Channel URL

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, newest first:

What are...my favorite theorems?
What is...algebraic geometry?
Magma in a nutshell.
What is...algebraic graph theory?
What is...geometric topology?
What is...representation theory?
What is...category theory?
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

TeX files

The TeX files for the presentations are freely available at: https://github.com/dtubbenhauer/My-TeX-files.git

A list of my videos

Playlist What are...my favorite theorems?

Topic: What is...hyperplane separation? - Cutting data into bits. Slides
Topic: What is...a coin toss run? - Why is this difficult? Slides
Topic: What is...the drunken bird constant? - Coming home, or not...? Slides
Topic: What is...the else function? - Counting else. Slides
Topic: What are...multiplicative compositions? - Additive < multiplicative. Slides
Topic: What is...Golomb–Dickman's constant? - Cycles and primes. Slides
Topic: What is...counting of abelian groups? - Commutative = easy. Slides
Topic: What is...the tree constant? - Trees are difficult. Slides
Topic: What is...tree counting? - n+1 and n-1. Slides
Topic: What is...the Cayley–Bacharach theorem? - Nine and nine! Slides
Topic: What is...Nagata's theorem? - Ill-behaved invariants. Slides
Topic: What are...Dehn invariants? - Cutting polyhedra. Slides
Topic: What is...the Gelfond–Schneider? - Logarithms and transcendence. Slides
Topic: What are...Mahler functions? - Self-similarity and transcendence. Slides
Topic: What is...Hilbert's Satz 90? - Number 90 is it! Slides
Topic: What is...the Yang–Mills mass gap? - One comes after zero. Slides
Topic: What is...the Hodge conjecture? - Topology and algebraic geometry. Slides
Topic: What are...the Navier–Stokes equations? - Fluids are difficult. Slides
Topic: What is...the Birch–Swinnerton-Dyer conjecture? - Counting, of course. Slides
Topic: What is...the 3d Poincaré conjecture? - Its a sphere? Its a sphere! Slides
Topic: What is...the Riemann hypothesis? - Critical strip free (almost). Slides
Topic: What are...crystal graphs? - Low temperature behavior. Slides
Topic: What is...Freudenthal's magic square? - Exceptional! Slides
Topic: What are...octonions? - Or: Division = good, associativity = bad. Slides
Topic: What is...planarity testing? - Or: Finding planar embeddings. Slides
Topic: What are...Borcherds–Kac–Moody algebras? - Or: Still emerging from matrices. Slides
Topic: What are...sporadic groups? - Or: Weird, but interesting. Slides
Topic: What are...Kac–Moody algebras? - Or: Emerging from matrices. Slides
Topic: What is...the complexity of embeddings? - Or: How difficult is drawing? Slides
Topic: What are...Hecke algebras? - Or: Counting, or rather not counting?! Slides
Topic: What is...the Bruhat decomposition? - Or: Lower and upper. Slides
Topic: What is...recurrent versus transient? - Or: Leaving or staying. Slides
Topic: What are...tree rotations? - Or: A surprisingly small bound. Slides
Topic: What are...IBIS groups? - Or: Perfectly broken symmetries. Slides
Topic: What are...Coxeter complexes? - Or: Spheres and points. Slides
Topic: What is...the partition number? - Or: To count or not to count... Slides
Topic: What are...Kronecker coefficients? - Or: Terribly difficult. Slides
Topic: What is...a Hopf algebra? - Or: Why we comultiply. Slides
Topic: What is...Padé approximation? - Or: Better than Taylor. Slides
Topic: What are...the groups of Galois theory? - Or: An ocean of symmetric groups. Slides
Topic: What is...Bass-Serre theory? - Or: Trees and groups. Slides
Topic: What are...computer conjectures? - Or: A computer can write poems, so... Slides
Topic: What are...computer proofs? - Or: Who needs mathematicians? Slides
Topic: What is...homotopy type theory? - Or: HoTT = Ho + TT. Slides
Topic: What is...the prime number theorem? - Or: Let us not count! Slides
Topic: What is...the balanced graph theorem? - Or: Sudden appearance. Slides
Topic: What is...the matrix equivalence theorem? - Or: One is ok. Two is, well... Three is impossible. Slides
Topic: What is...Drozd's theorem? - Or: The Jordan normal form doesn't get better... Slides
Topic: What is...Artin-Wedderburn's theorem? - Or: Matrices, of course. Slides
Topic: What is...convolution? - Or: Area, even without area. Slides
Topic: What is...symbolic integration? - Or: Symbolic integration rules! Slides
Topic: What is...Karatsuba's algorithm? - Or: Faster than expected. Slides
Topic: What are...alpha shapes and complexes? - Or: Topology and its applications. Slides
Topic: What are...Frobenius algebras and 2d TQFTs? - Or: Physics and math walk hand in hand. Slides
Topic: What is...Fagin's theorem? - Or: Almost always true, almost always false. Slides
Topic: What is...the Novikov-Boone-Britton theorem? - Or: Sometimes life is not decidable. Slides
Topic: What are...expander graphs? - Or: Sparse and connected. Slides
Topic: What is...Stone's duality? - Or: Graphs and logic. Slides
