Title of the course: First steps in Complex Geometry part 2
Instructor: MSc. Andrea Tomatis
Institution: Hochschule für Wirtschaft und Technik Berlin
Dates: 29 July – 4 August 2024
Prerequisites: Differential geometry, complex analysis
Level: Graduate, advanced undergraduate
Abstract: This is the second part of a three-week-long course in complex geometry.
Complex (differential) geometry started with Riemann’s definition of a Riemann surface, evolved through the work of the early algebraic geometers and developed greatly in the second half of the last century. It uses tools from several areas of mathematics among which differential geometry, several complex variables, homological algebra, partial differential equations. This makes it a relatively technical subject which may feel overwhelming to beginners.
The spirit of this three-week-long course will be to cover the main ideas involved in definitions and proofs rather than to go through all the gory details. We plan to cover reasonably large parts of chapters 0 and 1 of the classic book by Griffith and Harris Principles of Algebraic Geometry, with occasional forays into the other chapters. There is an accompanying exercise class run by Kadir Yiğit Yücel. It is advised to take both courses as they are complementary.
It is possible to attend the second or third week alone for students already familiar with chapter 0 of Griffith and Harris. As a prerequisite students should have taken a first course in differential geometry and complex analysis. Knowledge of differential topology and algebraic topology will surely help too but is not necessary and will not be assumed apart from a very basic acquaintance with homology and cohomology and the definition of a vector bundle.
Language: English