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Christian Schnell studies Hodge theory and the geometry and topology of complex algebraic varieties. His Stony Brook research page emphasizes applications of mixed Hodge modules to algebraic geometry.^[ref]

His lecture on the Appell–Humbert theorem describes holomorphic line bundles on a complex torus using a Hermitian form and compatible lattice data. Tensor product becomes addition of the forms and multiplication of the accompanying characters. The classification turns an abstract Picard group into explicit data that also help decide when a torus is projective.^[ref]