Collection of Combinatorics Videos

What is this: The following is a collection of links to videos in Combinatorics and related fields, which I think might be of interest to general audience. The division into areas is very approximate as many lectures span across several areas. If you know other videos worthy of inclusion, especially old ones, please let me know. -- IP

What to do with this: We answer all questions in this blog post (May 2, 2015).

Note: The order of sections is alphabetical, and is reverse historical within in each section. Unfortunately, some videos, especially older ones, have poor quality.

Combinatorics Areas: Additive and Arithmetic Combinatorics, Algebraic Combinatorics and Combinatorial Representation Theory, Algebraic Geometry, Tropical Geometry and Combinatorics, Algebraic Geometry, Tropical Geometry and Combinatorics, Analytic and Asymptotic Combinatorics, Cluster Algebras and Combinatorics, Combinatorial Number Theory, Combinatorial Probability, Combinatorial Statistical Physics, Combinatorics of Words, Computability Theory and Combinatorial Aspects of Logic, Combinatorial aspects of Functional Analysis and Free Probability, Discrete Geometry and Geometric Graph Theory, Enumerative and Bijective Combinatorics, Experimental Combinatorics, Expanders graphs, Extremal and Probabilistic Graph (and Hypergraph) Theory, Geometric Combinatorics and Convex Polyhedra, Graph Theory and Graph Limits, Infinitary Combinatorics, Integer Sequences, Linear Programming and Combinatorial Optimization, Partitions and q-Series, Probabilistic Combinatorics, Symmetric Combinatorial Structures, Theory (CS) and Combinatorial Applications, Tilings and Packings, Topological Combinatorics and Combinatorial Differential Geometry, Universality theorems.

Assorted Lectures: History of Combinatorics, General audience, Distinguished speakers and biographies, Graduate Courses and Extended Lecture Series, ICM in Seoul Combinatorics talks (2014), Lectures by Persi Diaconis, Lectures by Don Knuth.

Research and survey talks

Additive and Arithmetic Combinatorics

• Terence Tao, The Erdős Discrepancy Problem, UCLA Math Colloquium, video by IPAM, Oct 8, 2015.
• Terence Tao, Structure of Approximate Groups, IMA, Oct 1, 2014.
• Vitaly Bergelson, Ramsey Theory at the Junction of Additive and Multiplicative Combinatorics, IMA, Sep 30, 2014.
• Terence Tao, Introduction to Inverse Littlewood-Offord Theory, lectures one, two and three, IMA, Sep 29-30, 2014.
• Terence Tao, Expanding polynomials and an algebraic regularity lemma, IPAM, Mar 28, 2014 (see also here).
• Yufei Zhao, The Green-Tao theorem and a relative Szemerédi theorem, IAS, Mar 3, 2014 (see also here and there).
• Timothy Gowers, Erdős and arithmetic progressions (see also slides), Erdős 100, July 2, 2013.
• Ben Green, The sum-free set constant is ⅓ (see also slides), Erdős 100, July 1, 2013.
• Timothy Gowers, Quasi-random groups, IAS, June 16, 2010.
• Ben Green, Discrete Rigidity Phenomena, MSRI, Nov 3, 2008.
• Endre Szemerédi, On the sumsets of infinite sequences, MSRI, Aug 25, 2008 (handout).
• Izabella Laba, Harmonic Analysis and Additive Combinatorics, lectures one and two, MSRI, Aug 21-22, 2008.
• Vitaly Bergelson, An Introduction to Ideas and Methods of Ergodic Ramsey Theory, lectures one and two, MSRI, Aug 21, 2008.
• Terence Tao, Recent Developments in Arithmetic Combinatorics lecture series (also abstract), UW, Dec 4-6, 2007.
  • Lecture I. Additive Combinatorics and the Primes,
  • Lecture II. Additive Combinatorics and Random Matrices,
  • Lecture III. Sum-product Estimates, Expanders, and Exponential Sums.

Algebraic Combinatorics and Combinatorial Representation Theory

• Rosa Orellana, The Kronecker Coefficients, IPAM, Apr 10, 2015.
• Vic Reiner, Reflection groups and finite general linear groups, lectures one, two, three, and slides, CRM Pisa, Feb 9-13, 2015.
• Nantel Bergeron, Generalizations of Catalan numbers (interactive, static), FI, Nov 22, 2014.
• Greta Panova, Combinatorics and Complexity of Kronecker Coefficients, SITC, Sep 19, 2014 (see also here).
• Bernard Leclerc, From geometry to combinatorics: a memorial lecture for Alain Lascoux, FPSAC Chicago, July 1, 2014.
• Sergey Fomin, Andrei's theorems, NEU, Apr 24, 2013.
• Anne Schilling, A Murnaghan-Nakayama Rule for k-Schur Functions, BIRS, May 25, 2011.
• Alain Lascoux, Gaudin functions of any order, INI Apr 22, 2008.
• Anatoly Vershik, Some Problems of Asymptotic Representation Theory, MSRI, Mar 21, 2008 (large files).
• Mark Haiman, LLT polynomials, MSRI, Mar 20, 2008 (large files).
• Arun Ram, Combinatorics of Lie type, lectures one, two, and three, MSRI, Jan 22-24, 2008.
• Andrei Okounkov, Characters of Symmetric Groups, lectures one, two and three, MSRI, Jan 22-24, 2008.
• Georgia Benkart, Combinatorial Representation Theory - Old and New, MSRI, Jan 17, 2008.
• Christos Athanasiadis, Catalan and Narayana Numbers for Weyl Groups, MSRI, Nov 5, 2008 (large files).
• Joel Kamnitzer, Canonical bases for representations, UT Austin, Jan 25, 2006.
• Vic Reiner, Koszul algebras in combinatorics, MSRI, Mar 2003.
• Ian Macdonald, Constant Term Identities, Orthogonal Polynomials and Affine Hecke Algebras, ICM Berlin, Aug 20, 1998.

