Disclaimer

Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references or other sources. Moreover, after upload I am not able to change the YouTube videos anymore, so take everything with a pinch of salt. I can change the slides, so let me know if you have spotted any typos. In any case, here is a list all my YouTube videos, including slides. The order below is by playlist/topic, newest first:

  • My favorite theorems
  • What is...algebraic topology?
  • What is...algebra?
  • What is...linear algebra?
  • For my talks see here, for quantum topology see here, for Soergel bimodules see here
If there is something missing you would like to see (e.g. I forgot to upload slides, or you are missing a topic covered in a video, or there is a dead link, or...) then reach out: daniel.tubbenhauer@sydney.edu.au

A list of my videos

  • Playlist What are...my favorite theorems?
    1. Topic: What is...the difference between Eulerian and Hamiltonian graphs? - Or: They are not dual!? Slides
    2. Topic: What is...the curse of dimensionality? - Or: Hyperballs do not exist! Well, kind of... Slides
    3. Topic: What is...Polya's theorem? - Or: Birds get lost. Slides
    4. Topic: What are...Chebyshev polynomials? - Or: Fibonacci with signs? Slides
    5. Topic: What is...reverse mathematics? - Or: Thinking backwards. Slides
    6. Topic: What is...the axiom of choice? - Or: It works even if you don’t believe in it. Slides
    7. Topic: What is...the Mason-Stothers theorem? - Or: The ABC of polynomials. Slides
    8. Topic: What is...the pea and the sun paradox? - Or: One orange equals two oranges. Slides
    9. Topic: What is...the Robertson-Seymour theorem? - Or: Minors are majors. Slides
    10. Topic: What is...the Kuratowski-Wagner theorem? - Or: Forbidden pieces. Slides
    11. Topic: What is...the Jones polynomial? - Or: Resolving crossings. Slides
    12. Topic: What are...Catalan numbers? - Or: In praise of counting. Slides
    13. Topic: What is...the Abel-Ruffini theorem? - Or: Loops and roots. Slides
    14. Topic: What is...the art gallery theorem? - Or: How many cameras suffice? Slides
    15. Topic: What is...the finite Kakeya problem? - Or: A finite filling. Slides
    16. Topic: What is...Pick's theorem? - Or: Surprisingly simple. Slides
    17. Topic: What is...Kneser's conjecture? - Or: Coloring and topology. Slides
    18. Topic: What are...incarnations of the Borsuk-Ulam theorem? - Or: Topology or combinatorics or...? Slides
    19. Topic: What is...the Borromean impossibility theorem? - Or: Borromean rings do not exist! Slides
    20. Topic: What are...p-adic integers? - Or: Climbing infinite trees. Slides
    21. Topic: What are...Steiner systems? - Or: Finite geometry and puzzles. Slides
    22. Topic: What is...Heawood's conjecture? - Or: I need more than four colors. Slides
    23. Topic: What is...the Strassen algorithm? - Or: Divide and conquer. Slides
    24. Topic: What are...Gröbner bases? - Or: Minimal intersections. Slides
    25. Topic: What is...the chaos game? - Or: Deterministic versus random. Slides
    26. Topic: What is...the art of locating roots? - Or: Finding roots without finding them. Slides
    27. Topic: What is...the Schwartz-Zippel lemma? - Or: The art of not solving equations. Slides
    28. Topic: What are...random numbers? - Or: Compressible? Slides
    29. Topic: What is...Matiyasevich's theorem? - Or: I can't decide... Slides
    30. Topic: What is...the Burnside problem? - Or: Obviously not! Ah, well...? Slides
    31. Topic: What is...a cellular automaton? - Or: From simple rules to life. Slides
    32. Topic: What is...the diamond lemma? - Or: Can you win? Slides
    33. Topic: What is...Goodstein's theorem? - Or: Killing hydras. Slides
    34. Topic: What are...Monte Carlo experiments? - Or: The shotgun method. Slides
    35. Topic: What are...Artin braid groups? - Or: Topology via algebra. Slides
    36. Topic: What is...Frobenius' density theorem? - Or: Does it factor? Slides
    37. Topic: What is...an ADE classification? - Or: A strange reoccurring pattern. Slides
    38. Topic: What is...the discrete periodic table? - Or: Finite simple groups. Slides
    39. Topic: What is...the smooth periodic table? - Or: Simple Lie groups. Slides
    40. Topic: What is...the strong law of small numbers? - Or: There are not enough small numbers. Slides
