# MA613 Content

**Commitment:**

**Approximate contents:**

-> Introductory examples with easy calculations.

-> How to list the finite subgroups G in SL(2,CC), GL(2,CC), SL(3,CC)

-> Invariants of finite group actions on affine varieties

-> Klein's calculation of invariants

-> Invariants, equations, surface singularities and resolutions in algebraic geometry

-> Representation theory of finite groups

-> G-Hilb and G-Cons and calculations for Abelian groups

-> Moduli problems and correspondences

-> Introduction to DCat and Fourier-Mukai transforms

-> More general theory of DCat and the BKR proof

-> Hilb^n CC^2 and BKR following Haiman

-> Reid's recipe for Abelian groups

-> Theta stability, constellations

-> Other groups: some easy solvable groups, the terminal group 1/r(1,a,r-a) in GL(3,CC), some Abelian subgroups of SL(4,CC) and SL(n,CC)

-> etc.: motivic integration, topology, relations with string theory, Calabi-Yau 3-folds, CY3-algebras.