Algebraic Geometry, Tropical Geometry and Combinatorics

• Alexander Postnikov, The Combinatorics of the Grassmannian, lectures one, two, three and four, IAS HUJI, Jan 22-27, 2015.
• Thomas Lam, CDM Lecture Series, Harvard, Nov 22, 2014.
  • Totaly positivity, crystals, and Whittaker functions (also slides),
  • Totally nonnegative Grassmannian and the Amplituhedron (also slides).
• Mikhail Kapranov, Algebra of the infrared and secondary polytopes, IHES, June 23, 2014.
• June Huh, three positivity lectures:
  • Positivity of algebraic cycles and convexity of combinatorial geometries, MSRI, Dec 3, 2012,
  • Positivity of Chern classes of Schubert cells and varieties, FPSAC Chicago, July 1, 2014,
  • Rota's conjecture and positivity of algebraic cycles in toric varieties, IAS, Sep 25, 2014,
• Sergey Fomin, Enumeration of plane curves and labeled floor diagrams, MSRI, Oct 15, 2009.
• Federico Ardila, Minicourse: Linearity in the tropics, lectures one and two, MSRI, Aug 22-23, 2009.
• Lauren Williams, The tropical Grassmannian and its positive part, MSRI, Aug 23, 2009.
• Dave Bayer, The Coloring Torus of a Graph, Bay Area Discrete Math Day XII, Apr 15, 2006.

Analytic and Asymptotic Combinatorics

• Nicolas Curien, Planar Stochastic Hyperbolic Triangulations, BIRS, Sep 14, 2014.
• Petter Brändén, Zeros of multivariate polynomials in combinatorics, FPSAC Chicago, July 1, 2014.
• Nikhil Bansal, On the Number of Matroids, MSRWA, Sep 3, 2013
• Mireille Bousquet-Melou, Philippe Flajolet, founder of Analytic Combinatorics, MSRI, Jan 16, 2012.
• Jinho Baik, Random Permutations, lectures one, two, three and four, MSRI, July 6-9, 2009.
• Marc Noy, Graph classes with given 3-connected components: asymptotic counting and critical phenomena, INI Apr 7, 2008.
• Percy Deift, Asymptotics for random permutations, MSRI, Feb 1999.

Cluster Algebras and Combinatorics

• Sergey Fomin, Subtraction-free complexity, ICERM, Aug 28, 2014.
• Philippe Di Francesco, The combinatorics of non-commutative discrete integrable systems, ICERM, Aug 25, 2014.
• Vladimir Retakh, Noncommutative Laurent Phenomenon, NEU, Apr 24, 2013.
• Pavlo Pylyavskyy, Total positivity, loop groups and electrical networks, MSRI, Nov 1, 2012.
• Sergey Fomin, Introduction to cluster algebras, lectures one, two and three, MSRI, Aug 27-28, 2012.
• Lauren Williams, Mini Course: Basics of Cluster Algebras, lectures one and two, MSRI, Aug 22-23, 2012.
• Lauren Williams, Cluster Algebras and Cluster Combinatorics, lectures one, two, three, four and five, MSRI, Aug 1-5, 2011.
• Sergey Fomin, Total positivity and cluster algebras, MSRWA, Oct 15, 2010.
• Alexander Postnikov, Total positivity, matroids, and clusters, MSRI, Mar 18, 2008 (large files).
• Andrei Zelevinsky, Combinatorics of Coxeter elements and cluster algebras of finite type, MSRI, Mar 18, 2008 (large files).

Combinatorial Number Theory

• Marc Chamberland, The 3x+1 Problem: Status and Recent Work, see P1 and P2, Rutgers, Apr 12, 2013.
• Jeffrey Shallit, The complexity of Euclid's GCD algorithm, MSRI, Aug 2000.

Combinatorial Probability

• Santosh Vempala, Cool with a Gaussian: an O^*(n³) volume algorithm, IAS, Oct 13, 2014.
• Lauren Williams, Combinatorics of the asymmetric simple exclusion process, MSRI, Jan 18, 2012.
• Dana Randall, Tutorial: Counting and sampling on lattices, a computer science perspective, MSRI, Jan 13, 2012.
• Mary Cryan, Counting & Sampling Contingency Tables, HI, Apr 22, 2009.
• László Lovász, Volume computation: a status report, MSRI, Feb 3, 2005 (large files).
• James Fill, Perfect simulation of perpetuities using Coupling Into And From The Past, MSRI, Feb 2, 2005 (large files).
• Peter Winkler, Rapid Mixing: Some Old Problems and New Ideas, MSRI, Jan 13, 2005 (large files).
• David Aldous, Real-world Random Networks -- Overview, MSRI, Jan 13, 2005 (large files).
• James Propp, Random Walk and Random Aggregation, Derandomized, MSRWA, Nov 13, 2003.
• Santosh Vempala, How to compute the volume?, MSRI, October 2003.
• Peter Winkler, Mixing among the reals, MSRI, Feb 4, 2000 (large files).
• Igor Pak, Generating Random Group Elements, MSRI, Jan 2000.

