The main origin of this workshop lies in the relevance, in relation with the L-functions of arithmetic varieties and Arakelov geometry, of the basic categorical concept of an S-algebra, derived from the theory of Segal's Gamma-sets as described in the recent book of Dundas-Goodwillie-McCarthy. This unifying role is enhanced by some recent results of L. Hesselholt on the link of topological cyclic homology with fundamental constructions in p-adic Hodge theory, which jointly with Hesselholt's previous results on the de Rham Witt complex show that topological cyclic homology is a very good candidate for a Weil cohomology. Moreover, the discovery of the arithmetic site promoting the Riemann zeta function as the Hasse-Weil zeta function, and possessing geometric Frobenius correspondences, suggests a geometric framework for a global understanding of the L-functions of arithmetic varieties. This geometric framework is expected to be based on the theory of Grothendieck topoi and some suitable categorical constructions refining the epicyclic and cyclic categories. The need for a model category which bypasses the step connecting additive monoids to the associated groups is essential when dealing with characteristic one; the ideas developed by Joyal are expected to play a determinant role in that context.
The workshop is sponsored by the Mathematics Research Institute and the Department of Mathematics of the Ohio State University. Minorities, women, graduate students, postdocs, and early career mathematicians are especially encouraged to attend.