Topic: What is...Kasteleyn's theorem? - Or: Difficult, yet easy. Slides
Topic: What is...the commuting matrix theorem? - Or: Around 25%. Slides
Topic: What is...the Garden of Eden theorem? - Or: Ignored by life? Slides
Topic: What is...the Ax-Grothendieck theorem? - Or: Polynomials rule! Slides
Topic: What is...the choice zoo? - Or: No general choice, please! Slides
Topic: What is...a Hadamard matrix? - Or: Orthogonality exists! Or not? Slides
Topic: What are...independence results? - Or: Its true and its not true. Slides
Topic: What are...skein relations? - Or: Life knows somehow... Slides
Topic: What are...Riemann surfaces? - Or: Avoid choices! Slides
Topic: What is...counting of Tait colorings? - Or: Evaluating graphs. Slides
Topic: What is...a Tait coloring? - Or: Towards the four color theorem. Slides
Topic: What is...the Rado graph? - Or: The law of large numbers for graphs. Slides
Topic: What is...the LKB representation? - Or: Braids are linear. Slides
Topic: What is...Dirac's belt trick? - Or: 720 degree is it! Slides
Topic: What is...Fortune's algorithm? - Or: Parabolas and distance. Slides
Topic: What is...the genus of a graph? - Or: Building bridges. Slides
Topic: What is...the infinitude of prime knots? - Or: Euclid’s theorem for knots. Slides
Topic: What are...torus knots? - Or: Wind p times, wind q times. Slides
Topic: What is...Fáry's theorem? - Or: Straight lines everywhere. Slides
Topic: What is...the circle packing theorem? - Or: From circles to graphs and back. Slides
Topic: What is...exotic four space? - Or: Dimension four is weird!? Slides
Topic: What is...homotopy of spheres? - Or: Surprisingly hard!? Slides
Topic: What is...Hamming distance? - Or: Cubes! Slides
Topic: What is...the jeu de taquin? - Or: Teasing permutations. Slides
Topic: What is...coloring of numbers? - Or: From colors to set theory. Slides
Topic: What is...the dimension of a graph? - Or: 1d objects can be high dimensional? Slides
Topic: What is...crossing number additivity? - Or: Adding crossings adds crossings? Slides
Topic: What is...the Erdős–Gabbai theorem? - Or: Realizing graphs. Slides
Topic: What is...$(236c)^{11}$? - Or: That is a polynomial in c! Slides
Topic: What is...Whitney's embedding theorem? - Or: Projective spaces are nasty. Slides
Topic: What is...the square ice constant? - Or: Ice and 1.539601... Slides
Topic: What is...Bondy's theorem? - Or: Forgetting without loss. Slides
Topic: What is...P versus NP? - Or: Building a chair versus recognizing it. Slides
Topic: What is...a pointwise coloring of the plane? - Or: The chromatic number of the plane. Slides
Topic: What is...Hadwiger's conjecture? - Or: Coloring is difficult... Slides
Topic: What is...group growth? - Or: Small, medium-sized and big groups? Slides
Topic: What is...a limit line graph? - Or: Line graphs converge; in some sense... Slides
Topic: What is...card shuffling mathematically? - Or: Random walks. Slides
Topic: What are...zeta functions of languages? - Or: Counting voodoo. Slides
Topic: What is...a demon knot? - Or: Why wireless is great. Slides
Topic: What are...diagram algebras? - Or: Pictures in algebra and algebra in pictures. Slides
Topic: What are...spectra of Cayley graphs? - Or: Eigenvalues and characters. Slides
Topic: What is...Kronecker's theorem? - Or: Darts and polynomials. Slides
Topic: What is...the Robinson-Schensted correspondence? - Or: Boxes and permutations. Slides
Topic: What is...a greedy algorithm? - Or: Greed is good! Well... Slides
Topic: What is...the BEST theorem? - Or: de [B]ruijn, van Aardenne-[E]hrenfest, [S]mith, [T]utte. Slides
Topic: What are...set partitions? - Or: Prototypical lattices!? Slides
Topic: What is...Frucht's theorem? - Or: Graphs and symmetries. Slides
Topic: What are...randomized algorithms? - Or: Randomness rocks! Slides
Topic: What is...the Gauss-Bonnet theorem? - Or: Curvature and Euler. Slides
Topic: What are...prime knots? - Or: The prime numbers of knot theory!? Slides
Topic: What are...operads? - Or: Topological algebra. Slides
Topic: What is...Maschke's theorem? - Or: Blocks out of the blue. Slides
Topic: What is...Kazhdan-Lusztig combinatorics? - Or: It is nonnegative!? Slides
Topic: What is...a Voronoi diagram? - Or: Distance diagrammatically. Slides
Topic: What is...the Tutte polynomial? - Or: Counting using polynomials. Slides
Topic: What is...a Seifert surface? - Or: Soap and knots. Slides
Topic: What is...sphere packing? - Or: Honeycombs in higher dimensions. Slides
Topic: What is...Kolmogorov complexity? - Or: Shakespeare's work is not random. Slides
Topic: What is...the gnu function? - Or: Symmetries are wild. Slides
Topic: What is...a tropical curve? - Or: Straight curves. Slides
Topic: What is...Bézout's theorem? - Or: Counting intersections. Slides
Topic: What is...fuzzy logic? - Or: This video is 90% crap. Slides
Topic: What is...the Gauss-Wantzel theorem? - Or: Why 65537? Slides
Topic: What is...the small-world effect? - Or: Everyone knows everyone!? Slides
