# playlist (click the video's upper-left icon)
source: Centre International de Rencontres Mathématiques 2015年8月7日
Paul Turner: A hitchhiker's guide to Khovanov homology - Part I 1:10:14 Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities.
There are already too many introductory articles on Khovanov homology and certainly another is not needed. On the other hand by now - 15 years after the invention of subject - it is quite easy to get lost after having taken those first few steps.
What could be useful is a rough guide to some of the developments over that time and the summer school Quantum Topology at the CIRM in Luminy has provided the ideal opportunity for thinking about what such a guide should look like.
It is quite a risky undertaking because it is all too easy to offend by omission, misrepresentation or other. I have not attempted a complete literature survey and inevitably these notes reflects my personal view, jaundiced as it may often be. My apologies for any offence caused.
I would like to express my warm thanks to Lukas Lewark, Alex Shumakovitch, Liam Watson and Ben Webster.
Recording during the thematic meeting: "Geometric and quantum topology in dimension 3" the June 23, 2014 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
Paul Turner: A hitchhiker's guide to Khovanov homology - Part II 1:11:43
Paul Turner: A hitchhiker's guide to Khovanov homology - Part III 1:16:36
Paul Turner: A hitchhiker's guide to Khovanov homology - Part IV 1:04:26
Pierre Pansu: Differential forms and the Hölder equivalence problem - Part 1 1:22:00
Arnaud de mesmay: Discrete systolic geometry and decompositions of triangulated surfaces 26:09
Isabelle Gallagher: Some results on global solutions to the Navier-Stokes equations 51:38
Ludovic Rifford: Geometric control and sub-Riemannian geodesics - Part I 1:19:56
John Loftin: Some projective invariants of convex domains coming from [...] 1:14:35
Christian Bär: Characteristic initial value problem for wave equations on manifolds 46:14
Jean-Pierre Bourguignon: Revisiting the question of dependence of spinor fields and Dirac [...] 1:04:33
Anton Alekseev: Logarithms and deformation quantization 1:05:00
Toshitake Kohno: Quantum symmetry of conformal blocks and representations of braid [...] 59:54
Semyon Dyatlov: A microlocal toolbox for hyperbolic dynamics 56:39
Etienne Ghys: My favorite groups 22:43
John Pardon: Totally disconnected groups (not) acting on three-manifolds 53:51
Bert Wiest: Pseudo-Anosov braids are generic 58:25
John Pardon: Virtual fundamental cycles and contact homology 1:01:41
Emmy Murphy: Existence of Liouville structures on cobordisms 1:05:11
Tim Perutz: From categories to curve-counts in mirror symmetry 1:07:36
Jake Solomon: The degenerate special Lagrangian equation 1:06:16
Mohammed Abouzaid: Nearby Lagrangians are simply homotopic 58:56
Kai Cieliebak: On a question by Michele Audin 1:03:08
Sheel Ganatra: The Floer theory of a cotangent bundle, the string topology of the base and... 1:06:22
Nick Sheridan: Counting curves using the Fukaya category 1:11:23
Paul Gauduchon: Almost complex structures on quaternion-Kähler manifolds of positive type 1:02:35
Interview at CIRM: François Lalonde 44:38
Leonid Polterovich: Persistence modules and Hamiltonian diffeomorphisms - Part 4 1:02:24
Leonid Polterovich: Persistence modules and Hamiltonian diffeomorphisms - Part 1 57:54
Leonid Polterovich: Persistence modules and Hamiltonian diffeomorphisms - Part 2 50:56
Leonid Polterovich: Persistence modules and Hamiltonian diffeomorphisms - Part 3 59:14
Entretien au CIRM : Jean-Pierre SERRE avec Jean-Louis COLLIOT-THELENE 55:12
Interview Gérard Besson 7:04
Andras Vasy: Microlocal analysis for Kerr-de Sitter black holes 1:01:18
Martina Zähle: Curvature measures of random sets 42:02
Rolf Schneider: Hyperplane tessellations in Euclidean and spherical spaces 39:31
Showing posts with label A. (subjects)-Engineering & Physical Sciences-Mathematics-Geometry. Show all posts
Showing posts with label A. (subjects)-Engineering & Physical Sciences-Mathematics-Geometry. Show all posts
2017-09-01
2017-04-13
Differential Geometry by Norman J. Wildberger at at UNSW
# click the upper-left icon to select videos from the playlist
source: njwildberger 2013年8月1日
The first lecture of a beginner's course on Differential Geometry! Given by Assoc Prof N J Wildberger of the School of Mathematics and Statistics at UNSW. Differential geometry is the application of calculus and analytic geometry to the study of curves and surfaces, and has numerous applications to manufacturing, video game design, robotics, physics, mechanics and close connections with classical geometry, algebraic topology, the calculus of several variables and mostly notably Einstein's General Theory of Relativity.
