Summer Semester 2025

Complex Geometry

(rough) Aim of the course: To learn what complex manifolds are, and look at some examples.  We will learn about sheaves on complex manifolds and their cohomology. In particular, we will define the Dolbeault complex, and it's cohomology. The plan is then to learn about Kaehler manifolds, so that we can state and prove the Hodge decomposition of Dolbeault cohomology.  If time permits, we will dive a little deeper into Kaehler manifolds, and study examples. 

P.S. The language of instruction will be English.

Prerequisites: Linear algebra, complex analysis (=Funktionentheorie)

Registration: Send an email with your full name and Matrikelnummer either to me: aryaman.patel [add @math.uni-sb.de] or to Erik Paemurru: paemurru [add @math.uni-sb.de]

Schedule: Lectures once every week on Tuesdays 10am - 12pm in Seminar room 6 (E2.4), exercise classes on alternate Thursdays (room TBD). The schedule is flexible depending on the participants' preferences.

Exam: Oral exam at the end of the semester scheduled individually with participants.

Resources: Christian Schnell's notes available here