Topic: What are...hyperbolic groups? - Or: From groups to Cantor sets. Slides
Topic: What are...the three geometries? - Or: 0, 1 and $\infty$. Slides
Topic: What are...Chaitin's constants? - Or: Computing a glimpse of randomness. Slides
Topic: What is...a coherence theorem? - Or: Don't underestimate associativity. Slides
Topic: What is...Diffie-Hellman key exchange? - Or: How not to transfer the encryption key. Slides
Topic: What are...Ramsey numbers? - Or: Counting made difficult. Slides
Topic: What is...the Gessel-Viennot lemma? - Or: Determinants are graphs?! Slides
Topic: What is...elliptic addition? - Or: Torus games. Slides
Topic: What is...the fifteen theorem? - Or: What is special about 1,2,3,5,6,7,10,14,15? Slides
Topic: What is...roundness? - Or: My circle has corners! Slides
Topic: What is...the Jordan curve theorem? - Or: Come on, that's trivial... Slides
Topic: What is...a Coxeter group? - Or: What is...1,$\infty$,3,5,3,4,4,4,3,3,3,3,...? Slides
Topic: What is...the difference between Eulerian and Hamiltonian graphs? - Or: They are not dual!? Slides
Topic: What is...the curse of dimensionality? - Or: Hyperballs do not exist! Well, kind of... Slides
Topic: What is...Polya's theorem? - Or: Birds get lost. Slides
Topic: What are...Chebyshev polynomials? - Or: Fibonacci with signs? Slides
Topic: What is...reverse mathematics? - Or: Thinking backwards. Slides
Topic: What is...the axiom of choice? - Or: It works even if you don’t believe in it. Slides
Topic: What is...the Mason-Stothers theorem? - Or: The ABC of polynomials. Slides
Topic: What is...the pea and the sun paradox? - Or: One orange equals two oranges. Slides
Topic: What is...the Robertson-Seymour theorem? - Or: Minors are majors. Slides
Topic: What is...the Kuratowski-Wagner theorem? - Or: Forbidden pieces. Slides
Topic: What is...the Jones polynomial? - Or: Resolving crossings. Slides
Topic: What are...Catalan numbers? - Or: In praise of counting. Slides
Topic: What is...the Abel-Ruffini theorem? - Or: Loops and roots. Slides
Topic: What is...the art gallery theorem? - Or: How many cameras suffice? Slides
Topic: What is...the finite Kakeya problem? - Or: A finite filling. Slides
Topic: What is...Pick's theorem? - Or: Surprisingly simple. Slides
Topic: What is...Kneser's conjecture? - Or: Coloring and topology. Slides
Topic: What are...incarnations of the Borsuk-Ulam theorem? - Or: Topology or combinatorics or...? Slides
Topic: What is...the Borromean impossibility theorem? - Or: Borromean rings do not exist! Slides
Topic: What are...p-adic integers? - Or: Climbing infinite trees. Slides
Topic: What are...Steiner systems? - Or: Finite geometry and puzzles. Slides
Topic: What is...Heawood's conjecture? - Or: I need more than four colors. Slides
Topic: What is...the Strassen algorithm? - Or: Divide and conquer. Slides
Topic: What are...Gröbner bases? - Or: Minimal intersections. Slides
Topic: What is...the chaos game? - Or: Deterministic versus random. Slides
Topic: What is...the art of locating roots? - Or: Finding roots without finding them. Slides
Topic: What is...the Schwartz-Zippel lemma? - Or: The art of not solving equations. Slides
Topic: What are...random numbers? - Or: Compressible? Slides
Topic: What is...Matiyasevich's theorem? - Or: I can't decide... Slides
Topic: What is...the Burnside problem? - Or: Obviously not! Ah, well...? Slides
Topic: What is...a cellular automaton? - Or: From simple rules to life. Slides
Topic: What is...the diamond lemma? - Or: Can you win? Slides
Topic: What is...Goodstein's theorem? - Or: Killing hydras. Slides
Topic: What are...Monte Carlo experiments? - Or: The shotgun method. Slides
Topic: What are...Artin braid groups? - Or: Topology via algebra. Slides
Topic: What is...Frobenius' density theorem? - Or: Does it factor? Slides
Topic: What is...an ADE classification? - Or: A strange reoccurring pattern. Slides
Topic: What is...the discrete periodic table? - Or: Finite simple groups. Slides
Topic: What is...the smooth periodic table? - Or: Simple Lie groups. Slides
Topic: What is...the strong law of small numbers? - Or: There are not enough small numbers. Slides
Topic: What is...Arrow's theorem? - Or: Why voting is always flawed (and is still a good idea). Slides
Topic: What are...the seventeen wallpaper groups? - Or: Mathematics, architecture and decorative art. Slides
Topic: What is...the philosophy of generating functions? - Or: How to encode counting problems. Slides
Topic: What is...the Reidemeister theorem? - Or: Knotting stings in 2d. Slides
Topic: What is...Euler's polyhedron formula? - Or: 2000 years of not doing the count. Slides
Topic: What is...the Brouwer fixed point theorem? - Or: Why lines need to cross. Slides
Topic: What is...the Lucas theorem? - Or: Playing with digits. Slides
Topic: What is...the Gershgorin circle theorem? - Or: Circling the eigenvalues. Slides
Topic: What is...the Perron-Frobenius theorem? - Or: The leading terms. Slides

