## The Arithmetic Site - Alain Connes, Caterina Consani

Alain Connes, Collège de France, IHES, The Ohio State University Distinguished Professor of Mathematics, will present a lecture course on *"The Arithmetic Site"* with the first introductory lecture on **May 5, 2:00 - 3:30 in CH 240** given by Caterina Consani of The Johns Hopkins University. There will be a tea after this first talk at 3:30 - 4:30 in MW 724. Dr. Connes will continue the mini-course to be held:

- May 6, 10:00 - 11:30
- May 7, 2:00 - 3:30
- May 8, 10:00 - 11:30
- May 12, 10:30 - 12:00, final lecture

all in CH240.

**Abstract**: We have uncovered, in our joint work with C. Consani, the *"Arithmetic Site"* : an object of algebraic geometry deeply related to the non-commutative geometric approach to RH. The set of points of the *"Arithmetic Site"* over the maximal compact subring of the tropical semifield coincides with the non-commutative space quotient of the adèle class space of the field of rational numbers by the action of the maximal compact subgroup of the idele class group. As we showed earlier this is the space that yields the correct counting function to obtain the complete Riemann zeta function as Hasse-Weil zeta function. The action of the Frobenius automorphisms of the tropical semifield on the above points corresponds to the action of the multiplicative group of positive real numbers on the adele class space that yields the expected counting function. The *"Arithmetic Site"* is an object of algebraic geometry, the underlying space is a topos and the structure sheaf is made by semirings of characteristic 1. The square of the arithmetic site is also well-defined and the Frobenius correspondences parametrized by positive real numbers, are interpreted as subvarieties of this square. I will also discuss the link between the arithmetic site and cyclic homology through its relation with the epicyclic site.

## Daniel Wise to be the Spring 2015 Zassenhaus Lecturer

Daniel T. Wise, of the Department of Mathematics and Statistics of McGill University, will be the Zassenhaus Lecturer April 20 - 22, 2015. Daniel specializes in geometric group theory and 3-manifolds.

The Zassenhaus Lecture Committee consisted of Jim Cogdell, Michael Davis, Hsian-hua Tseng, and Avner Friedman.

## Luis Caffarelli to be the Fall 2014 Radó Lecture

Luis Caffarelli is to be the 2014 Fall Radó Lecturer. Luis is Professor of Mathematics at the Institute for Computational Engineering and Science, University of Texas at Austin. Luis Caffarelli is a leading expert in free boundary problems and nonlinear partial differential equations.

The Radó Lecture Committee consisted of Vitaly Bergelson, Jeff McNeal, Henri Moscovici and Avner Friedman.

## Mission Of the Institute

The aim of the Mathematics Research Institute is to promote research interactions in the mathematical sciences among Ohio State faculty and researchers worldwide. This is achieved through support of weekly seminars, distinguished visitors program, special years and conferences, and by support of travel and research programs of OSU faculty.