Combinatorial Statistical Physics

• Gilles Schaeffer, Random Planar Structures and Statistical Mechanics, INI Apr 22, 2015.
• Greta Panova, Statistical mechanics via asymptotics of symmetric functions, ICERM, Apr 17 2015 (see also an IMA talk here).
• Kari Eloranta, The Shape of Ice, ICERM, Apr 14 2015.
• Andrea Sportiello, The limit shape of the Abelian Sandpile identity, ICERM, Apr 14 2015.
• Xavier Viennot, The birth of new domain: Combinatorial Physics (also slides), IMSc, Chennai, India, Feb 12, 2015.
• Doron Zeilberger, The Amazing 3ⁿ Theorem and its even more Amazing Proof, see P1 and P2, Rutgers, Sep 27, 2012
• Kurt Johansson, Particle and dimer asymptotics in the Aztec diamond, BIRS, Sep 24, 2012.
• Mireille Bousquet-Melou, Exactly solvable classes of self-avoiding walks, MSRI, Jan 13, 2012 (see also here).
• Peter Winkler, Forceless Physics: Models with Hard Constraints, MSRI, Jan 13, 2012.
• Christian Krattenthaler, Combinatorics of Discrete Lattice Models, MSRI, Jan 12, 2012.
• Anthony Guttmann, Tutorial: Statistical and mathematical physics of discrete lattice models, MSRI, Jan 12, 2012.
• Hugo Duminil-Copin, Self-avoiding walks on the honeycomb lattice, MSRWA, June 30, 2010.
• Cyril Banderier, Enumeration and asymptotics of random walks and maps, INI Apr 11, 2008.

Combinatorics of Words

• Igor Pak, Words in linear groups, random walks, automata and P-recursiveness, BIRS, March 9, 2015.
• Jason Bell, Algebraic aspects of automatic sequences, FI, April 23-23, 2013.
  • Lecture 1 (interactive, static).
  • Lecture 2 (interactive, static).
• Kiran Kedlaya, Christol's theorem and its analogue for generalized power series, FI, April 23-23, 2013.
  • Lecture 1 (interactive, static, slides).
  • Lecture 2 (interactive, static, slides).

Computability Theory and Combinatorial Aspects of Logic

• Denis Hirschfeldt, Five and a Half Approaches to Algorithmic Randomness, BIRS, Mar 10, 2015.
• Jeremy Avigad, Computability and uniformity in ergodic theory, BIRS, Mar 10, 2015.
• Terence Tao, A regularity lemma for definable sets over finite fields, and expanding polynomials, MSRI, Feb 6, 2014.
• Lou van den Dries, Model theory and multiplicative combinatorics, lectures one, two and three, MSRI, Feb 4-7, 2014.
• Ehud Hrushovski, Around Approximate Subgroups, MSRI/Berkeley, Feb 3, 2014.

Combinatorial aspects of Functional Analysis and Free Probability

• Alexandru Nica, Combinatorial Aspects of Free Probability Theory, lectures one, two, three, four, IAS HUJI, Jan 19-25, 2015.
• Nik Weaver, Falsifying Kadison-Singer, (interactive, static, info), FI, Sep 10, 2012.

Discrete Geometry and Geometric Graph Theory

• András Gyárfás, Combinatorics of Intervals (also abstract), CEU, March 18, 2015.
• János Pach, On the number of crossings between curves, BIRS, Feb 11, 2015.
• János Pach, Accidental Meetings, IMA, Nov 11, 2014.
• Imre Bárány, Curves in R^d Intersecting Every Hyperplane at Most d+1 Times, IMA, Nov 10, 2014.
• Jozsef Solymosi, On the Sum-Product Problem, IMA, Oct 2, 2014.
• János Pach, My Happy Ending Problem (see also slides), IMA, Sep 10, 2014.
• Konrad Swanepoel, Some results and problems related to the Sylvester-Gallai theorem, IPAM, March 27, 2014.
• Shakhar Smorodinsky, Introduction to combinatorial geometry via hard Erdős problems, lectures one, two and three, IPAM, March 11-12, 2014.
• Nathan Kaplan, Polynomials over Finite Fields and the Finite Field Kakeya Conjecture, IPAM, March 11, 2014.
• Micha Sharir, Algebraic techniques for incidence problems, series of two IPAM lectures, Spring 2014:
  • Consumer report,
  • Consumer demand.
• Endre Szemerédi, On discrete geometry problems, Saint Petersburg, Jan 24, 2014.
• Géza Tóth, The Erdős-Szekeres Theorem for lines (see also here), CEU, Nov 29, 2013
• Noga Alon, Minimal majority sequences, IAS, Oct 15, 2013.
• János Pach, Incidence results on the plane and distinct distances, BIRS, Oct 3, 2013.
• János Pach, Paul Erdős and the beginnings of geometric graph theory, Erdős 100, July 2, 2013.
• Larry Guth, Marston Morse Lectures, IAS, Mar 12-13, 2013.
  • Unexpected Applications of Polynomials in Combinatorics,
  • What is Special About Polynomials? (Perspectives from Coding theory and Differential Geometry),
  • The Codimension Barrier in Incidence Geometry.
  See also his two other lectures on the same subject:
  • The Polynomial Method and Applications From Finite Field Kakeya to Distinct Distances, IAS, Apr 22, 2011,
  • Erdős Distinct Distance Problem in the Plane, IAS, Dec 14, 2010.
• Terence Tao, Sets with few ordinary lines, Princeton, Feb 11, 2013 (see also here and slides).
• Noga Alon, Strong and Weak Epsilon Nets and Their Applications (another version: P1 and P2), IAS, Nov 7, 2011.
• Imre Bárány, Extremal Problems for Convex Lattice Polytopes, IAS, Mar 15, 2010.
• Ron Graham, Euclidean Ramsey Theory, MSRI, Aug 2003.
• János Pach, Geometric Graph Theory, lectures one and two, MSRI, Aug 2003.
• Jeff Lagarias, Density of Sphere Packing (also slides), MSRI, Aug 2003.

