Riemann, Topology and Physics
(2 lectures; 2024) Lecture 1: Riemann’s Cuts and Green’s First Identity Lecture 2: Green’s First Identity, AB Effect and Helicity in Multiconnected Domains… Continue reading
Gallery of Fluid Motion
Gallery of Fluid Motion • Topological collapse of a Möbius soap film Topological transition of a Möbius soap film that develops rapidly a twist fold singularity as changes from a one-sided film surface to a two-sided film surface. • Topological dynamics of quantum vortex knots and links Direct numerical simulation of the interaction and reconnection … Continue reading
Topological collapse of a Möbius soap film
Topological transition of a Möbius soap film developing a twist fold singularity Twist fold singularity from a Möbius soap film collaps… Continue reading
Topological dynamics of quantum vortex knots and links
Reconnection of two vortex ring defects Flight of a vortex loop from the reconnection of two vortex ring defects Topological cascade of a Hopf link of vortex defects to unlinked loops Topological cascade of the minimal surface of a link of vortex defects Head-on collision of two anti-parallel vortex ring defects Topological collapse of a … Continue reading
Advanced Courses Video Lectures
School Courses • Riemann, Topology and Physics (2 lectures; 2024) Two lectures given for the doctoral course “Interdisciplinary Frontiers in Theoretical Physics” held at the Beijing University of Technology (BJUT). • Elements of Topological Vortex Dynamics (5 lectures; 2023) An advanced summer school course held at the Institut d’Études Scientifiques de Cargèse. • An Introduction … Continue reading
Elements of Topological Vortex Dynamics
(5 lectures; 2023) Lecture 1: Kelvin’s Topological Vortex Dynamics Lecture 2: Helicity and Linking Numbers Lecture 3: From Linking Numbers to Vortex Torus Knots Lecture 4: De-Singularisation of the Biot-Savart Law and Vortex Reconnection Lecture 5: On Vortex Reconnection and Topological Cascade of Vortex Knots… Continue reading
Keynote Lectures and Webinars
Review Talks, Webinars and Short Communications • Keynote lectures and webinars Keynote presentations and webinars on new advancements and progress in the field. • Seminars at international meetings and conferences Short communications of new results at special thematic sessions. Click on to visit and subscribe to my YouTube Channel!… Continue reading
Knots and Applications: An Elementary Introduction
(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
An Introduction to Topological Fluid Dynamics
(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
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