    41. Topic: What is...Arrow's theorem? - Or: Why voting is always flawed (and is still a good idea). Slides
    42. Topic: What are...the seventeen wallpaper groups? - Or: Mathematics, architecture and decorative art. Slides
    43. Topic: What is...the philosophy of generating functions? - Or: How to encode counting problems. Slides
    44. Topic: What is...the Reidemeister theorem? - Or: Knotting stings in 2d. Slides
    45. Topic: What is...Euler's polyhedron formula? - Or: 2000 years of not doing the count. Slides
    46. Topic: What is...the Brouwer fixed point theorem? - Or: Why lines need to cross. Slides
    47. Topic: What is...the Lucas theorem? - Or: Playing with digits. Slides
    48. Topic: What is...the Gershgorin circle theorem? - Or: Circling the eigenvalues. Slides
    49. Topic: What is...the Perron-Frobenius theorem? - Or: The leading terms. Slides
  • Playlist What is...algebraic topology?; for the lecture website see Click
    1. Topic: What is...the cohomology ring? - Or: Polynomials, of course. Slides
    2. Topic: What is...the cohomology ring intuitively? - Or: Counting intersections. Slides
    3. Topic: What is...the universal coefficient theorem? - Or: Working integrally rocks. Slides
    4. Topic: What is...the Mayer-Vietoris sequence? - Or: More than the sum of its parts!? Slides
    5. Topic: What is...a (co)homology theory? - Or: Shut up and calculate. Slides
    6. Topic: What is...relative homology? - Or: Calculations modulo subspaces. Slides
    7. Topic: What is...cohomology? - Or: Reversing arrows. Slides
    8. Topic: What is...homology categorifying? - Or: Modules, polynomials and numbers. Slides
    9. Topic: What is...cellular homology? - Or: Winding around. Slides
    10. Topic: What are...simplicial and singular homology? - Or: Cycles modulo boundaries. Slides
    11. Topic: What are...simplicial complexes? - Or: Triangles everywhere. Slides
    12. Topic: What is...homology intuitively? - Or: What is a hole? Slides
    13. Topic: What are...examples of fundamental groups? - Or: One of my favorite lists. Slides
    14. Topic: What is...a Cayley complex? - Or: Groups geometrically. Slides
    15. Topic: What are...covering space action? - Or: Deck transformations and friends. Slides
    16. Topic: What is...a covering space? - Or: A topological Galois correspondence. Slides
    17. Topic: What is...the Seifert-Van Kampen theorem? - Or: Cut and compute. Slides
    18. Topic: What is...the fundamental group? - Or: How not to hang pictures on walls. Slides
    19. Topic: What are...operations on cell complexes? - Or: Cell by cell. Slides
    20. Topic: What are...cell complexes? - Or: Constructed from discs. Slides
    21. Topic: What is...homotopy? - Or: The same shape!? Slides
    22. Topic: What is...algebraic topology? - Or: Translating from topology to algebra. Slides
  • Playlist What is...algebra?
    1. Topic: What are...solvable polynomials? - Or: Field and Galois theory, application 3. Slides
    2. Topic: What is...the Kronecker–Weber theorem? - Or: Field and Galois theory, application 2. Slides
    3. Topic: What are...the limits of straightedge and compass? - Or: Field and Galois theory, application 1. Slides
    4. Topic: What are...the Galois groups of finite fields? - Or: Finite fields are easy. Slides
    5. Topic: What is...the fundamental theorem of Galois theory? - Or: From roots to groups and back. Slides
    6. Topic: What are...Galois extensions? - Or: Shuffling roots. Slides
    7. Topic: What are...group actions on fields? - Or: The beginning of Galois theory. Slides
    8. Topic: What are...normal and separable extensions? - Or: Linear factors matter. Slides
    9. Topic: What are...minimal polynomials? - Or: Minimal relations. Slides
    10. Topic: What are...field extensions? - Or: Adjoining roots. Slides
    11. Topic: What are...(finite) fields? - Or: Fields are relatively rare. Slides
    12. Topic: What are...irreducible polynomials? - Or: Analogs of primes. Slides
    13. Topic: What is...a unique factorization domain? - Or: Primes! Slides
    14. Topic: What is...an Euclidean domain? - Or: Generalizing division with remainder. Slides
    15. Topic: What is...the Chinese remainder theorem? - Or: Arranging rectangles. Slides
