The goal of the seminar is to study the basics of Hodge theory, including the Hodge and Lefschetz decompositions on the cohomology of a Kähler manifold. We will follow Claire Voisin's Hodge Theory and Complex Algebraic Geometry I (Amazon).
If time permits, we can study Serre's GAGA paper, which has quite a different flavour, to relate the results obtained in complex geometry to the algebraic world. The article is available online.
The book has a small but useful selection of exercises (typically between 1 and 4 per chapter), and I encourage everyone to look at them as well. I will distribute them weekly to those interested.
Organisers: Remy van Dobben de Bruyn, Sébastien Picard.
Time and location: Monday 16:30-18:00 in Math 622.
|20 Jan||Organisational meeting (Math 206)|
|2 Feb||Remy van Dobben de Bruyn||Dolbeault complex||1 & 2|
|9 Feb||Sébastien Picard||Kähler metrics (lecture notes)||3|
|16 Feb||Joshua Seaton||Sheaves and cohomology||4|
|23 Feb||Qixiao Ma||Laplacians||§ 5.1|
|2 Mar||Xuan Wu||Elliptic differential operators||§ 5.2, 5.3.1|
|9 Mar||Pablo Portilla||The Hodge decomposition||§ 6.1|
|16 Mar||Spring break|
|23 Mar||Sebastian Mueller||Lefschetz decomposition||§ 6.2|
|30 Mar||Sébastien Picard||The Hodge index theorem||§ 6.3|
|6 Apr||Shizhang Li||Hodge structures and polarisations||§ 7.1 - 7.2.2|
|13 Apr||Remy van Dobben de Bruyn||Frölicher spectral sequence||8|
|20 Apr||Raju Krishnamoorthy||Families and deformations||9|
|27 Apr||Phil Engel||Variation of Hodge structure||10|
|4 May||Yifei Zhao||GAGA||Serre's paper|