Playlist What is...algebraic geometry?

Topic: What is...the identity theorem? - Or: Complex versus algebraic geometry. Slides
Topic: What are...regular functions? - Or: Analogs of continuous functions. Slides
Topic: What is...the dimension of a variety? - Or: A space in a space in a space... Slides
Topic: What is...the Zariski topology in algebra? - Or: From topology to algebra. Slides
Topic: What is...the Zariski topology? - Or: Varieties are closed, by definition. Slides
Topic: What is...the coordinate ring? - Or: Polynomial functions and varieties. Slides
Topic: What is...Hilbert's Nullstellensatz? - Or: The zero-locus-theorem. Slides
Topic: What are...ideals of sets? - Or: Enter, algebra! Slides
Topic: What are...conic sections? - Or: Light cones and walls. Slides
Topic: What are...algebraic varieties? - Or: Zeros! Slides
Topic: What is...algebraic geometry? - Or: Polynomials, and more. Slides

Playlist Magma in a nutshell, lecture notes: Click

Topic: Magma in a nutshell - part 5.
Topic: Magma in a nutshell - part 4.
Topic: Magma in a nutshell - part 3.
Topic: Magma in a nutshell - part 2.
Topic: Magma in a nutshell - part 1.
Topic: Magma in a nutshell - part 0. Slides

Playlist What is...algebraic graph theory?