Enumerative and Bijective Combinatorics

• Ira Gessel, Counting Permutations with Even Valleys and Odd Peaks (see also slides), IMA, Nov 13, 2014.
• Richard Stanley, Some Catalan Musings (see also slides), IMA, Nov 10, 2014.
• Sylvie Corteel, Dimers on Rail Yard Graphs, FPSAC Chicago, July 2, 2014.
• Doron Zeilberger, The past and future of enumerative combinatorics, see P1 and P2, Rutgers, April 7, 2014.
• Vince Vatter, 321-avoiding permutations, see P1 and P2, Rutgers, Mar 7, 2013.
• Xavier Viennot, Des arbres dans les étoiles, des arbres dans les grains de lumière (in French, slides, 59Mb.), Nancy, May 30, 2013.
• Xavier Viennot, Combinatorial operators and quadratic algebras (see slides: P1 and P2), IMSc, Chennai, India, Mar 1, 2012.
• Christian Krattenthaler, Determinants and Pfaffians in Enumerative Combinatorics (see also slides), BIRS, Feb 1, 2011.
• Richard Stanley, A Survey of Alternating Permutations, PIMS, Jan 14, 2011.
• Richard Ehrenborg, Counting Pattern Avoiding Permutations Via Integral Operators, IAS, Nov 23, 2010 (another version: P1 and P2).
• David Bressoud, Developments in Alternating Sign Matrices, see P1, P2, P3, P4 and P5, Rutgers, Oct 14, 2010.
• Dominique Foata, Tangent and Secant q-Calculus and (t,q)-Calculus, see P1, P2, P3, P4 (see also slides), Jun 2, 2010.
• Doron Zeilberger, Guesseling (large file), University of Auckland, New Zealand, Dec 2008 (see also talk review by P.J. Cameron, search for "deliberately provocative").
• Christian Krattenthaler, Exact enumeration of plane partitions and rhombus tilings, INI Apr 24, 2008.
• Xavier Viennot, Alternative tableaux, permutations and partially asymmetric exclusion process, INI Apr 23, 2008.
• Olivier Bernardi, A bijection for covered maps on orientable surfaces, INI Apr 21, 2008.
• Christian Krattenthaler, Identities for fully packed loop configurations and semistandard tableaux, INI Apr 11, 2008.
• Olivier Bernardi, A bijection between subgraphs and orientations based on the combinatorics of the Tutte polynomial, INI Apr 8, 2008.
• Xavier Viennot, Introduction to the theory of heaps of pieces with applications to statistical mechanics and quantum gravity, INI Apr 7, 2008.
• Richard Stanley, Increasing and decreasing subsequences, ICM Madrid, Aug 24, 2006.
• Xavier Viennot, Combinatoire Algebrique et Enumerative, FPSAC Montreal, June 1992; see:
  • P1: A survey of Polyomino Enumeration,
  • P2: La magie des tableaux de Young.

Experimental Combinatorics

• Sinai Robins, Equality of Dedekind sums: experimental data, and theory, ICERM, July 24, 2014.
• Alin Bostan, Efficient Experimental Mathematics for Lattice Path Combinatorics, ICERM, July 23, 2014.
• Manuel Kauers, On a new algorithm for computing hyperexponential solutions of P-finite differential equations, see P1 and P2, Rutgers, July 18, 2013.
• Bruno Salvy, Automatic Proofs of Identities, IRMACS Centre, Jan 17, 2011 (related slides).
• Doron Zeilberger, 3x+1, Erdős Memorial Lecture , AMS-MAA, Mar 27, 2010.

Expanders graphs

• Dan Spielman, lecture series, IAS, Nov 3-6, 2014:
  • Sparsification of graphs and matrices,
  • The solution of the Kadison-Singer problem,
  • Ramanujan graphs of every degree.
• Ori Parzanchevski, Simplicial complexes as expanders, lectures zero, one and two, IAS, Oct 1, 2013, Jan 28, 2014, and Feb 4, 2014.
• Alex Lubotzky, High Dimensional Expanders and Ramanujan Complexes, IAS, Feb 12, 2013.
• Zeev Dvir, Monotone Expanders -- Constructions and Applications, IAS, April 22, 2011.
• Jean Bourgain, Expansion in Linear Groups and Applications, IAS, Sep 24, 2010 (see also here and there).
• Avi Wigderson, Expander graphs: Applications and combinatorial constructions, lectures one and two, IAS, June 15, 2010.
• Martin Kassabov, Constructions of Expanders Using Group Theory, Nov 3, 2009.

