# Alan Stapledon (University of Sydney)

## Friday 23rd August, 12:05-12:55pm, Carslaw 373

### Representations on the cohomology of hypersurfaces and mirror symmetry

String theory predicts that Calabi-Yau spaces occur in 'mirror' pairs $$(X,Y)$$. When $$X$$ and $$Y$$ are smooth this means that the Hodge diamond of $$X$$ is the mirror image of the Hodge diamond of $$Y$$. We present a new construction that produces infinitely many new 'mirror' pairs of Calabi-Yau orbifolds, and give an explicit description of the corresponding Hodge diamonds. The key is a more general representation theoretic result. Namely, we give an explicit description of the representation of a finite group acting on the cohomology of a hypersurface of a projective toric variety.