Topic: What are...representable matroids 2? - Or: How to rule out matrices. Slides
Topic: What are...representable matroids? - Or: Matrices and matroids. Slides
Topic: What are...matroid embeddings? - Or: This actually only about greedoids... Slides
Topic: What is...a greedy algorithm 2? - Or: Greedy for matroids. Slides
Topic: What is...a greedy algorithm 1? - Or: Greedy in general. Slides
Topic: What is...the lattice of flats? - Or: The properties of inclusion. Slides
Topic: What are...cryptomorphisms? - Or: Many definitions = good! Slides
Topic: What are...transversal matroids? - Or: More examples from graph theory. Slides
Topic: What are...linearly independent sets? - Or: All bases are of the same size. Slides
Topic: What is a...matroid? - Or: Bases, forests, partitions and friends. Slides
Topic: What are...colorings of random graphs? - Or: Concentrated colors. Slides
Topic: What are...cliques in random graphs? - Or: Peaks! Slides
Topic: What is...the diameter of random graphs? - Or: The same diameter!? Slides
Topic: What are...symmetries of random graphs? - Or: There are no symmetries! Slides
Topic: What is...true for almost all graphs? - Or: Many, many edges... Slides
Topic: What are...subgraphs of random graphs? - Or: A lot of edges. Slides
Topic: What are...random graph models? - Or: Different, yet the same. Slides
Topic: What are...random graphs? - Or: Random is maybe not so random... Slides
Topic: What is...the Tutte polynomial counting? - Or: Its counting a lot! Slides
Topic: What is...the complexity of the Tutte polynomial? - Or: Easy or difficult? Slides
Topic: What is...Tutte universality? - Or: Everyone discovers the same polynomial. Slides
Topic: What is...the Tutte polynomial? - Or: More counting! Slides
Topic: What is...chromatic detection? - Or: Determined by colorings. Slides
Topic: What is...the chromatic polynomial? - Or: Polynomials and colors. Slides
Topic: What are...graph polynomials? - Or: Easy problems, not hard problems. Slides
Topic: What is...graph drawing? - Or: The Laplacian draws graphs. Slides
Topic: What are...clustering methods? - Or: Partitioning made easy. Slides
Topic: What is...the Laplace matrix? - Or: Taking the degree into account. Slides
Topic: What is...spectral Hamiltonicity? - Or: The second largest - part 3. Slides
Topic: What is...the edge expansion constant? - Or: The second largest - part 2. Slides
Topic: What are...the second eigenvalue's contributions? - Or: Not quite canonical. Slides
Topic: What are...applications of the spectrum? - Or: The spectrum knows a lot! Slides
Topic: What are...graphs with small spectrum? - Or: ADE is it! Slides
Topic: What are...example of spectra? - Or: Let us compute! Slides
Topic: What is...path counting via eigenvalues? - Or: Paths “=” matrix powers “=” largest eigenvalue. Slides
Topic: What is...path counting? - Or: Paths “=” matrix powers. Slides
Topic: What are...adjacency matrices? - Or: Graphs “=” matrices. Slides
Topic: What is...algebraic graph theory? - Or: It's a matrix! Slides

Playlist What is...geometric topology?

Topic: What is...braid group cryptography? - Or: Applications 2 (topology in cybersecurity). Slides
Topic: What are...knots and DNA? - Or: Applications 1 (topology in biochemistry). Slides
Topic: What is...the unknotting problem? - Or: How to detect the unknot?! Slides
Topic: What is...the h-cobordism theorem in action? - Or: Towards the Poincaré conjecture. Slides
Topic: What is...the h-cobordism theorem? - Or: Nice manifolds between manifolds. Slides
Topic: What is...the Poincaré conjecture? - Or: Spheres will be spheres. Slides
Topic: What is...4d Kirby calculus again? - Or: Knots and four manifolds, part 2. Slides
Topic: What is...4d Kirby calculus? - Or: Knots and four manifolds, part 1. Slides
Topic: What is...a handle decomposition? - Or: Handles and even more handles! Slides
Topic: What are...four manifolds? - Or: Movies and colors! Slides
Topic: What is...a Heegaard diagram? - Or: Handle diagrams. Slides
Topic: What is...a Heegaard splitting? - Or: Attaching handles. Slides
Topic: What are...lens spaces? - Or: The birth of geometric topology!? Slides
Topic: What are...homology spheres? - Or: Spheres, but not really... Slides
Topic: What is...the linking matrix? - Or: Kirby calculus on matrices. Slides
Topic: What is...Kirby calculus? - Or: Knots and three manifolds, part 2. Slides
Topic: What is...Dehn surgery? - Or: Knots and three manifolds. Slides
Topic: What are...three manifolds? - Or: A glimpse of 4d. Slides
Topic: What is...the chromatic number of a surface? - Or: Graphs on surfaces. Slides
Topic: What are...knotted surfaces? - Or: Codimension 2. Slides
Topic: What is...the classification of surfaces? - Or: Punctures, handles, projective planes. Slides
Topic: What are...words for surfaces? - Or: How to “read” surfaces. Slides
Topic: What are...combinatorial surfaces? - Or: Words and friends. Slides
Topic: What are...surfaces? - Or: Spheres and friends. Slides
Topic: What are...homeomorphisms? - Or: Rubber geometry. Slides
Topic: What is...a knot homology? - Or: Vector spaces, not numbers. Slides
Topic: What is...the bracket polynomial? - Or: Jones and co. Slides
Topic: What are...knot groups? - Or: Never forget the complement. Slides
Topic: What is...the knot genus? - Or: Minimal surfaces and knots. Slides
Topic: What is...the Alexander polynomial? - Or: Alexander-Conway skein calculus. Slides
Topic: What is...the knot determinant? - Or: Enter, linear algebra. Slides
Topic: What is...a knot coloring? - Or: A colorful approach. Slides
Topic: What are...knots? - Or: Why knot?! Slides
Topic: What is...geometric topology? - Or: It's a disc! Slides

Playlist What is...representation theory?