Extremal and Probabilistic Graph (and Hypergraph) Theory

• Mikllós Simonovits, Various types of phase transitions in extremal graph theory, ICERM, Feb 10, 2015.
• Peter Keevash, The Existence of Designs, lectures one, two, three and four, IAS HUJI, Jan 18-23, 2015.
• Alexander Razborov, Flag Algebras: An Interim Report (see also slides), IMA, Sep 11, 2014.
• David Conlon, Ramsey Multiplicity, IMA, Sep 11, 2014.
• Jacob Fox, Extremal Combinatorics, Geometry, and Algebra, IMA, Sep 11, 2014.
• Jeff Kahn, On Erdős-Ko-Rado for Random Hypergraphs, IMA, Sep 10, 2014.
• Jeong Han Kim, A tale of models for random graphs, MIPT, Apr 29, 2014.
• Alan Frieze, Randomly coloring random graphs, ICERM, Mar 21, 2014.
• Endre Szemerédi, On the Absorbing Method, Saint Petersburg, Jan 20, 2014.
• Penny Haxell, Extremal hypergraphs for Ryser's conjecture, BIRS, Oct 1, 2013.
• Vojtěch Ródl, On two Ramsey type problems for K_t+1-free graphs, Erdős 100, July 4, 2013.
• Noga Alon, Paul Erdős and Probabilistic Reasoning (see slides), Erdős 100, July 3, 2013.
• Jacques Verstraete, On a conjecture of Erdős and Simonovits, BIRS, Aug 21, 2012.
• Jacob Fox, Graph regularity and counting lemmas, IAS, June 5, 2012.
• David Conlon, Combinatorial Theorems in Random Sets, IAS, Nov 22, 2010.
• Jacob Fox, The Graph Removal Lemma, IAS, Nov 8, 2010.
• Igor Rivin, Spectral Geometry of Random Graphs, IAS, Oct 20, 2010.
• Michael Krivelevich, Embedding spanning trees in random graphs, MSRWA, Aug 10, 2010.
• Joel Spencer, Finding Needles in Exponential Haystacks, MSRNE, May 12, 2010 (see slides; also here and there).
• Noga Alon, Eliminating Cycles in the Torus, MSRWA, Oct 1, 2009.
• László Lovász, Which graphs are extremal graphs?, MSRWA, Aug 7, 2007 (see also here, May 27, 2013).
• Joel Spencer, The Giant Component, MSRWA, July 13, 2004.
• Noga Alon, Discrete Mathematics: methods and challenges, ICM Beijing, Aug 23, 2002.
• Ehud Friedgut, The Probabalistic Method, MSRI, Spring 2000.
• Donald Knuth, The Birth of the Giant Component, MSRI, Feb 1999.

Geometric Combinatorics and Convex Polyhedra

• Karim Adiprasito, Whitney numbers via measure concentration in representation varieties, IAS, Mar 3, 2015.
• Egon Schulte, Colorful polytopes, associahedra and cyclohedra, BIRS, Feb 13, 2015.
• Gabor Domokos, Story of the Gömböc, FI, Nov 25, 2014.
• Martin Henk, Geometry of Numbers: Convex Bodies and Lattice Points, BMS, Oct 31, 2014.
• Eran Nevo, Around the g-conjecture, FPSAC Chicago, July 1, 2014.
• Gayane Panina, Moduli space of planar polygonal linkage: a combinatorial description, HIM, Nov 6, 2013.
• Steven Gortler, A survey of Global and Universal Rigidity, with new results, BIRS, July 17, 2012.
• Günter Ziegler, On Delaunay Polytopes and on Associahedra, PIMS, July 30, 2010.
• Richard Stanley, Hyperplane Arrangements and Special Relativity, MSRI, Nov 4, 2004 (large files).
• Volkmar Welker, Real Rootedness and Unimodality in Discrete Geometry, MSRI, Nov 4, 2004 (large files).
• Louis Billera, Geometric enumeration from a quasisymmetric point of view, MSRI, Nov 2003.
• Alexander Bobenko, Geometry from combinatorics: Surfaces made from circles, MSRI, Nov 2003.
• Kevin Woods, Generating functions for sets of lattice points, MSRI, Nov 2003.
• Günter Ziegler, 4-Dimensional Polytopes, lectures one and two, MSRI, Aug 2003.
• Gil Kalai, Graphs and Skeleta of Polytopes, lectures one and two, MSRI, Aug 2003.
• Bernd Sturmfels, State Polytopes (see also notes), MSRI, July 30, 2003.
• Branko Grünbaum, Small polyhedral models of the torus, the projective plane and the Klein bottle (see also slides), place and date unknown.

Graph Theory and Graph Limits

• László Lovász, Automorphisms of Graphons, MSRNE, Apr 23, 2015.
• Alexander Razborov, Continuous Combinatorics, Stockholm, Mar 18, 2015.
• Chris Godsil, An overview of the Matching Polynomial, MSRI, March 9, 2015.
• Noga Alon, Graphs, vectors and integers, IAS, Dec 1, 2014.
• Paul Seymour, Colouring graphs with no odd holes, IAS, Sep 22, 2014.
• Noga Alon, Bipartite Decomposition of Graphs (see also slides), IMA, Sep 9, 2014.
• Maria Chudnovsky, Coloring Graphs with Forbidden Induced Subgraphs, IMA, Sep 10, 2014.
• Paul Seymour, Variants of Woodall's conjecture, BIRS, Oct 3, 2013.
• Lex Schrijver, Graph invariants and some algebra, geometry and analysis, IAS, June 5, 2012.
• László Lovász, two lectures on graph limits:
  • Graph limit theory: an overview, IAS, June 4, 2012,
  • The Mathematical Challenge of Large Networks, IAS, Oct 24, 2011.
• Noga Alon, On Graphs and Communication, Technion, May 9, 2012.
• Paul Seymour, Colouring Tournaments, IAS, Dec 13, 2010.
• Noga Alon, Color Coding, Balanced Hashing and Approximate Counting (also abstract), OU, Israel, March 2, 2009.
• Robin Thomas, K_t-minors, BIRS, Oct 2, 2008.
• László Lovász, Simons Lectures, MSRI, Nov 2003.
  
