Mathematics Colloquia and Seminars

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The Riemann-Roch theorem is a classical result in Algebraic Geometry that calculates the Euler characteristic of sheaf cohomology groups on Riemann surfaces based on the topology of the surface. I will describe sheaf cohomology, divisors on curves and give a proof of the Riemann-Roch theorem, along using the Riemann-Roch theorem to give the set of points on a torus the structure of a group. If time permits, I will state (but not prove) a generalization, the Hirzebruch-Riemann-Roch theorem.