Topic: What is...chemical representation theory? - Or: Applications (rep theory in chemistry). Slides
Topic: What is...a local-global principle? - Or: Small determines big. Slides
Topic: What is...a defect? - Or: Measuring complexity. Slides
Topic: What is...a block? - Or: Decomposing a problem. Slides
Topic: What are...Brauer characters? - Or: Ignore the ground field. Slides
Topic: What is...modular representation theory? - Or: Division made hard. Slides
Topic: What is...the Tsetlin library? - Or: Sorting books made easy. Slides
Topic: What is...the Ehrenfest model? - Or: Rep theory and diffusion. Slides
Topic: What are...the simples of the transformation monoid? - Or: Through strands, again. Slides
Topic: What are...the simples of the Brauer monoid? - Or: Through strands. Slides
Topic: What is...the Brauer monoid? - Or: 1d cobordisms! Slides
Topic: What is...the CMP theorem? - Or: Clifford-Munn-Ponizovskiĭ theorem a.k.a. H-reduction. Slides
Topic: What are...Green cells? - Or: Measuring information loss. Slides
Topic: What is...representation theory of monoids? - Or: What to expect. Slides
Topic: What is...the Young lattice? - Or: Representations of symmetric groups, part 4. Slides
Topic: What is...Frobenius' character formula? - Or: Representations of symmetric groups, part 3. Slides
Topic: What are...Specht modules? - Or: Representations of symmetric groups, part 2. Slides
Topic: What are...Young diagrams? - Or: Representations of symmetric groups, part 1. Slides
Topic: What is...Frobenius reciprocity? - Or: Back-and-forth. Slides
Topic: What are...induction and restriction? - Or: How to find lost information! Kind of... Slides
Topic: What is...Burnside's theorem? - Or: Groups and representations. Slides
Topic: What is...Lagrange's theorem for representations? - Or: Divisibility. Slides
Topic: What is...finite Fourier analysis? - Or: Fourier and finite groups. Slides
Topic: What is...the dual group? - Or: Groups of characters. Slides
Topic: What is...the regular representation? - Or: Action on itself. Slides
Topic: What are...Schur's orthogonality relations? - Or: An orthonormal basis. Slides
Topic: What are...examples of character tables? - Or: The ATLAS of finite groups and co. Slides
Topic: What is...a character table? - Or: The gist of the matter!? Slides
Topic: What are...characters? - Or: Polynomials! Slides
Topic: What is...Schur's lemma? - Or: Matrices rarely commute. Slides
Topic: What is...semisimplicity? - Or: The finite group miracle. Slides
Topic: What is...the Jordan-Hölder theorem? - Or: Like prime numbers. Slides
Topic: What are...indecomposable representations? - Or: The elements! Well, kind of... Slides
Topic: What is...a simple representation? - Or: The elements! Slides
Topic: What are...intertwiners? - Or: Maps between representations. Slides
Topic: What are...modules? - Or: Linear symmetries. Slides
Topic: What are...representations? - Or: Matrices are cool! Slides
Topic: What is...representation theory? - Or: Lets make life linear! Slides

Playlist What is...category theory?

Topic: What are...props? - Or: Applications 2 (category theory in signal processing). Slides
Topic: What are...TQFTs? - Or: Applications 1 (category theory in mathematics). Slides
Topic: What are...2-categories? - Or: Categories in categories. Slides
Topic: What are...braided categories? - Or: Braids and categories. Slides
Topic: What is...duality in categories? - Or: Rigid and pivotal categories. Slides
Topic: What are...string diagrams, take 2? - Or: Two-dimensional algebra. Slides
Topic: What is...strictification? - Or: MacLane's coherence theorem. Slides
Topic: What are...monoidal categories? - Or: Monoids categorified. Slides
Topic: What are...Kan extensions? - Or: Recover information; kind of... Slides
Topic: What is...Beck's monadicity theorem? - Or: Categories via actions. Slides
Topic: What are...algebras? - Or: Actions in action. Slides
Topic: What are...monads? - Or: The natural numbers as functors. Slides
Topic: What are...adjoint functors diagrammatically? - Or: Zigzag! Slides
Topic: What are...string diagrams? - Or: Diagrammatic algebra. Slides
Topic: What is...the adjoint functor theorem? - Or: Identities are free! Slides
Topic: What are...examples of adjoint functors? - Or: Adjoints occur almost everywhere. Slides
Topic: What are...adjoint functors? - Or: Life is not invertible. Slides
Topic: What are...continuous functors? - Or: Functors not functions. Slides
Topic: What is...a complete category? - Or: Real numbers!? Slides
Topic: What are...limits? - Or: Universal diagrams. Slides
Topic: What are...universal properties? - Or: Abstract nonsense in perfection. Slides
Topic: What are...(co)equalizers? - Or: Why kernels? Slides
Topic: What are...pushouts and pullbacks? - Or: Faces “equal” relations. Slides
Topic: What are...products and coproducts? - Or: Vector spaces rock! Slides
Topic: What are...initial and terminal objects? - Or: Another reason why zero is great! Slides
Topic: What is...a concrete category? - Or: Set-based is cool, well sometimes ;-) Slides
Topic: What is...the Yoneda lemma? - Or: Shoot on sight. Slides
Topic: What is...a subcategory? - Or: The symmetric groups and cobordisms. Slides
Topic: What is...the skeleton? - The bare minimum. Slides
Topic: What is...equivalence? - Or: Equal means...? Slides
Topic: What are...natural transformations? - Maps between functors. Slides
Topic: What are...properties of functors? - Or: Preserving diagrams. Slides
Topic: What are...functors? - Maps between categories. Slides
Topic: What is...monic-epic-iso? - Or: Not quite injective-surjective-bijective. Slides
Topic: What is...the duality principle? - Flipping arrows. Slides
Topic: What are...(commuting) diagrams? - Or: Graphs and paths. Slides
Topic: What is...a category? - Arrows in action. Slides
Topic: What is...category theory? - Or: Organizing ideas. Slides

