A L G E B R A I C    C O M B I N A T O R I C S,   S p r i n g   2 0 1 1

Lectures: Monday, Wednesday and Friday, 12pm-1pm, in Science Center 310.

Lecturer: Paul Bourgade, office hours Wednesday 2-3pm, you also can email me (bourgade@math.harvard.edu) to set up an appointment or just drop by (Science Center 341).

Course description: the first part of the course concerns methods in enumerative combinatorics, such as generating functions, partially ordered sets and enumeration under group actions. Statistics of permutation groups will be a recurrent application of these general methods. The second part will be more properly about algebraic combinatorics, considering the links between representation theory, symmetric functions and Young tableaux. Important applications will be about random matrices from compact groups and, once again, permutation groups, by considering the statistics of longest increasing subsequences.

Prerequisites: notions on finite groups and linear algebra, no prior knowledge about combinatorics is required.

Textbooks: references often followed in this course will be Enumerative Combinatorics, by Stanley, volumes 1 and 2, and Representation Theory: A First Course, by Fulton and Harris.

Grading: problem sets (50%), midterm (15%) and a final project (35%).

A tentative schedule for this course is:

Problem sets.