Mathematics

Deformation theory, introduced by Grothendieck in his seminar talks "Fundaments de la Géométre Algébrique", is the algebraic counterpart of the approach taken by Kodaira, Spencer, Nirenberg and Kuranishi to study small deformations of complex manifolds. In this talk I'll introduce the notions of deformation of an algebraic scheme, the notion of functor of Artin rings and I'll give give some example of those. Then I'll try to explain the notion of tangent space to a functor of Artin rings and give some example of computations in special cases. If time permits, I'll try to define the notion of obstruction space, give some examples and give an idea of how these tangent/obstruction spaces are linked with the local-to-global spectral sequence of Ext.