Wednesday, May 4, 2016 - 10:30am to 11:25am

Thursday, May 5, 2016 - 10:30am to 11:25am

Friday, May 6, 2016 - 10:30am to 11:25am

Monday, May 9, 2016 - 10:30am to 11:25am

Cockins 240

**Title:** The scaling site and Rieman-Roch of type II

**Speaker: **Alain Connes (College de France, IHES, and OSU)

**Abstract:** I will explain the joint work with C. Consani in which we develop algebraic geometry in characteristic one using the « scaling site » as a tropical curve which allows us to transpose the basic step of the geometric proof of RH for curves in finite characteristic. The frontier of the subject is the Riemann-Roch theorem, and I will discuss the RR in tropical geometry and the type II Riemann-Roch for the periodic orbits associated to primes as analogues of the Jacobi elliptic curves, as well as the analogues of theta functions.