Conferenza di Enrico Bombieri a Roma (8 giugno 2010): Zeta and L-functions Yesterday and Tomorrow

Dipartimento di Matematica

Università di Roma "Tor Vergata": COLLOQUIA DI DIPARTIMENTO 2010

Enrico Bombieri
Institute for Advanced Study at Princeton, New Jersey

Zeta and L-functions Yesterday and Tomorrow

Martedì 8 giugno 2010 ore 14.00
Aula G2C della Facoltà di Scienze M.F.N.Università di Roma "Tor Vergata"

Abstract: This lecture is a panorama of zeta and L-functions. The Riemann, Dirichlet, Dedekind zeta functions, and Hecke L-functions are introduced. This is followed by the second way of introducing L-functions, via Galois extensions and Artin L-functions. This is followed by the third way of defining L-functions, via automorphic functions. The interrelation of these three classes leads to the modern theory with basic conjectures and the Langlands program. The geometric point of view is also given, with zeta functions of varieties over finite fields, with an outline of Weil's proof of the Riemann hypothesis for curves over a finite field. The lecture concludes with the modern conjectures and developments and about the analytic theory of zeta and L-functions and open problems.

Organizzazione Colloquia:
Elisabetta Strickland, strickla@mat.uniroma2.it tel 06 7259 4683

Chairman della seduta: Ciro Ciliberto