  • Graph homomorphisms, statistical physics and quasirandom graphs,
  • Tillings, geometric representations and discrete analytic functions.

Infinitary Combinatorics

• Péter Komjáth, Finite substructures of uncountable graphs and hypergraphs (see also slides), Erdős 100, July 5, 2013.
• Daniel Mauldin, Steinhaus' problem on simultaneous tilings of the plane (see also slides), Erdős 100, July 2, 2013.

Integer Sequences

• Igor Pak, Counting with Wang tiles (see also slides), IMA, Nov 14, 2014.
• Jeffrey Shallit, 40 Years with Sloane's Integer Sequences, see P1 and P2 (see slides), DIMACS, Oct 10, 2014.
• Neil Sloane, The OEIS: The Major Problems, see P1 and P2, DIMACS, Oct 9, 2014.
• John Conway, On Unsettleable Sequences, see P1 and P2, DIMACS, Oct 9, 2014.
• Neil Sloane, The On-Line Encyclopedia of Integer Sequences: The First Hundred Years, see P1 and P2, Rutgers, Feb 7, 2013.

Linear Programming and Combinatorial Optimization

• Alexander Barvinok, Thrifty Approximations of Convex Bodies by Polytopes, IMA, Feb 26, 2015.
• Alexander Barvinok, Computing Partition Functions in Hard Problems of Combinatorial Enumeration, IMA, Nov 12, 2014.
• Shmuel Onn, MSRI workshop lectures one, two, three, four, five, six and seven, MSRI, Aug 9-13, 2010.
• Matthias Köppe, MSRI workshop lectures one, two, three, four, five, six and seven, MSRI, Aug 9-13, 2010.
• Jesús De Loera, When combinatorial computing meets algebraic computing: Hilbert's Nullstellensatz and Combinatorial Infeasibility (large file, see slides), University of Auckland, New Zealand, Dec 18, 2008.

Partitions and q-Series

• Frank Garvan, Congruences and relations for the Fishburn numbers, ICERM, Jul 23, 2014.
• George Andrews, The Enigmatic Lost Book of Ramanujan (large file, also abstract), NCSU, Sep 20, 2013.
• Frank Garvan, The Dyson Rank of Partitions, see P1, P2 and P3, Rutgers Apr 25, 2013.
• George Andrews, The Meaning of Ramanujan and His Lost Notebook, UIUC, Apr 26, 2011.
• Frank Garvan, The Andrews spt-function and higher-order generalizations, IRMACS Centre, Jan 17, 2011.
• David Bressoud, The Joys of Mathematics with Doron, see P1, P2, P3, P4, and slides, Rutgers, May 28, 2010.
• George Andrews, False Theta Functions, Mock Theta Functions, and Orthogonal Polynomials, see P1, P2, P3, P4 and P5, Rutgers, May 27, 2010.

Probabilistic Combinatorics

• Ron Peled, Probabilistic Existence of Regular Combinatorial Structures, IAS HUJI, Jan 22, 2015.
• Noga Alon, Random Cayley Graphs, IAS, Nov 25, 2013 (see also here).
• Jacob Fox, Stanley-Wilf limits are typically exponential, IAS, Oct 7, 2013 (see also here or there).
• Gil Kalai, Analysis of Boolean Functions: advances and challenges, MSRWA, Nov 25, 2013 (see also here, slides).
• Nati Linial, Local Combinatorics, Or: What To Do With All Those Gigantic Graphs?, SITC, Aug 29, 2013.
• Tomasz Łuczak, Threshold functions: a historical overview and slides, Erdős 100, July 4, 2013.
• Raghu Meka, Combinatorial Discrepancy (3 lectures), DIMACS, June 2013.
• Gil Kalai, Influences, Traces, Tribes, and Perhaps Also Thresholds, IAS, Feb 4, 2013.
• Nati Linial, What are higher-dimensional permutations and how many are they?, BIRS, Aug 23, 2012.
• Asaf Shapira, Ramsey-Theory, Integer Partitions and a New Proof of The Erdős-Szekeres Theorem, BIRS, Aug 21, 2012.
• Noga Alon, Voting Paradoxes and Combinatorics, IAS, Oct 13, 2010.
• Alexander Holroyd, Random Sorting Networks, PIMS, Jan 15, 2010.

Symmetric Combinatorial Structures

• Péter Pálfy, Around the Černý conjecture (also abstract), CEU, Feb 16, 2015.
• László Babai, Finite Groups and Complexity Theory: from Leningrad to Saint Petersburg via Las Vegas, St. Petersburg, Russia, June 16, 2011.
• Cheryl Praeger, Regular permutation groups and Cayley graphs (see slides), PRIMA Congress, July 9, 2009.
• Peter Cameron, Synchronization and permutation groups (large file, see also slides), University of Auckland, New Zealand, Dec 2008.
• Peter Cameron, A Markov chain for certain triple systems, INI, March 25, 2008.

Theory (CS) and Combinatorial Applications

• Shachar Lovett, Information Theory in Combinatorics, lectures one and two, SITC, Jan 13-14, 2015.
• Avi Wigderson, Green Family Lecture Series, IPAM, May 19-21, 2014.
  
