|Location:||MSRI: Simons Auditorium|
Free divisors are certain non-normal hypersurfaces in a complex manifold, whose singular loci have nice algebraic properties: the Jacobian ideals are Maximal Cohen Macaulay modules for the hypersurface rings.
In this talk we give a short introduction to free divisors, also to their original definition (due to K. Saito) via logarithmic derivations and logarithmic differential forms, and indicate in which areas of mathematics they appear.
Then we talk about a conjecture about the singularities of some well-known free divisors, namely, normal crossing divisors. Finally we move on to logarithmic residues, a recent topic of interest, and to a conjecture about relationship between the logarithmic residue and the normalization of a free divisor.