# Hyperplane arrangements associated to symplectic quotient singularities

Namikawa associated to any conic symplectic singularity a hyperplane arrangement which is deeply intertwined with its geometry. For example, Bellamy proved that for a symplectic quotient singularity the cohomology of the complement of this arrangement encodes the number of minimal models of the singularity. For the symplectic singularity associated to a complex reflection group we were able to prove that the Namikawa arrangement coincides with the degenericity locus of the number of torus fixed points of the corresponding Calogero-Moser deformation. This has a series of remarkable consequences, especially it proves a conjecture by Bonnafé and Rouquier. Using representation theory and sophisticated computer algebraic methods, we could compute this arrangement explicitly for several exceptional complex reflection groups. The arrangements seem to be of a new kind, and many more are out there. This is joint work with Gwyn Bellamy (Glasgow) and Travis Schedler (London), and with Cédric Bonnafé (Montpellier).

### 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 Travis Scrimshaw.