11/30/2011
Gisbert Wuestholz
IAS
Periods of integrals
An old problem of Leibniz asks about the possibility of squaring ovals. The problem goes back to a dispute with Newton about the correctness of Lemma XXVIII in the Principia. In the talk we shall give first a historical account of the problem and then explain how the Analytic Subgroup Theorem is applied to give a solution of the problem adapted to modern times. We further discuss a very far going conjecture of Kontsevich on periods of rational integrals and relate it to the Leibniz problem.