ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 39 Korepanov, Igor, South Ural State University, Russia Integrability in higher dimensions The most general construction of integrable equations in 2 + 1 discrete dimensions and their solutions seems to be using some kind of functional tetrahedron equation and its algebro-geometric solutions. In the talk, some underlying general constructions (involving e. g. abelian categories), as well as recent developments and generalizations of this idea are discussed, including generalizations to 3 + 1 dimensions. Part of these results is joint work with R. M. Kashaev and S. M. Sergeev. Reference: R. M. Kashaev, I. G. Korepanov and S. M. Sergeev, Functional Tetrahedron Equation, solv-int/9801015, accepted for publication in Theor. Math. Phys. (1998).