PhD Course "Topics in Advanced Geometry" - II part

[ZUDDAS DANIELE]

The second part of the PhD Course "Topics in Advanced Geometry" will be held by me from 7 March to 18 April every Thursday, 16:00 - 18:00 in Room 4C - H2bis, University of Trieste main campus (but we will skip Thursday 28 March because is holiday).
The part of the Course held by Prof. Fabio Perroni will keep the previously announced schedule.

The topics that we shall address are as follows

The Course will be an introduction to the theory of fibre bundles and vector bundles, in particular the following topics will be covered:
  • connections and curvatures;
  • holomorphic vector bundles;
  • line bundles and Picard varieties;
  • obstructions to the existence of linearly independent sections;
  • Chern classes and their axioms;
  • Universal bundles. 

References
  • S. Kobayashi, K. Nomizu. Foundations of differential geometry.
  • H. Madsen, J. Tornehave. From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes   (Cambridge University Press).
  • C. Birkenhake, H. Lange. Complex Abelian Varieties (Springer).
  • N. Steenrod. The Topology of Fibre Bundles (Princeton Mathematical Series).


All interested people, in particular PhD students and postdocs, are welcome.

Daniele Zuddas