Playlist What is...algebraic topology?; for the lecture website see Click

Topic: What is...persistent homology? - Or: Applications 2 (topology in data analysis). Slides
Topic: What are...some applications of topology? - Or: Applications 1 (topology in mathematics). Slides
Topic: What is...the Hurewicz theorem? - Or: Homotopy and homology. Slides
Topic: What are...Eilenberg-MacLane spaces? - Or: They are not spheres. Slides
Topic: What is...cellular approximation of spaces? - Or: My polynomials have cells. Slides
Topic: What is...cellular approximation? - Or: I miss my space-filling curves... Slides
Topic: What is...Whitehead's theorem? - Or: A perfect invariant!? Slides
Topic: What are...homotopy groups? - Or: Spheres in spaces. Slides
Topic: What are...examples of (co)homology groups? - Or: Another of my favorite lists. Slides
Topic: What is...Alexander duality? - Or: Horned spheres!? Slides
Topic: What is...Poincaré duality? - Or: My face is 0-dimensional. Slides
Topic: What is...orientability? - Or: A homological definition. Slides
Topic: What is...the Künneth formula? - Or: Multiplication vs. tensor product. Slides
Topic: What is...the cohomology ring? - Or: Polynomials, of course. Slides
Topic: What is...the cohomology ring intuitively? - Or: Counting intersections. Slides
Topic: What is...the universal coefficient theorem? - Or: Working integrally rocks. Slides
Topic: What is...the Mayer-Vietoris sequence? - Or: More than the sum of its parts!? Slides
Topic: What is...a (co)homology theory? - Or: Shut up and calculate. Slides
Topic: What is...relative homology? - Or: Calculations modulo subspaces. Slides
Topic: What is...cohomology? - Or: Reversing arrows. Slides
Topic: What is...homology categorifying? - Or: Modules, polynomials and numbers. Slides
Topic: What is...cellular homology? - Or: Winding around. Slides
Topic: What are...simplicial and singular homology? - Or: Cycles modulo boundaries. Slides
Topic: What are...simplicial complexes? - Or: Triangles everywhere. Slides
Topic: What is...homology intuitively? - Or: What is a hole? Slides
Topic: What are...examples of fundamental groups? - Or: One of my favorite lists. Slides
Topic: What is...a Cayley complex? - Or: Groups geometrically. Slides
Topic: What are...covering space action? - Or: Deck transformations and friends. Slides
Topic: What is...a covering space? - Or: A topological Galois correspondence. Slides
Topic: What is...the Seifert-Van Kampen theorem? - Or: Cut and compute. Slides
Topic: What is...the fundamental group? - Or: How not to hang pictures on walls. Slides
Topic: What are...operations on cell complexes? - Or: Cell by cell. Slides
Topic: What are...cell complexes? - Or: Constructed from discs. Slides
Topic: What is...homotopy? - Or: The same shape!? Slides
Topic: What is...algebraic topology? - Or: Translating from topology to algebra. Slides

Playlist What is...algebra?

