## University of Sydney Algebra Seminar

# 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.