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数学视频

Projective geometry

Daniel Chan. Projective geometry. Projective line, projective plane.

Algebraic geometry

Daniel Chan. Algebraic Geometry. First glimpses.

Richard Borcherds. Algebraic Geometry I. Varieties.

• Algebraic geometry 15 Projective space
• Algebraic geometry 20 Grassmannians
• Algebraic geometry 21 Projective space bundles

Richard Borcherds. Algebraic Geometry II. Schemes.

• Schemes 4: f * and f^ 1
• Schemes 29: Invertible sheaves over the projective line
• Schemes 30: f* and f *
• Schemes 32: The line bundles O(n) on projective space
• Schemes 33: Vector bundles on the projective line

Projective line bundles

Daniel Chan. Vector bundles.

Fredric Schuller: Lectures on Geometrical Anatomy of Theoretical Physics

• Tensor space theory I: over a field - Lec 08
• The Lie group SL(2,C) and its Lie algebra sl(2,C) - lec 15
• Principal fibre bundles - Lec 19
• Associated fibre bundles - Lec 20
• Connections and connection 1-forms - Lec 21
• Parallel transport - Lec 23

Daniel Chan. User's guide to coherent sheaves.

• The sheaf property
• Coherent sheaves on the projective line
• Coherent sheaves on projective varieties
• Classification of coherent sheaves on the projective line
• Vector Bundles and Locally Free Sheaves
• Invertible sheaves of rational functions
• Tensor products and sheaf Hom of coherent sheaves

Daniel Chan. Cohomology of coherent sheaves. Example of criterion for a smooth curve to be isomorphic to the projective line.

Taylor Dupuy. Introduction to Fiber Bundles Very generally in terms of schemes.

Taylor Dupuy. Deformation Theory of Line Bundles Part 1.

• Taylor Dupuy. Classification of Line Bundles on Schemes.

Modules

Daniel Chan. Introduction to modules.

Homological algebra

Daniel Chan. Homological algebra: First glimpses. Cohomology as obstruction.

Spinors

Eigenchris. Spinors for Beginners.

• Spinors for Beginners 22: Dirac Equation and Gamma Matrices Deep Dive (+ chirality)

Particle Physics

DrPhysicsA. Particle Physics

• The Standard Model
• Particle Physics 5: Basic Introduction to Gauge Theory, Symmetry & Higgs

Tensors

• Eigenchris. Tensors for Beginners. Also: Tensor Calculus. Relativity.

Special Relativity and General Relativity

DrPhysicsA. Special and General Relativity.

• Einstein Field Equations - for beginners!

Symplectic geometry

• Quantum Physics Missing Link Discovered... [Geometric Quantization]

Information geometry

Melvin Leok. Information Geometry and its Applications

• Parallel Transport of Vectors
• Exponential family of probability distributions
• Maximum entropy principle and e-projection
• Wolfram Institute Live Science | Inference, uncertainty and Hopf fibration

Watch and Learn

• Fun Applications of Geometric Algebra! by Logan Lim
• Introduction to modular forms and elliptic curves by Kenny Li
• An Algebraic Proof of the Fundamental Theorem of Algebra by Blake Madill
• Math-Life Balance. K-Theory Wonderland.
• Representation of Lorentz Group and Clifford algebra-I
• Representation of Lorentz Group and Clifford algebra-II

Watch and Relax

• Math-Life Balance. Interviews.
  • Interview with Max Karoubi.
  • Interview with Ravi Vakil.
  • Interview with Peter Scholze.

More Sources

Easy general

• Infinite Series
• Numberphile
• Mathologer

Talk collections

• Institute for Advanced Study: Mathematics
• Institute for Advanced Study
• Clay Mathematics Videos
• Oxford: The Secrets of Mathematics
• Max Planck Science Symplectic geometry, algebraic geometry, differential geometry
• Collected by Xuan Gottfried Yang
• Alexander Grothendieck channel
• Collected by "Graduate Mathematics" Number theory, Riemann hypothesis

Course collections

• Park City Mathematics Institute
• NPTEL videos, Alternate catalog
• MIT Open Courseware. Math Department.
• List of math class videos

College Math

• 3 blue 1 brown Linear algebra, Partial differential equations
• Academy of Khan
  • Tensor Calculus
  • Complex Variables and Functions

Overviews of Math

• Oliver Knill. Playlists. Great theorems.
• Oliver Knill. Media.

