Generalized Kac-Moody algebras, automorphic forms and hyperbolic reflection groups

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The project is divided into 3 parts:1. Calculation of twisted denominator identities of the fake monster superalgebra and their application in 3 cases:a) Construction of new examples of generalized Kac-Moody superalgebras and explicit description of their simple roots and root multiplicities.b) Construction of new automorphic forms and description of their product expansions.c) Investigation whether some of the twisted denominator functions define functions on moduli spaces of varieties.2. Prove that the physical states of a chiral N=2 superstring moving on a torus form a generalized Kac-Moody superalgebra of rank 2.3. Describe closed and heterotic strings by higher dimensional vertex algebras and study the symmetries arising here.