3:00–4:00 pm Eckhart Hall, Room 202
Title: The minimal exponent of hypersurface singularities
Abstract:
The log canonical threshold of a polynomial is an invariant of singularities that can be defined in terms of integrability conditions, but which arises in various other contexts and admits different characterizations. A refinement of this invariant is Saito's minimal exponent, whose definition relies on the theory of \(b\)-functions, an important concept in \(D\)-module theory. The new information (by comparison with the log canonical threshold) provides a numerical measure of rational singularities. In this talk, I will give an introduction to minimal exponents, highlighting recent progress and open questions.