Topics in Combinatorics IV
Epiphany 2024
e-mail: pavel dot tumarkin at durham dot ac dot uk Office: MCS3009; Phone: 334-3085 Office hours: Mon 14:15-15:00 and by appointment |
Textbooks: |
Preliminary course content (subject to change): Root systems, Dynkin diagrams, the Cartan-Killing classification; generalized Cartan matrices, affine Dynkin diagrams and Weyl groups; reflection groups and Coxeter groups, word problem in Coxeter groups, the Bruhat order; Coxeter elements, polynomial invariants, exponents; Coxeter-Catalan combinatorics, the root poset, the Catalan arrangement, generalised associahedra.
Schedule:
Handouts: (lecture notes, intended to be more or less up to date)
Problems classes:
How an exam could look like: A compilation of homework problems which could be considered as an example of an exam paper. Solutions can be found in the HW solutions sheets.
Homeworks: There will be weekly homework assignments. Selected exercises are to be handed in on weeks 13, 15, 17, and 19