    16. Topic: What is...Hilbert's basis theorem? - Or: Algebra meets geometry (once again). Slides
    17. Topic: What is...localization? - Or: Why fractions matter. Slides
    18. Topic: What is...the calculus of ideals? - Or: Ideals are like numbers. Slides
    19. Topic: What are...subrings and ideals? - Or: Two valid substructures. Slides
    20. Topic: What is...a ring? - Or: Generalizing the integers. Slides
    21. Topic: What is...the Jordan-Hölder theorem? - Or: The elements of group theory. Slides
    22. Topic: What are...matrix groups? - Or: The most important groups?! Slides
    23. Topic: What is...the classification of abelian groups? - Or: Factoring numbers. Slides
    24. Topic: What are...the Sylow theorems? - Or: Canonical substructures? Slides
    25. Topic: What is a...Cayley graph? - Or: Graphs and groups. Slides
    26. Topic: What are...actions, orbits and stabilizers? - Or: How many ways are there to...? Slides
    27. Topic: What is...the symmetric group? - Or: Why strings can shuffle numbers. Slides
    28. Topic: What are...the isomorphism theorems? - Or: Basic rules of algebra generalize. Slides
    29. Topic: What is...a (normal) subgroup? - Or: Why care about the difference? Slides
    30. Topic: What is...a group? - Or: Abstract symmetries. Slides
    31. Topic: What is...algebra? - Or: How to not solve polynomial equations. Slides
  • Playlist What is...linear algebra?
    1. Topic: What is...a projective space? - Or: My lines cross. Slides
    2. Topic: What is...an affine map? - Or: Translations in action. Slides
    3. Topic: What is...an affine space? - Or: I lost my origin. Slides
    4. Topic: What is...the symmetric algebra? - Or: Polynomials in vector spaces. Slides
    5. Topic: What is...the exterior algebra? - Or: Anticommuting polynomials. Slides
    6. Topic: What are...tensor products? - Or: How to multiply vector spaces and matrices. Slides
    7. Topic: What is...a quotient vector space? - Or: Identifying information. Slides
    8. Topic: What is...the dual vector spaces? - Or: Two flipped sides. Slides
    9. Topic: What is...the LU decomposition? - Or: Lower-upper. Slides
    10. Topic: What is...Gaussian elimination? - Or: How to find intersections. Slides
    11. Topic: What is...a system of linear equations? - Or: Intersections matter. Slides
    12. Topic: What is...Sylvester's law of inertia? - Or: Signatures is linear algebra. Slides
    13. Topic: What is...the spectral theorem? - Or: My eigenvalues are real! Slides
    14. Topic: What is...an isometry? - Or: Tessellations of my walls. Slides
    15. Topic: What is...orthogonality? - Or: Flavors of 90 degrees. Slides
    16. Topic: What is...an inner product? - Or: Generalizing angles and lengths. Slides
    17. Topic: What is...a linear subspace? - Or: Hyperplanes and friends. Slides
    18. Topic: What is...the exponential of a matrix? - Or: Nilpotent vanishing. Slides
    19. Topic: What is...the Jordan normal form again? - Or: How to find and compute a gold standard. Slides
    20. Topic: What is...the Jordan normal form? - Or: Why (almost) all matrices are diagonalizable. Slides
    21. Topic: What is...diagonalization? - Or: Finding the right coordinate system. Slides
    22. Topic: What are...traces? - Or: The best? matrix invariant. Slides
    23. Topic: What are...eigenvalues and eigenvectors? - Or: Linear fixed points. Slides
    24. Topic: What is...the characteristic polynomial? - Or: Matrix roots. Slides
    25. Topic: What is...the permanent? - Or: The trivial representation. Slides
    26. Topic: What is...the determinant? - Or: Signed permutations. Slides
    27. Topic: What are...direct sums? - Or: How to add vector spaces and matrices. Slides
    28. Topic: What is...a change of basis? - Or: Moving, rotating and scaling axes. Slides
    29. Topic: What is...a linear map? - Or: Linear algebra done right. Slides
    30. Topic: What is...matrix multiplication? - Or: Why the definition is not random. Slides
    31. Topic: What is...a matrix? - Or: Incarnations of the same beast. Slides
    32. Topic: What is...a basis? - Or: A notion of dimension. Slides
    33. Topic: What is...a vector space? - Or: Geometry à la Descartes. Slides
    34. Topic: What is...linear algebra? - Or: Everything is linear. Slides