1 “... methods of algebraic geometry, complex analysis, the theory of harmonic maps, and topology. Making...”

2 “... of research using the methods of partial differential equations as well as differential and algebraic geometry...”

3 “... with the case of complex analytic automorphic forms because of their connection with algebraic geometry, and so...”

4 “... of very recent arithmetic algebraic geometry, including Grothendieck's etale cohomology theory, Deligne...”