# MAT1305 Calabi-Yau Manifolds

**Course information**

Code: MAT1305S

Instructor: Marco Gualtieri

Class schedule: T3-5 and R3-4 in BA6180

Marking Scheme: Exercises, attendance, and presentations.

**Notes and references**

The notes contain exercises, which are to be handed in. In the beginning I follow very closely the first text below.

- Notes 1: The Legendre family of elliptic curves, introduction to periods
- Notes 2: Gauss-Manin connection for the Legendre family
- Notes 3: Asymptotics and derivative of periods
- Notes 4: Picard-Fuchs equation
- Notes 5: Jet bundles, Hypergeometric functions, and moduli stacks
- Notes 6: Higher genus curves and period mappings
- Notes 7: Mixed Hodge structures
- Notes 8: Introduction to K3 surfaces
- Notes 9: Constructing elliptic K3 surfaces with large Neron-Severi group
- Kreuzer-Skarke plot of toric hypersurface CY3s, https://arxiv.org/abs/hep-th/0002240

I will use a combination of textbooks and papers, which will be linked here.

- Period Mappings and Period Domains, by Carlson, Muller-Stach, and Peters
- Calabi-Yau Manifolds and related Geometries, by Gross, Huybrechts and Joyce.
- Lectures on Special Lagrangian Submanifolds, by Hitchin

**Topics**

We plan to describe several methods for constructing Calabi-Yau manifolds, and to develop some of the main tools which are used in studying them. The material will include Hodge theory, variation of Hodge structure, Picard-Fuchs equations, and an introduction to Mirror Symmetry. I am gearing the course towards beginning graduate students, and so it is an opportunity to learn some of the basic tools of algebraic geometry.