Milnor fibres, noncrossing partitions and noncrossing algebras

Speaker: Yang Zhang
Affiliation: University of Queensland

Abstract

In singularity theory the Milnor fibre describes the topology of the space near a singular point of a hypersurface. In this talk, I will introduce a combinatorial approach to computing the (co)homology of the Milnor fibre of the hyperplane arrangement associated to a finite Coxeter group.  This is based on a simplicial complex of the Milnor fibre, whose construction involves the noncrossing partition lattice of a finite Coxeter group. For any noncrossing partition lattice, I will define a finite dimensional graded algebra, called noncrossing algebra. This has similarities with the Orlik-Solomon algebra in the theory of hyperplane arrangement. Then I will show you how to use this algebra to compute cohomology groups of the Milnor fibres, hyperplane complements, and Artin groups.