This course will mainly focus on various counting techniques
and problems arising in the context of hyperplane
arrangements. We shall also discuss order theoretic
structures, Mobius inversion, incidence algebras and the Euler
characteristic. Throughout the course Coxeter arrangements
(that arise due to actions of finite reflection groups) and
their deformations will serve as runnning examples.
By the end of the first month everybody is expected to choose
their project topic.
Line arrangements and some classical problems, posets and
Mobius inversion, hyperplane arrangements,
deletion-restriction, Zaslavsky's theorem, graphical
arrangements, matroids, the finite field method, ESA, interval
order, Shi and Catalan arrangements, free arrangements.