Topics in Combinatorics IV
Epiphany 2025
e-mail: pavel dot tumarkin at durham dot ac dot uk Office: MCS3009; Phone: 334-3085 Office hours: Tue 14:30-15:30 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 (many of these are actually exam questions from previous years). 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 14, 16, 18, and 20