Conformal, Integrable and Topological Theories, Graphs and Coxeter Groups

Abstract

I review three different problems occuring in two dimensional field theory: 1) classification of conformal field theories; 2) construction of lattice integrable realizations of the latter; 3) solutions to the WDVV equations of topological field theories. I show that a structure of Coxeter group is hidden behind these three related problems.

21 pages, uuencoded, tex, 5 figures included, uses harvmac and epsf (Talk delivered at the International Conference of Mathematical Physics, Paris 18-23 July 1994)