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| Name | Geometry of Delta Sets |
| Video Uploader | Video From Oliver Knill |
| Upload Date | This Video Uploaded At 04-07-2024 16:35:19 |
| Video Discription | Some Slides from a presentation done on July 3rd 2024. 00:00 Welcome: Drone footage of Bentley college 00:18 The main Object: (G,D,R) delta set 00:27 Simplicity Clarity Generality 00:37 Short code as Algorithmic Poetry 00:43 Code example computing cohomology 00:53 Code example constructing manifolds 01:07 Brevity: Brainfuck Programming language 01:29 Running Brainfuck code online 01:38 Can AI generate a Brainfuck interpreter 01:46 Formatted version of Brainfuck interpreter 01:53 Is there a Brainfuck to an ultimate theory? 01:57 Dirac, Pauli and Bohr fooling around 02:02 Harmonices Mundi by Kepler 02:07 Physics Theories GR-QM-GUT-TOE-CFT-SM 02:17 Examples of mathematical theories 02:27 Example of physical theories 02:37 Examples of theorems in mathematics 02:42 But doing it in the finite is blasphemy 02:58 Why finite geometry? 03:07 Foundations: a constructive approach 03:17 Herman Weyl: What is a sphere 03:38 Bernhard Riemann: quanta as parts of a manifold 03:48 Gino Fano: finite geometries 03:53 Vietoris-Rips complex 04:11 Heisenberg and Jordan: quantization of space 04:17 Arthur Ruark: discrete number of discrete data 04:27 Hartland Snyder: Quantized Space-Time 04:33 David Finkelstein: points of space time in assembly 04:44 Richard Feynman and Marvin Minsky in 1982 04:48 Wolfram Physics approach 04:52 Finite geometries: Graphs, Quivers, Delta Sets 05:02 Hypergraphs have no derivatives in general 05:12 Simple graphs define canonically hypergraphs 05:24 Whitney functor 05:32 From scratch recursive implementation 05:37 Quivers: graphs allowing multiple edges and loops 05:48 Quivers have a calculus 05:52 Quivers define spectra 05:56 There are upper bounds on all eigenvalues 06:00 And a lower bound on all eigenvalues 06:04 An illustration of these bounds 06:08 Illustration code available on ArXiv 06:13 Eilenberg-Zilber Delta sets in 1950 06:23 Abstract delta sets: computer science approach 06:33 Delta sets allow operations on them 06:40 They also carry a nice topology 06:48 There are theorems: like on Euler characteristic 06:53 Some folks behind these theorems 06:57 Four special things about finite geometry 07:13 Curvature constraints: Victor Eberhard 07:23 Stability of the vacuum problem in math 07:37 Discrete Sard theorem: No singularities 07:43 Coordinates can become non-commutative 07:49 Apropos: Descartes on coordinates 07:53 Is related to the problem of Cartesian products 08:02 Discrete Sard theorem 08:15 Discrete Level sets 08:18 Discrete level sets animation 08:26 Discrete manifolds in the finite 08:43 How does calculus look like in 50 years? 08:53 We currently teach standard calculus 09:03 A future syllabus might look different 09:14 A wave front problem in the discrete 09:20 A wave front on a cube: expected to get dense 09:42 A wave front on a torus: expected to get dense 09:54 A wave front on a Riemannian manifold 10:07 Quadratic cohomology: currently under investigation 10:28 Hoping to get invariants for knots 10:38 Drone footage: time to get back to Arlington 10:50 The end |
| Category | Science & Technology |
| Tags | delta set | brainfuck programming language | geometry on finite sets |
