01:06:02

Quantum Versus Classical Vortex Dynamics

01:14:59

Riemann, Topology and Physics - Lecture 1 (of 2)

01:24:59

Riemann, Topology and Physics 2 - Lecture 2 (of 2)

54:46

Quantum Vortex Knots and Links under Zero Helicity Condition

01:13:15

A Topological Route to Superfluid Turbulence

53:22

On the Energy and Helicity of Inflexional Magnetic Braids

00:51

Topological transition of a Möbius soap film developing a twist fold singularity

00:22

Twist fold singularity from a Möbius soap film collapse

00:16

New defects creation from a twist phase superposition on two vortex ring defects

00:28

New defect creation from a twist phase superposition on a vortex ring defect

00:19

Reconnection of two vortex ring defects

00:27

Topological cascade of a Hopf link of vortex defects to unlinked loops

00:35

Topological cascade of the minimal surface of a link of vortex defects

00:26

Head-on collision of two anti-parallel vortex ring defects

00:18

Topological collapse of a torus knot (2,3) vortex defect

00:15

Topological collapse of a torus knot (2,5) vortex defect

00:25

Topological collapse of a torus knot (2,7) vortex defect

00:43

Topological collapse of a torus knot (2,9) vortex defect

00:33

Topological cycle of three vortex ring defects

00:35

Topological cycle of two vortex loop defects

00:33

Creation of a trefoil vortex knot from the interaction of two unlinked, vortex loop defects

00:23

Flight of a vortex loop from the reconnection of two vortex ring defects

01:26:45

On Vortex Reconnection and Topological Cascade of Vortex Knots - Lecture 5 (of 5)

01:51:34

On the De-Singularization of the Biot-Savart Law and Vortex Reconnection - Lecture 4 (of 5)

01:50:19

From Linking Numbers to Vortex Motion and Torus Knots - Lecture 3 (of 5)

01:50:36

Helicity and Linking Numbers - Lecture 2 (of 5)

01:47:35

Kelvin's Topological Vortex Dynamics - Lecture 1 (of 5)

52:50

On Quantum Vortex Knots and Links

43:47

The Beautiful Interplay of Topology and Physics

52:27

Multi-valued Potentials and Physical Reality

48:20

Minimal Unlinking Pathways as Geodesics in Knot Polynomial Space

34:33

Vortex Reconnection in Classical and Quantum Systems

43:14

Pathways as Geodesic Flows in Polynomial Space

01:02:57

Topological Cascade Through Vortex Reconnection

19:54

Defect Production by Phase Twist Injection as Aharonov-Bohm Effect

01:04:31

Geometric Devils in Topological Dynamics

01:52:18

Introduction to Topological Fluid Dynamics - Lecture 7 (of 7)

01:27:44

Introduction to Topological Fluid Dynamics - Lecture 6 (of 7)

01:32:54

Introduction to Topological Fluid Dynamics - Lecture 5 (of 7)

01:26:45

Introduction to Topological Fluid Dynamics - Lecture 4 (of 7)

01:31:26

Introduction to Topological Fluid Dynamics - Lecture 3 (of 7)

01:34:39

Introduction to Topological Fluid Dynamics - Lecture 2 (of 7)

01:21:11

Introduction to Topological Fluid Dynamics - Lecture 1 (of 7)

39:57

Quantum Vortex Dynamics by Seifert Surface Information

01:52:37

Knots and Applications 3: An Elementary Introduction (in Italian)

02:17:25

Knots and Applications 2: An Elementary Introduction (in Italian)

02:00:32

Knots and Applications 1: An Elementary Introduction (in Italian)

41:03

Vortex Knots Cascade by HOMFLYPT Polynomial

37:19

Knot Polynomials as New Tools in Turbulence Research

23:44

Open Problems in Knot Theory and Applications -- Forward Look and Plenary Discussion

17:37

On the Energy Spectrum of Magnetic Knots and Links

01:01:24

Topological Fluid Mechanics: from Gauss' Linking Number to Modern Topological Dynamics

22:05

Impulse of Vortex Knots from Diagram Projections

01:00:47

Recent Progress in Topological Fluid Dynamics: from Helicity to Jones Polynomials

09:16

On Călugăreanu's Theorem