Japan-U.S. Mathematics Institute (JAMI) and Johns Hopkins University, Department of Mathematics is sponsoring a conferences on Primes and Knots

March 7 - 16, 2003

The program is anchored by two weekend programs: the focus of the first is the emerging subject of `arithmetic topology', centered on geometric analogies between knots and primes, between Galois groups of number fields and fundamental groups of three-manifolds, between Alexander and Iwasawa theory. Much of this work is driven by a desire to understand global structure of number fields in terms of ideas motivated by knot theory. Recent developments in the theory of quantum knot invariants defines the second focus of the program. Here researchers in three-dimensional topology bring to bear new and very sophisticated constructions from number theory, one of which is the Grothendieck-Teichm\"uller group of automorphisms of algebraic curves considered as a coherent system. This object is important in conformal field theory as well as in number and knot theory. It exists in several variants (profinite, prounipotent...), whose relations are very much in the process of being discovered. The program uses hyperbolic geometry to interpolate between these extremes.

Other points of contact between these fields will also be represented: dynamical zeta-functions, multi-zeta values, Arakelov geometry... We expect a very interesting conference. The program is supported by the National Science Foundation, and we are particularly interested in supporting interested younger researchers.