## Geometry Seminar - Abstracts

### Talk

10 February 2016, 16:00 - 17:00, in HG00.310

**Gert Heckmann**
(Radboud Universiteit)

*Hyperbolic Coxeter groups and quartic curves*

### Abstract

The Weyl group of type E_{7} has a presentation as factor group of
the Coxeter group on the tetrahedral diagram T_{10} (by definition the
simply laced Coxeter diagram with for its 10=(4+6) nodes the 4 vertices
and the 6 midpoints of the edges of a tetrahedron and as simple bonds the
12 half edges) modulo deflation of the free octagons. We shall explain
this presentation in geometric terms (through the moduli space of maximal
real smooth quartic curves). This is joint work with Sander Rieken, and
generalizes a previously obtained similar presentation for the Weyl group
of type E_{6} in connection with maximal real (that is 27 real lines) smooth
cubic surfaces.

We shall give a pedestrian review of Coxeter group theory and
subsequently explain the desired presentation using results of the thesis
by Sander Rieken (also to be explained a little).