Title of the course: First steps in complex geometry 1
Instructor: MSc. Andrea Tomatis
Institution: Hochschule fuer Technik und Wirtschaft Berlin
Dates: 21-27 July 2025
Prerequisites: Differential Geometry, Complex Analysis
Level: Graduate, advanced undergraduate
Abstract: This course is the first part of a three-week series on complex geometry, a field that began with Riemann’s concept of a Riemann surface and evolved through algebraic geometry and modern mathematics. It integrates tools from differential geometry, several complex variables, homological algebra, and partial differential equations. We will primarily use Principles of Algebraic Geometry by Griffiths and Harris, focusing on the key ideas behind definitions and proofs, with less emphasis on technical details.
A complementary exercise class, led by Kadir Yiğit Yücel, is available and highly recommended.
Students familiar with the foundational concepts of complex geometry may join in the second or third week. Prerequisites include a basic knowledge of differential geometry and complex analysis (with Complex Analysis by Freitag and Busam suggested as a reference). While familiarity with differential and algebraic topology is helpful, only a basic understanding of homology, cohomology, and vector bundles is required.
Language: English