Devils in Topological Dynamics Knot Polynomials as a New Tool in Turbulence Research Topological Fluid Mechanics – From Gauss’ Linking Number … Continue reading
