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.

About Pure mathematics seminars

We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.

Seminars are usually held on Tuesdays from 3pm to 3.50pm.

Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.

Information for speakers

Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.

Contact us

To volunteer to talk or to suggest a speaker, email Ole Warnaar or Ramiro Lafuente.

Venue

Priestley Building (67)
Room: 442