Bob Howlett University of Sydney Coxeter groups and invariant cones Friday 26th September, 12:05-12:55pm, Carslaw 373. Every Coxeter group W has at least one faithful representation as a group generated by reflections acting on a real vector space V. If W is finite then the hyperplanes corresponding to the reflections in W cut V into regions (known as chambers) that are in bijective correspondence with the elements of W. If W is infinite the union of the chambers corresponding to elements of W is not the whole of V but a certain convex subset, known as the Tits cone. In this talk I will describe what I know about the Tits cone, in the hope that someone in the audience will be able to help me understand it more fully.