Friedrich Ernst Peter Hirzebruch

Research centers on algebraic geometry , algebraic topology and relations to number theory. He formulated and proved the Riemann-Roch theorem for projective algebraic varieties of arbitrary dimension (Princeton, Institute for Advanced Stud, 1953). In joint papers with M.F. Atiyahm the K-theory was developed and applications given (1959-1970). Later he studied Hilbert modular surfaces in relation to algebraic geometry, modular forms and number theory. His interest in algebraic surfaces continued (ramified covers of the projective plane along line arrangements). The Riemann-Roch theorem and the index theorem of Atiyah-Singer became fundamental for the theory of elliptic genera to which he made some contributions.