Topic: What are...solvable polynomials? - Or: Field and Galois theory, application 3. Slides
Topic: What is...the Kronecker–Weber theorem? - Or: Field and Galois theory, application 2. Slides
Topic: What are...the limits of straightedge and compass? - Or: Field and Galois theory, application 1. Slides
Topic: What are...the Galois groups of finite fields? - Or: Finite fields are easy. Slides
Topic: What is...the fundamental theorem of Galois theory? - Or: From roots to groups and back. Slides
Topic: What are...Galois extensions? - Or: Shuffling roots. Slides
Topic: What are...group actions on fields? - Or: The beginning of Galois theory. Slides
Topic: What are...normal and separable extensions? - Or: Linear factors matter. Slides
Topic: What are...minimal polynomials? - Or: Minimal relations. Slides
Topic: What are...field extensions? - Or: Adjoining roots. Slides
Topic: What are...(finite) fields? - Or: Fields are relatively rare. Slides
Topic: What are...irreducible polynomials? - Or: Analogs of primes. Slides
Topic: What is...a unique factorization domain? - Or: Primes! Slides
Topic: What is...an Euclidean domain? - Or: Generalizing division with remainder. Slides
Topic: What is...the Chinese remainder theorem? - Or: Arranging rectangles. Slides
Topic: What is...Hilbert's basis theorem? - Or: Algebra meets geometry (once again). Slides
Topic: What is...localization? - Or: Why fractions matter. Slides
Topic: What is...the calculus of ideals? - Or: Ideals are like numbers. Slides
Topic: What are...subrings and ideals? - Or: Two valid substructures. Slides
Topic: What is...a ring? - Or: Generalizing the integers. Slides
Topic: What is...the Jordan-Hölder theorem? - Or: The elements of group theory. Slides
Topic: What are...matrix groups? - Or: The most important groups?! Slides
Topic: What is...the classification of abelian groups? - Or: Factoring numbers. Slides
Topic: What are...the Sylow theorems? - Or: Canonical substructures? Slides
Topic: What is a...Cayley graph? - Or: Graphs and groups. Slides
Topic: What are...actions, orbits and stabilizers? - Or: How many ways are there to...? Slides
Topic: What is...the symmetric group? - Or: Why strings can shuffle numbers. Slides
Topic: What are...the isomorphism theorems? - Or: Basic rules of algebra generalize. Slides
Topic: What is...a (normal) subgroup? - Or: Why care about the difference? Slides
Topic: What is...a group? - Or: Abstract symmetries. Slides
Topic: What is...algebra? - Or: How to not solve polynomial equations. Slides

Playlist What is...linear algebra?

Topic: What is...a projective space? - Or: My lines cross. Slides
Topic: What is...an affine map? - Or: Translations in action. Slides
Topic: What is...an affine space? - Or: I lost my origin. Slides
Topic: What is...the symmetric algebra? - Or: Polynomials in vector spaces. Slides
Topic: What is...the exterior algebra? - Or: Anticommuting polynomials. Slides
Topic: What are...tensor products? - Or: How to multiply vector spaces and matrices. Slides
Topic: What is...a quotient vector space? - Or: Identifying information. Slides
Topic: What is...the dual vector spaces? - Or: Two flipped sides. Slides
Topic: What is...the LU decomposition? - Or: Lower-upper. Slides
Topic: What is...Gaussian elimination? - Or: How to find intersections. Slides
Topic: What is...a system of linear equations? - Or: Intersections matter. Slides
Topic: What is...Sylvester's law of inertia? - Or: Signatures is linear algebra. Slides
Topic: What is...the spectral theorem? - Or: My eigenvalues are real! Slides
Topic: What is...an isometry? - Or: Tessellations of my walls. Slides
Topic: What is...orthogonality? - Or: Flavors of 90 degrees. Slides
Topic: What is...an inner product? - Or: Generalizing angles and lengths. Slides
Topic: What is...a linear subspace? - Or: Hyperplanes and friends. Slides
Topic: What is...the exponential of a matrix? - Or: Nilpotent vanishing. Slides
Topic: What is...the Jordan normal form again? - Or: How to find and compute a gold standard. Slides
Topic: What is...the Jordan normal form? - Or: Why (almost) all matrices are diagonalizable. Slides
Topic: What is...diagonalization? - Or: Finding the right coordinate system. Slides
Topic: What are...traces? - Or: The best? matrix invariant. Slides
Topic: What are...eigenvalues and eigenvectors? - Or: Linear fixed points. Slides
Topic: What is...the characteristic polynomial? - Or: Matrix roots. Slides
Topic: What is...the permanent? - Or: The trivial representation. Slides
Topic: What is...the determinant? - Or: Signed permutations. Slides
Topic: What are...direct sums? - Or: How to add vector spaces and matrices. Slides
Topic: What is...a change of basis? - Or: Moving, rotating and scaling axes. Slides
Topic: What is...a linear map? - Or: Linear algebra done right. Slides
Topic: What is...matrix multiplication? - Or: Why the definition is not random. Slides
Topic: What is...a matrix? - Or: Incarnations of the same beast. Slides
Topic: What is...a basis? - Or: A notion of dimension. Slides
Topic: What is...a vector space? - Or: Geometry à la Descartes. Slides
Topic: What is...linear algebra? - Or: Everything is linear. Slides