2 Stunden pro Woche, Dienstag 15-17 Uhr, RUD 25, 2.006.

Organiser: Michael Kemeny

"Any area of mathematics is a kind of deformation theory.'' Kontsevich-Soibelman, rephrasing I. Gelfand.
A central concept in modern mathematics is the notion of the "moduli space" parametrising all mathematical objects of a given kind.
Deformation theory is then the local study of this moduli space. In this seminar (which will function largely as a lecture series), we aim to define what a moduli space is and
give dimension bounds on this space as well as criteria for when it is smooth.

As well as developing the general theory, we will
discuss many examples from algebra (deformations of rings, algebras and Lie algebras), complex analysis (deformations of complex manifolds, deformations
of analytic singularity types) and algebraic geometry (curves, morphisms).