MS Seminar (Mathematics - String Theory)

Speaker: Alan Stapledon (U of Sydney)
Title: Representations on the cohomology of hypersurfaces and mirror symmetry
Date: Wed, Dec 18, 2013, 13:15 - 14:45
Place: Seminar Room B
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Abstract: 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.