Modular Algebraic Independence.
Professor M. Waldschmidt will be visiting CMI for the period December 3–23 2009 and January 11–29, 2010. He shall be giving a course of lectures on transcendence. The central goal of his lectures is to introduce the basic tools for the remarkable works of Nesterenko. His works can be regarded as one of the first "truly modular" theorems on algebraic independence, viz.: Let q be a non-zero complex (or p-adic) number of absolute value <1; then, at least three of the numbers q, P(q), Q(q), R(q) are algebraically independent. Here P, Q, R are Ramanujan's notation for the Eisenstein series E2, E4 and E6 respectively. A striking consequence is an answer to a folklore conjecture that π and eπ are algebraically independent.
Lecture schedule for December