This lecture summarizes the basic topics of the course, the unique point of view of the lecturer, and then heads straight into a survey of classical curves, starting with the line, then the conic sections (ellipse, parabola, hyperbola), then moving to classical ways of generating new curves from old ones. These techniques include the Conchoid construction of Nicomedes, the Cissoid construction of Diocles, the Pedal curve construction and the evolute and involute introduced by Huygens. This lecture should be viewed in conjunction with MathHistory16: Differential Geometry.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .
Differential Geometry
A beginner's course on Differential Geometry. We present a systematic and sometimes novel development of classical differential differential, going back to Euler, Monge, Dupin, Gauss and many others. Our approach is more algebraic than usual; we are interested in making the theory more elementary and at the same time more general; extending quite a few results to finite fields for example, and minimizing the role of all but basic calculus. The geometrical side of things will be emphasized, and includes some pertinent theory from projective geometry. We also want to avoid the logical difficulties, usually completely ignored, in basing the subject on the so-called `real numbers': our theory has the rational numbers firmly at the heart of the subject, with quadratic extensions employed when necessary. In this sense the course is much more elementary than the usual treatments.
Topics include looking at classical curves and surfaces, in particular both parametrized and algebraic curves and surfaces. We approach the local study via tangent lines/planes and tangent conics/quadrics following the algebraic approach to calculus championed by Lagrange (and Euler before him). Curvature is the key to the subject, and we present a careful step by step treatment of this subject starting from curves to surfaces, with a variety of interesting classical applications and results.
DiffGeom1: Classical curves 44:11
DiffGeom2: Introduction to GeoGebra 14:20
DiffGeom3: Parametrized curves and algebraic curves 41:14
DiffGeom4: The differential calculus for curves, via Lagrange! 48:27
DiffGeom5: Tangent conics and tangent quadrics 49:16
DiffGeom6: Visualizing the folium surface with GeoGebra 23:51
DiffGeom7: Differential geometry with finite fields 49:43
DiffGeom8: The differential calculus for curves (II) 48:15
DiffGeom9: Projective view of conics and quadrics 38:31
DiffGeom10: Duality, polarity and projective linear algebra 37:27
DiffGeom11: Duality, polarity and projective linear algebra (II) 48:26
DiffGeom12: Metrical structure and curvature of a parabola 44:07
DiffGeom13: Curvature for the general parabola 47:55
DiffGeom14: Quadratic curvature for algebraic curves 33:08
DiffGeom15: Quadratic curvature for algebraic curves (cont) 36:11
DiffGeom16: Curvature, turning numbers and winding numbers 48:24
DiffGeom17: Curvature, turning numbers and winding numbers (cont) 48:01
DiffGeom18: The Frenet Serret equations 50:31
DiffGeom19: The Frenet Serret equations (example) 23:02
DiffGeom20: Geometric and algebraic aspects of space curves 54:56
DiffGeom21a: An introduction to surfaces 42:44
DiffGeom21b: A tutorial: some differential geometry problems 46:32
DiffGeom22: More general surfaces 52:35
DiffGeom23: Paraboloids and associated quadratic forms 46:38
DiffGeom24: Topological spaces and manifolds 50:14
DiffGeom25: Manifolds, classification of surfaces and Euler characteristic 46:17
DiffGeom26: Classification of 2-manifolds and Euler characteristic 45:50
DiffGeom28: Curvature for the general paraboloid 46:14
DiffGeom29: Curvature for general algebraic surfaces 49:05
DiffGeom30: Examples of curvatures of surfaces 42:49
DiffGeom31: Meusnier, Monge and Dupin I 49:04
DiffGeom32: Meusnier, Monge and Dupin II 48:16
DiffGeom33: Meusnier, Monge and Dupin III 54:38
DiffGeom34: Gauss, normals and fundamental forms 51:27
DiffGeom35: Gauss's view of curvature and the Theorema Egregium 43:46
source: njwildberger 2013年8月1日
The first lecture of a beginner's course on Differential Geometry! Given by Assoc Prof N J Wildberger of the School of Mathematics and Statistics at UNSW. Differential geometry is the application of calculus and analytic geometry to the study of curves and surfaces, and has numerous applications to manufacturing, video game design, robotics, physics, mechanics and close connections with classical geometry, algebraic topology, the calculus of several variables and mostly notably Einstein's General Theory of Relativity.
