Hodge theory reading seminar


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.

Date Speaker Title Chapter
20 Jan Organisational meeting (Math 206)
26 Jan Cancelled
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