(4 lectures; 2026) Lecture 1: Helicity Conservation and its Topological Interpretation Lecture 2: Magnetic Relaxation and Groundstate Energy of Knots and Links Lecture 3: Change of Topology Due to Physical Surgery (Reconnection) Lecture 4: Topological Cascade of Vortex Knots by Knot Polynomials… Continue reading
(2 lectures; 2025) Lecture 1: Helicity Conservation and its Topological Interpretation Lecture 2: Twist-Fold Processes and Energy Relaxation in Natur… Continue reading
(2 lectures; 2025) Lecture 1: Magnetic Helicity in Ideal MHD: Definition and Conservation Lecture 2: Ampère’s theorem, Solid Angle and Emergence of Linking… Continue reading
(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 • 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 transition of a Möbius soap film developing a twist fold singularity Twist fold singularity from a Möbius soap film collaps… Continue reading
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
• Knots and Their Interdisciplinary Applications (4 Lectures: 2026) Lectures given for the Oberwolfach Seminar held at the Oberwolfach Mathematical Institute (MFO). • Helicity, Energy and Reidemeister Twist Move (2 Lectures: 2025) Lectures given for the Master course in “Theoretical Physics” held at the Beijing University of Technology (BJUT). • Magnetic Helicity, Ampère’s Theorem and … 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 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