  • Randomness and Pseudorandomness,
  • Permanent & Determinant: Non-identical Twins,
  • Matrix Rank - Extensions, Applications and Open Problems.
• Aravind Srinivasan, Progress on algorithmic versions of the Lovász Local Lemma, IAS, Apr 7, 2014.
• Shachar Lovett, Applications of additive combinatorics in theoretical computer science, IPAM, Mar 14, 2014.
• Avi Wigderson, In search of explicit matrices that behave like random ones, IAS, Feb 7, 2014.
• Lance Fortnow, A Personal View of the P versus NP Problem, CMI, Oct 3, 2013.
• Madhu Sudan, The method of multiplicities, St. Petersburg, Russia, June 18, 2011.
• Alexander Shen, Kolmogorov Complexity as a Language, St. Petersburg, Russia, June 15, 2011.
• Manindra Agrawal, The Arithmetic Complexity of Euler Function, St. Petersburg, Russia, June 14, 2011.
• Dima Grigoriev, Complexity lower bounds for algebraic computation trees, St. Petersburg, Russia, June 14, 2011.
• Ryan O'Donnell, The Unique Games Conjecture, IAS, Apr 20, 2011.
• Luca Trevisan, Regularity Lemmas in graph theory, additive combinatorics and TCS, lectures one and two, IAS, June 15, 2010.
• Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis, IAS, Feb 9, 2009.
• Avi Wigderson, Randomness Extractors, MSRI, Nov 4, 2008.

Tilings and Packings

• Jeffrey Lagarias, Packing Space with Regular Tetrahedra, ICERM, Apr 20, 2015.
• Boris Solomyak, Aperiodic tilings, ICERM, Feb 12, 2015.
• Jed Yang, Hard Tiling Problems with Triangles and Rhombi (see also slides), IMA, Nov 12, 2014.
• Rick Kenyon, Discrete analytic functions and integrability, Cornell, June 23, 2014.
• Craig Kaplan, Metamorphoses and deformations of tilings, BMS, June 06, 2014.
• Roger Penrose, Forbidden crystal symmetry in mathematics and architecture and Q&A, The Royal Institution, Jan 16, 2014.
• Peter J. Lu, Decagonal and Quasicrystalline Tilings in Medieval Islamic Architecture, Harvard, 2007.

Topological Combinatorics and Combinatorial Differential Geometry

• Nati Linial, High Dimensional Combinatorics: A Combinatorial Perspective of Simplicial Complexes, IAS HUJI, Jan 18, 2015.
• Isabella Novik, Lower Bound Theorems and a Generalized Lower Bound Conjecture for Balanced Simplicial Complexes, IMA, Nov 13, 2014.
• Matthew Kahle, Topology of Random Flag Complexes, PIMS Oct 5, 2012.
• Matthew Kahle, The neighborhood complex of a random graph, MSRI, Oct 2, 2006 (large files).
• Yuliy Baryshnikov, Topological Variants of Arrow Theorem, MSRI, Sep 8, 2006 (large files).
• Eric Babson The Topology of Maps between Graphs, MSRI, Sep 7, 2006 (large files).
• Günter Ziegler, Kneser and Tverberg: On the power of topological methods in Combinatorics, MSRI, Sep 5, 2006 (large files).
• Michael Falk, The Combinatorics and Topology of Hyperplane Arrangements, MSRI, Aug 23, 2004 (large files).
• Gil Kalai, A topological colorful Helly theorem, MSRWA, Aug 19, 2003.
• Robin Forman, Topics in Combinatorial Differential Geometry, lectures one and two, MSRI, August 2003.
• Anders Björner, Combinatorics and Homology of Graph Properties, MSRI, Oct 15, 1998.

Universality theorems

• Igor Pak, Universality theorems in Algebra and Geometry, Stony Brook, Sep 25, 2014.
• Karim Adiprasito, New Construction for projectively unique polytopes, HIM, Nov 6, 2013.
• Nikolai Mnëv, Positive side of universality theorems, HIM, Nov 5, 2013.
• Bernd Sturmfels, Universality of Nash Equilibria, HIM, Nov 4, 2013.
• Michael Kapovich, Introduction to geometric universality, HIM, Nov 4, 2013.
• Ravi Vakil, Murphy's Law in algebraic geometry: Badly-behaved moduli spaces, MSRI, Jan 27, 2008.

ICM in Seoul Combinatorics talks (Aug 15-20, 2014)

• Maria Chudnovsky, Coloring graphs with forbidden induced subgraphs.
• David Conlon, Combinatorial theorems relative to a random set.
• Ben Green, Approximate algebraic structure.
• Jacob Fox, The graph regularity method: variants, applications, and alternative methods.
• Alan Frieze, Random Structures and Algorithms.
• Nets Katz, The flecnode polynomial: a central object in incidence geometry (see also here).
• Michael Krivelevich, Positional games.
• Marc Noy, Random planar graphs and beyond.
• Grigori Olshaski, The Gelfand-Tsetlin graph and Markov processes.
• János Pach, Geometric intersection patterns and the theory of topological graphs.
• Vojtěch Ródl, Quasi-randomness and the regularity method in hypergraphs.
• Nikhil Srivastava, Ramanujan graphs and the solution of the Kadison-Singer problem.
• Angelika Steger, The determinism of randomness and its use in combinatorics.

