- I. Hopf monoids in species
- Aug 23. Species and enumeration. Cauchy and substitution products.
- Aug 25. Monoids in species. Free monoids. Comonoids and bimonoids.
- Aug 30. Monoidal categories. Monoids and comonoids. Convolution.
- Sep 1. Braided monoidal categories. Bimonoids and Hopf monoids. Antipode.
- Sep 6. Linearization. Hopf monoids in vector species. Antipode of L.
- Sep 8. q-braiding. q-deformation of L. Connected bimonoids.
- Sep 13. Antipode formulas. Examples.
- Sep 15. Group of characters. Reciprocal of a power series.
- Sep 20. Substitution of power series and Lagrange inversion.
- Sep 22. Polynomial invariants. Chromatic polynomial and order polynomial.
- Sep 27. Reciprocity. Antipode of E and L and the Coxeter complex.
- Sep 29. Coxeter complex and Tits product. Higher Hopf monoid axioms. Antipode as Euler characteristic of a pair.
- Oct 4. Normal fans of polytopes. Standard permutahedron and generalized permutahedra.
- Oct 6. Hopf monoid of generalized permutahedra and related examples.
- II. Hyperplane arrangements
- Oct 11. No class (Fall break)
- Oct 13. Real hyperplane arrangements. The braid arrangement. Faces and flats. Tits monoid and sign sequences.
- Oct 18. Tits monoid and partial order on faces. Species and Hopf monoids relative to a hyperplane arrangement.
- Oct 20. Hopf monoids as modules over the Janus algebra.
- Oct 25. Review of Möbius functions. Weisner's formula. Algebra of a lattice. Semimodular lattices.
- Oct 27. Zaslavsky's formula for chambers and faces. Restriction and contraction. Characters.
- Nov 1. Primitive elements. Lie and Zie elements. Dimensions of Lie and Zie.
- Nov 3. Generic hyperplanes. Dynkin idempotent. Zaslavsky for bounded chambers. Dynkin basis of Lie.
- Nov 8. Braid arrangement, classical Dynkin. Global operads.
- Nov 10. Joyal-Klyachko-Stanley.
- Nov 15. Lunes. Lune category.
- III. More on monoidal categories
- Nov 17. Schur functors, Schur-Weyl duality. Fock functors.
- Nov 22. Monoidal functors.
- Nov 24. No class (Thanksgiving).
- Nov 29. Simplicial objects and chain complex functor.
- Dec 1. 2-monoidal categories. Eckmann-Hilton argument.
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