## University of Sydney Algebra Seminar

# Alan Stapledon (University of British Columbia)

## Friday 21st May, 12.05-12.55pm, Carslaw 175

### Representations of hypersurfaces and equivariant Ehrhart theory

We give an explicit description of the representations of a finite group acting on the cohomology of a `general' invariant hypersurface in a toric variety. We show how this naturally leads to an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes, and prove several equivariant versions of classical results. As an example, we show how the representations of a Weyl group acting on the cohomology of the toric variety associated to a root system naturally appear.