Introductory Combinatorics Lectures

History of Combinatorics

• Robin Wilson, lectures at Gresham College:
  • The Mathematics that Counts, Oct 10, 2013.
  • How to grow trees, Feb 1, 2006.
  • Four Colours Suffice?, Oct 21, 2002.
  • Maps, Maidens and Molecules, Oct 17, 2002

Assorted talks aimed at general audience

• Cris Moore, Cryptography and Privacy in a Quantum World (see also slides), C4, Jan 21, 2015.
• Florian Frick, What is ... the ham sandwich theorem?, BMS, Dec 5, 2014.
• Don Zagier, Asymptotics, ICTP, Nov 6, 2014.
• Ron Graham, What is Graham's Number? and How Big is it?; see also Extra footage, Numberphile, July 2014.
• Adam Streck, What is ... a random graph?, BMS, May 9, 2014.
• Jesko Hüttenhain, What is ... (algebraic) complexity theory?, BMS, Feb 6, 2014.
• Stephen Wolfram, Computation and the Future of Mathematics, Oxford, Jan 15, 2014.
• Felix Günther, What is ... the Fabricius-Bjerre theorem?, BMS, June 22, 1012.
• Angus Macintyre, Undecidable and Decidable Problems in Mathematics, Gresham College, May 17, 2011.
• Anne Schilling, Crystal Bases--What is it all about?, MSRI, Jan 16, 2008.
• Timothy Gowers, Multiplying and dividing whole numbers: why it is more difficult than you might think, Gresham College, May 22, 2007.
• Victor Klee, Shapes of the future: Some problems in geometry, Films: 2-dim and 3-dim, MAA, date unknown.

Distinguished speakers lecture series and biographies

• Bruce Reed, How I learned to do mathematics, (interactive, static, info), FI-PIMS, Nov 11, 2014.
• Avi Wigderson, Kurt Gödel and Computer Science, IAS, Nov 16, 2006.
• Jean-Pierre Serre, How to write mathematics badly, Harvard, c. 2006.
• Paul Hoffman, The Man Who Loved Only Numbers, 2000; see also this lecture, and N Is a Number: A Portrait of Paul Erdős, 1993.

Graduate Courses and Extended Lecture Series

• Robert Sedgewick, Analytic Combinatorics, MOOC from Coursera and Princeton (free registration).
• Federico Ardila has a Teaching Page with videos of several introductory combinatorics courses:
  • Matroids,
  • Polytopes,
  • Coxeter groups,
  • Hopf algebras and combinatorics,
  • Combinatorial commutative algebra,
  • Enumerative combinatorics.
• Robert Morris, Extremal and Probabilistic Combinatorics (see also here and notes), IMPA, Jan-Feb 2012.
• Marcel Jackson, Lectures in Computability and Intractability, ICE-EM/AMSI Summer School, 2006.
  Lectures: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 (large files).
• Francis Su, Geometric Combinatorics, MSRI, May 2004.
  Lectures: 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.
• Jesus De Loera, Francisco Santos and Joerg Rambau, Triangulations of Point Sets: Applications, Structures, Algorithms, MSRI, Jul 2003.
  Lectures: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23.

Collection of Lectures by Persi Diaconis (order reversed for clarity)

• From Shuffling Cards to Walking Around the Building, ICM Berlin, 27 Aug, 1998.
• Are there Q-deformations of Hyperplanes that are Useful for Shuffling?, MSRI, Nov 1, 2004 (large files).
• Importance Sampling vs. Markov chain Monte Carlo, MSRI, Jan 31, 2005 (large files).
• From Characterization to Algorithm, MSRI, Sep 7, 2006 (large files).
• Projection Purist: A Review and Extensions, MSRI, Sep 8, 2006 (large files).
• 9/21-Talk on Application of Toplogy, MSRI, Sep 21, 2006.
• Graph homomorphisms and the birthday problem, Oct 3, 2006 (large files).
• Harnessing chance; the case of random packing, MSRI, Jan 27, 2008.
• What the heck is Haar measure?, MSRI, July 6, 2009.
• The four classical groups U(n), O(n), Sp(n), and S_n, MSRI, July 7, 2009.
• Applications, Extensions and Questions, MSRI, July 8, 2009.
• Who Needs Positivity?, UA, 2011.
• An Introduction to Additive Combinatorics Via "Carries", GATech, Aug 28, 2012.
• Poincaré's Probability, IHP, Nov 23, 2012.
• The Search for Randomness, UW, Nov 2013.

Donald Knuth's Christmas Tree and Other Stanford Lectures

• (3/2)-ary Trees, Dec 3, 2014.
• Planar Graphs and Ternary Trees, Dec 12, 2013.
• Trees and chordal graphs, Dec 18, 2012.
• Spanning Trees and Aspects, Dec 8, 2009.
• Sideways Heaps, Dec 3, 2007.
• Cool Graphs, June 6, 2007.
• Trees, Rivers, and RNA, Dec 6, 2006.
• Platologic Computation, Oct 24, 2006.
• Integer Partitions and Set Partitions: A Marvelous Connection, May 6, 2005.
• Sand Piles and Spanning Trees, Dec 13, 2004.
• Hooray for Probability Theory, Oct 29, 2004.
• Finding All Spanning Trees, Dec 16, 2003.
• Chains of Subsets, Dec 3, 2002.
• Totally Acyclic Digraphs (Spiders) and How To Squish Them, Dec 5, 2000.
• The Joy of Asymptotics, May 30, 2000.
• Dancing Links, Feb 22, 2000.
• Trees and Alphabetic Codes, Dec 3, 1998.
• Constructing Bubblesort at Random: One-Dimensional Particle Physics, Oct 27, 1998.
• Lattices of Trees, Part I, Dec 3, 1997.
• The Associative Law, or the Anatomy of Rotations in Binary Trees, Nov 30, 1993.

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Last updated: May 10, 2015