Topics in Algebraic Surfaces, Scuola Normale Superiore,  Fall 2023

A short synopsis of lectures.

 Namibian International Spring School in Mathematics October 2022

Lecture Notes

Nairobi Workshop August 2018


Mirror symmetry and Fano orbifolds (IMPA, Jan-Feb 2017)


Galois Theory

Click here

Mirror symmetry for Fano orbifolds (Trieste, 01–12 August 2016)

Here is an examples sheet for the course. In time we will also add lecture notes

Introduction to Mixed Hodge Theory (LSGNT, 26th Feb 2016)

Here is a writeup of the lecture in PDF

M3P21 Geometry II: Algebraic Topology (Spring 2015)


Here are the (unofficial) notes written up by Edoardo Fenati and Tim Westwood based on the course as given in 2014


sheet 1sheet 2sheet 3sheet 4

solutions 1solutions 2solutions 3

New perspectives on the classification of Fano manifolds (Udine 29 Sep-03 Oct 2014)

Udine examples

Extremal Laurent Polynomials (Grenoble School on “Moduli of curves and Gromov-Witten theory” June 2011)

Here are the notes based on my 4 lectures at the School PDF

New Methods in Orbifold Gromov-Witten Theory (Pisa June 2008)

Pisa examples

Higher dimensional minimal models and flips (Grenoble June-July 2007)


K3 Surfaces (Lent 2005)


Number Theory (Michaelmas 2004)


Groups Rings and Fields (Lent 2003)


Basic Algebraic Geometry (Michaelmas 2002)

Examples egsht1egsht2