Final Report Summary - GELANDERINDGEOMRGD (Independence of Group Elements and Geometric Rigidity)
Among the achievements of this project are: A fixed point theorem in L1 space, which gave the optimal solution to the long standing Derivation Problem. A precise formula for the asymptotic number of arithmetic Riemann surfaces. Proving that most hyperbolic manifolds are non-arithmetic. Establishing various conjectures concerning the asymptotic of L2-invariants of lattices in Lie groups. Developing the theory of Invariant Random Subgroups in Lie groups. A proof that a lattice in Lie group can by generated by a set of size not grater than the co-volume. A proof of the generalised Chern conjecture for manifolds which are locally a product of plans. Producing the first example of a locally compact simple group without lattices.