Webrelaunch 2020

Seminar on Kähler Geometry (Summer Semester 2019)

Schedule
Seminar: Thursday 14:00-15:30 SR 2.67
Lecturers
Lecturer Prof. Dr. Wilderich Tuschmann (Institute Spokesman)
Office hours: by appointment - please contact me by email;
Room 1.002 Kollegiengebäude Mathematik (20.30)
Email: tuschmann@kit.edu
Lecturer Dr. Jan-Bernhard Kordaß
Office hours: By appointment.
Room 1.021 Kollegiengebäude Mathematik (20.30)
Email: kordass@kit.edu

The talks will be based on Part II and III in Moroianu's book [Mor07].
Participants are assumed to be familiar with basics in differential geometry as outlined in Part I (ibid.).

Talks:

  1. Introduction to complex differential geometry (25 April and 2 May)
  2. Complex, holomorphic and hermitian vector bundles (9 May)
  3. Geometry of Kähler metrics (16 May)
  4. Hodge- and Dolbeault theory (6 June)
  5. Chern classes and the Ricci Form (13 June)
  6. The Calabi-Yau theorem and Kähler-Einstein metrics (27 June)
  7. Geometric interpretations of Weitzenböck formulae (4 July)
  8. Kodaira's vanishing theorem and Ricci-flat metrics
  9. Examples of Calabi-Yau manifolds

References

  • [GH94] Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1994, Reprint of the 1978 original. MR 1288523
  • [Huy05] Daniel Huybrechts, Complex geometry, Universitext, Springer-Verlag, Berlin, 2005, An introduction. MR 2093043
  • [Mor07] Andrei Moroianu, Lectures on Kähler geometry, London Mathematical Society Student Texts, vol. 69, Cambridge University Press, Cambridge, 2007. MR 2325093