An Introduction to Derived Geometry
Albin Grataloup (Université de Montpellier)
Friday 15th November 14:00-15:00 Maths 311B
Derived geometry is a generalisation of ordinary geometry that aims to obtain better behaved quotients and intersection.
It enables us to treat geometric singularities or G-equivariant geometry almost as if we were dealing with ordinary geometry.
There have been many instances of derived constructions starting with Serre's intersection formula (1950-1960) computing
the number (with multiplicity) of intersections of algebraic curves to various ad-hoc homological resolutions for
singular intersections and quotient spaces created by physicists in order to quantise gauge theories. Derived geometry turns
these constructions into natural geometric operations.
In this introduction, we aim to motivate the need for derived geometry and explain how the homotopical algebra appearing in
derived geometry helps us to treat what would be pathological behaviors in classical geometry as if they were generic.