heart geometry modern developments link representation theory invariant theory areas diverse holonomy differential operators theory several complex variables automorphic forms number theory automorphic forms generalization modular forms general analytic functions perhaps several complex variables similar transformation properties generalization involves replacing modular group psl sub sub '''r''' chosen congruence subgroup semisimple lie group ''g'' discrete subgroup '' '' modular forms viewed differential forms quotient upper half space '''''h''''' psl sub sub '''r'''
Formal science Mathematics Pure mathematics Algebra Representation theory