Lie theory preliminaries

• Algebraic topology
  • Curtis McMullen - Algebraic topology - The Geometry of 3 Manifolds
  • The Mystery of 3-Manifolds - William Thurston
• Federico Ardila
  • Coxeter groups
  • Polytopes
  • Hopf Algebras and Combinatorics, Index and Overview by Sara Billey

Lie theory

• Continuous groups in physics
• Continuous Groups for Physicists
  • Video named "17". End of general theory of Lie group and Lie algebra.
  • "18" Classification of compact semisimple Lie algebras and Lie groups and their representation theory. Complexification. Direct sum of semisimple and solvable Lie algebras.
  • "19" root systems
  • "20" simple roots
  • "22" orthogonal, symplectic Lie algebras, table of their properties
  • "23" unitary Lie algebra An, exceptional algebras
  • "24" Representation theory, starting spinors
  • "25" Spinors
• Amritanshu Prasad: Representation Theory: A Combinatorial Viewpoint

Complex analysis, Riemann surfaces

• Complex Analysis P. A. S. Sree Krishna Course
  • Properties of Mobius Transformations
• Introduction to Riemann Surfaces and Algebraic Curves
  • The Idea of a Riemann Surface T.E.Venkata Balaji
• Advanced Complex Analysis Dr. T.E. Venkata Balaji

Physics

• DoctorPhys: Theoretical Physics including basic Lie theory
• DrPhysicsA: Particle Physics
• Leonard Susskind: The Theoretical Minimum
  • Quantum Mechanics
  • Leonard Susskind: General Relativity, Notes
  • Particle Physics 2: Standard Model
    • Group theory: Part 2
• The Mathematical Formalism of Quantum Mechanics
• Quantum Fields, Strings, and Black Holes: A Primer for Non Experts

Algebraic geometry preliminaries

• Daniel Chan Tensors, affine geometry, projective geometry, vector bundles, category theory, homological algebra, modules, algebraic geometry.
• Taylor Dupuy Model theory, mathematical logic, Grothendieck, algebraic geometry
  • Fiber bundles
• Harpreet Bedi Homology, cohomology, etc.
• Introductory homological algebra by Rishi Vyas

Algebraic geometry, classical

• Basic Algebraic Geometry: Varieties, Morphisms, Local Rings, Function Fields and Nonsingularity
• ML Baker on Elliptic curves and modular forms
• Miles Reid. Algebraic surfaces.
• Assorted Geometry videos

Category theory

• The Catsters and Catsters overview, Another overview.
• Applied Category Theory David Spivak, Brendan Fong On Youtube
• David Spivak. Seven Sketches in Compositionality

Grothendieck theory

• Nickolas Rollick: Algebraic Geometry: Sheaves
• What is a Motive? Pierre Deligne
• Peter Arndt. Motivic Verona.

Topos theory

• Toposes in Como. Olivia Caramello et al
• Daniel Murfet: Topos theory
• André JOYAL - 1/4 A crash course in topos theory : the big picture

Other branches

• Field theory
  • 3.2 Properties of finite fields
• Analytic Combinatorics - Robert Sedgewick

Original thinkers

• An Intuitive Introduction to Motivic Homotopy Theory - Vladimir Voevodsky
• The Problem of Modelling the Mathematical Mind
• Mikhael Gromov - 2/6 Probability, symmetry, linearity, In a Search for a Structure, Part 1: On Entropy. Misha Gromov.

Math podcasts

List of podcasts

• Math podcasts

Talks with mathematicians

• My Favorite Theorem
• Numberphile
• Travels in a Mathematical World
• Breaking Math Podcast
• Relatively Prime
• Mathematical Moments from the American Mathematical Society
• Women in Math: The Limit Does Not ExistPro Unlimited

Previously watched

Physics

• John Baez. Unsolved Mysteries in Fundamental Physics.