This lecture summarizes the basic topics of the course, the unique point of view of the lecturer, and then heads straight into a survey of classical curves, starting with the line, then the conic sections (ellipse, parabola, hyperbola), then moving to classical ways of generating new curves from old ones. These techniques include the Conchoid construction of Nicomedes, the Cissoid construction of Diocles, the Pedal curve construction and the evolute and involute introduced by Huygens. This lecture should be viewed in conjunction with MathHistory16: Differential Geometry.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .
Differential Geometry
A beginner's course on Differential Geometry. We present a systematic and sometimes novel development of classical differential differential, going back to Euler, Monge, Dupin, Gauss and many others. Our approach is more algebraic than usual; we are interested in making the theory more elementary and at the same time more general; extending quite a few results to finite fields for example, and minimizing the role of all but basic calculus. The geometrical side of things will be emphasized, and includes some pertinent theory from projective geometry. We also want to avoid the logical difficulties, usually completely ignored, in basing the subject on the so-called `real numbers': our theory has the rational numbers firmly at the heart of the subject, with quadratic extensions employed when necessary. In this sense the course is much more elementary than the usual treatments.
Topics include looking at classical curves and surfaces, in particular both parametrized and algebraic curves and surfaces. We approach the local study via tangent lines/planes and tangent conics/quadrics following the algebraic approach to calculus championed by Lagrange (and Euler before him). Curvature is the key to the subject, and we present a careful step by step treatment of this subject starting from curves to surfaces, with a variety of interesting classical applications and results.
DiffGeom1: Classical curves 44:11
DiffGeom2: Introduction to GeoGebra 14:20
DiffGeom3: Parametrized curves and algebraic curves 41:14
DiffGeom4: The differential calculus for curves, via Lagrange! 48:27
DiffGeom5: Tangent conics and tangent quadrics 49:16
DiffGeom6: Visualizing the folium surface with GeoGebra 23:51
DiffGeom7: Differential geometry with finite fields 49:43
DiffGeom8: The differential calculus for curves (II) 48:15
DiffGeom9: Projective view of conics and quadrics 38:31
DiffGeom10: Duality, polarity and projective linear algebra 37:27
DiffGeom11: Duality, polarity and projective linear algebra (II) 48:26
DiffGeom12: Metrical structure and curvature of a parabola 44:07
DiffGeom13: Curvature for the general parabola 47:55
DiffGeom14: Quadratic curvature for algebraic curves 33:08
DiffGeom15: Quadratic curvature for algebraic curves (cont) 36:11
DiffGeom16: Curvature, turning numbers and winding numbers 48:24
DiffGeom17: Curvature, turning numbers and winding numbers (cont) 48:01
DiffGeom18: The Frenet Serret equations 50:31
DiffGeom19: The Frenet Serret equations (example) 23:02
DiffGeom20: Geometric and algebraic aspects of space curves 54:56
DiffGeom21a: An introduction to surfaces 42:44
DiffGeom21b: A tutorial: some differential geometry problems 46:32
DiffGeom22: More general surfaces 52:35
DiffGeom23: Paraboloids and associated quadratic forms 46:38
DiffGeom24: Topological spaces and manifolds 50:14
DiffGeom25: Manifolds, classification of surfaces and Euler characteristic 46:17
DiffGeom26: Classification of 2-manifolds and Euler characteristic 45:50
DiffGeom28: Curvature for the general paraboloid 46:14
DiffGeom29: Curvature for general algebraic surfaces 49:05
DiffGeom30: Examples of curvatures of surfaces 42:49
DiffGeom31: Meusnier, Monge and Dupin I 49:04
DiffGeom32: Meusnier, Monge and Dupin II 48:16
DiffGeom33: Meusnier, Monge and Dupin III 54:38
DiffGeom34: Gauss, normals and fundamental forms 51:27
DiffGeom35: Gauss's view of curvature and the Theorema Egregium 43:46
2017-04-12
Hyperbolic Geometry - Norman J Wildberger at UNSW
# click the upper-left icon to select videos from the playlist
source: UNSWelearning 2011年5月1日
