📚 Teaching

Toric Geometry

Undergraduate course, ETHZ, Spring 2025

Toric varieties provide a rich class of examples in algebraic geometry that bridge combinatorics and geometry, making them an ideal starting point for exploring the interplay between these fields. We will introduce toric varieties, study their combinatorial and abstract structures, and examine their basic geometry, including Picard groups, cohomology, and singularities.

Riemann Surfaces

Undergraduate course, ETHZ, Spring 2024

A first introduction to the theory of Riemann surfaces. These are beautiful objects that sit at the intersection of algebra, geometry, and analysis. We covered the theorems of Riemann–Hurwitz, Riemann–Roch, and Abeli–Jacobi, as well as the basics of Hurwitz theory.

Misc

Moduli spaces of Riemann surfaces
PhD mini-course held at the Les Houches school Quantum Geometry, Les Houches, Summer 2024
Lecture notes, Exercises
Hurwitz numbers and Gromov–Witten theory
PhD mini-course held at Gaëtan Borot’s group retreat, Hiddensee, Summer 2022
Notes
Topology
Exercise classes, UniTS, Spring 2017
Exercise sheets, Topological relations
Linear algebra
Exercise classes, UniTS, Fall 2016
Exercise sheets, Plane rotations, Fibonacci sequence, Jordan form

Alessandro Giacchetto

📚 Teaching

Toric Geometry

Riemann Surfaces

Misc