Week 2 Oct 10

Reading group [Marc Truter, Introduction to Moduli problems and GIT] (2-3pm Thursday C1.06)

Week 3 Oct 17

Reading group [Arnaud Vilpert, Moduli problems] (12-1pm Thursday D1.07)

Week 4 Oct 24

Reading group [Chunkai Xu, Groups and actions] (12-1pm Thursday D1.07)

Joe Malbon (3-4pm Thursday D1.07)

Classification of Algebraic Varieties

Classification - the identification of similar objects and the distinction of different ones, as well as the construction of spaces that parametrise such equivalence classes - is a guiding meta-principle in algebraic geometry. It was realised around the turn of the last century that isomorphisms are too rigid a notion of equivalence for classification to be achievable, and that the more flexible notion of birational equivalence should be used instead. This point of view was successfully applied to algebraic surfaces, whose birational classification was more or less completed by the 1950s.

For higher-dimensional varieties, it is often said that all varieties are birationally (and conjecturally) constructed from Fano, Calabi-Yau, and canonically polarised varieties, and thus classification may proceed inductively based on dimension. In this talk, I will explain the birational classification of varieties from the viewpoint of the minimal model program, which is an algorithm that constructs varieties in this inductive way. If time permits, I will explain the application of the minimal model program to the construction of moduli spaces, which parametrise equivalence classes of varieties with similar properties, and illustrate some of my own work on the construction of the moduli space of a particular family of K-polystable Fano threefolds.

Week 5 Oct 31

Reading group [Alvaro Gonzalez Hernandez, Affine GIT](12-1pm Thursday D1.07)

Week 6 Nov 7

Reading group [Tommaso Faustini, Projective GIT] (12-1pm Thursday D1.07)

Thamarai Valli (3-4pm Thursday D1.07)

Week 7 Nov 14

Reading group [Marc Truter, Stability] (12-1pm Thursday D1.07)

Week 8 Nov 21

Reading group [Chunkai Xu, Moduli of vectors bundles]  (12-1pm Thursday D1.07)

Michela Barbieri (3-4pm Thursday D1.07)

Week 9 Nov 28

Reading group [Pieze Liu, Hypersurfaces and blowups] (12-1pm Thursday D1.07)

Week 10 Dec 5

Reading group [TBD] (12-1pm Thursday D1.07)

Xuanchun Lu (3-4pm Thursday D1.07)