Hyperbolic Geometry - N J Wildberger
This is a complete and relatively elementary course explaining a new, simpler and more elegant theory of non-Euclidean geometry; in particular hyperbolic geometry. It is a purely algebraic approach which avoids transcendental functions like log, sin, tanh etc, relying instead on high school algebra and quadratic equations. The theory is more general, extending beyond the null circle, and connects naturally to Einstein's special theory of relativity.
This course is meant for mathematics majors, bright high school students, high school teachers, engineers, scientists, and others with an interest in mathematics and some basic algebraic skills.
Norman Wildberger is also the discoverer of Rational Trigonometry, an important new direction for classical trigonometry (and which really ought to be revolutionizing mathematics education!!)
His YouTube site Insights into Mathematics at user: njwildberger also contains series on MathFoundations, History of Mathematics, LinearAlgebra, Rational Trigonometry and even one called Elementary Mathematics (K-6) Explained.
Universal Hyperbolic Geometry 0: Introduction 23:13 This is the introductory lecture to a series on hyperbolic geometry which introduces a radically new and improved way of treating the subject, making it more algebraic and logical, with improved computational power and many new theorems. In this lecture we summarize the differences between this UNIVERSAL HYPERBOLIC GEOMETRY and traditional courses taught at universities. We briefly review some of the framework introduced by Lobachevsky, Bolyai and Gauss.
1: Apollonius and polarity 40:38
2: Apollonius and harmonic conjugates 38:22
3: Pappus' theorem and the cross ratio 21:38
4: First steps in hyperbolic geometry 37:14
5: The circle and Cartesian coordinates 35:54
6: Duality, quadrance and spread in Cartesian coordinates 50:38
7a: The circle and projective homogeneous coordinates 37:40
7b: The circle and projective homogeneous coordinates (cont.) 24:17
8: Computations with homogeneous coordinates 44:32
9: Duality and perpendicularity 33:11
10: Orthocenters exist! 44:06
11: Theorems using perpendicularity 37:28
12: Null points and null lines 36:20
13: Apollonius and polarity revisited 26:31
14: Reflections in hyperbolic geometry 31:23
15: Reflections and projective linear algebra 50:29
16: Midpoints and bisectors 36:41
17: Medians, midlines, centroids and circumcenters 34:09
18: Parallels and the double triangle 29:35
19: The J function, sl(2) and the Jacobi identity 42:27
20: Pure and applied geometry--understanding the continuum 38:44
21: Quadrance and spread 35:54
22: Pythagoras' theorem in Universal Hyperbolic Geometry 36:14
23: The Triple quad formula in Universal Hyperbolic Geometry 39:11
24: Visualizing quadrance with circles 34:34
25: Geometer's Sketchpad and circles in Universal Hyperbolic Geometry 25:22
26: Trigonometric laws in hyperbolic geometry using Geometer's Sketchpad 20:20
27: The Spread law in Universal Hyperbolic Geometry 24:21
28: The Cross law in Universal Hyperbolic Geometry 35:26
29: Thales' theorem, right triangles and Napier's rules 42:35
30: Isosceles triangles in hyperbolic geometry 32:46
31: Menelaus, Ceva and the Laws of proportion 42:05
32: Trigonometric dual laws and the Parallax formula 35:47
33: Spherical and elliptic geometries: an introduction 32:14
34: Spherical and elliptic geometries (cont.) 44:19
35: Areas and volumes for a sphere 32:14
36: Classical spherical trigonometry 34:48
37: Perpendicularity, polarity and duality on a sphere 31:54
38: Parametrizing and projecting a sphere 38:43
39: Rational trigonometry: an overview 33:08
40: Rational trigonometry in three dimensions 31:20
source: UNSWelearning 2011年5月1日
Hyperbolic Geometry - N J Wildberger
This is a complete and relatively elementary course explaining a new, simpler and more elegant theory of non-Euclidean geometry; in particular hyperbolic geometry. It is a purely algebraic approach which avoids transcendental functions like log, sin, tanh etc, relying instead on high school algebra and quadratic equations. The theory is more general, extending beyond the null circle, and connects naturally to Einstein's special theory of relativity.
