Mathematical Sciences: Generalized Theta Functions, Hypergeometric and Conformal Field Theory

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9504884 Silvotti The proposed research lies in the interface of algebraic geometry and quantum field theory. The investigator proposes to give a complete and direct topological description of the models of conformal field theory corresponding to generalized theta functions in terms of cohomology spaces. The cohomology to be used is the cohomology of multivalued holomorphic differential forms on the affine complement of hypersurfaces in complex algebraic varieties. The proposed research brings together very classical problems in function theory with the latest development in mathematical physics (quantum field theory). The underlying physical theory was originally introduced to describe the critical behavior of a class of statistical systems on planar lattices.