Author: Jan-Erik Roos (Department of Mathematics, Stockholm University,
SE-10691 STOCKHOLM, Sweden
email: jeroos@matematik.su.se)
Title: Theorems and conjectures in homological algebra inspired by
computer calculations.
Abstract: I will give a survey of some recent results in homological
algebra, related to commutative ring theory and algebraic geometry, some
of them first found by computer experiments and then proved "by hand".
These results cover e.g. the strange homological structure of certain
defining ideals of monomial curves (partly joint work with Sturmfels
and Fr\"oberg),
characterizations of Koszul algebras , structure of the homotopy
Lie algebra and also the structure of the (double) Yoneda Ext-algebra
of a local commutative noetherian ring etc. The computer programs used
are BERGMAN (by J\"orgen Backelin and others), CBAS (by Clas L\"ofwall)
and ANICK (by Victor Ufnarovskij, Alexander Podoplelov, J. Backelin and others)
as well as the more familiar Macaulay2 (by Dan Grayson and Mike Stillman).