This course is meant for mathematics majors, bright high school students, high school teachers, engineers, scientists, and others with an interest in mathematics and some basic algebraic skills.
Norman Wildberger is also the discoverer of Rational Trigonometry, an important new direction for classical trigonometry (and which really ought to be revolutionizing mathematics education!!)
His YouTube site Insights into Mathematics at user: njwildberger also contains series on MathFoundations, History of Mathematics, LinearAlgebra, Rational Trigonometry and even one called Elementary Mathematics (K-6) Explained.
Universal Hyperbolic Geometry 0: Introduction 23:13 This is the introductory lecture to a series on hyperbolic geometry which introduces a radically new and improved way of treating the subject, making it more algebraic and logical, with improved computational power and many new theorems. In this lecture we summarize the differences between this UNIVERSAL HYPERBOLIC GEOMETRY and traditional courses taught at universities. We briefly review some of the framework introduced by Lobachevsky, Bolyai and Gauss.
1: Apollonius and polarity 40:38
2: Apollonius and harmonic conjugates 38:22
3: Pappus' theorem and the cross ratio 21:38
4: First steps in hyperbolic geometry 37:14
5: The circle and Cartesian coordinates 35:54
6: Duality, quadrance and spread in Cartesian coordinates 50:38
7a: The circle and projective homogeneous coordinates 37:40
7b: The circle and projective homogeneous coordinates (cont.) 24:17
8: Computations with homogeneous coordinates 44:32
9: Duality and perpendicularity 33:11
10: Orthocenters exist! 44:06
11: Theorems using perpendicularity 37:28
12: Null points and null lines 36:20
13: Apollonius and polarity revisited 26:31
14: Reflections in hyperbolic geometry 31:23
15: Reflections and projective linear algebra 50:29
16: Midpoints and bisectors 36:41
17: Medians, midlines, centroids and circumcenters 34:09
18: Parallels and the double triangle 29:35
19: The J function, sl(2) and the Jacobi identity 42:27
20: Pure and applied geometry--understanding the continuum 38:44
21: Quadrance and spread 35:54
22: Pythagoras' theorem in Universal Hyperbolic Geometry 36:14
23: The Triple quad formula in Universal Hyperbolic Geometry 39:11
24: Visualizing quadrance with circles 34:34
25: Geometer's Sketchpad and circles in Universal Hyperbolic Geometry 25:22
26: Trigonometric laws in hyperbolic geometry using Geometer's Sketchpad 20:20
27: The Spread law in Universal Hyperbolic Geometry 24:21
28: The Cross law in Universal Hyperbolic Geometry 35:26
29: Thales' theorem, right triangles and Napier's rules 42:35
30: Isosceles triangles in hyperbolic geometry 32:46
31: Menelaus, Ceva and the Laws of proportion 42:05
32: Trigonometric dual laws and the Parallax formula 35:47
33: Spherical and elliptic geometries: an introduction 32:14
34: Spherical and elliptic geometries (cont.) 44:19
35: Areas and volumes for a sphere 32:14
36: Classical spherical trigonometry 34:48
37: Perpendicularity, polarity and duality on a sphere 31:54
38: Parametrizing and projecting a sphere 38:43
39: Rational trigonometry: an overview 33:08
40: Rational trigonometry in three dimensions 31:20
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