Course progress

[TTAG]: Topics in Transcendental Algebraic Geometry, P. Griffiths.
[MSAG]: Mirror Symmetry and Algebraic Geometry, Cox-Katz.
[PMPD]: Period Mappings and Period Domains, Carlson-Muller-Stach-Peters.

This is a not very detailed record on what happened in each course meeting. There should be course recordings in 北大教学网.

Mar 02: We briefly overviewed the B-model prediction of the celebrated genus mirror symmetry for the quintic [MSAG, Ch 1-2].
Mar 04: We introduced Hodge structures, polarized Hodge structures, and variation of polarized Hodge structures [TTAG, Ch I].
Mar 09: We reviewed variation of Hodge structures, and discussed an example of elliptic curves for the monodromy computation [TTAG, Ch I].
Mar 16: We continued the discussion of the Gauss-Manin connection computation of the example $y^2=x(x-1)(x-\lambda)$. Then we proceeded to the Chern connection and the curvature computation for Hodge bundles [TTAG Ch II].
Mar 18: We continued the computation on Chern connection and Gauss-Manin connection. We showed several constraints on the VHS when the base of VHS is compact (the theorem of fixed part, orthogonal decomposition w.r.t. the action, etc.). [TTAG Ch II]
Mar 23: Ahlfors lemma and the curvature, monodromy of VHS over a punctured disk [TTAG Ch II]. An example of genus 2 curves over a punctured disk; introduction to mixed Hodge structures [PMPD Ch I].
Mar 30: Mixed Hodge structures, limiting Hodge structure: definition and why we should now use the naive one. [TTAG Ch IV]
Apr 1: Review of the mixed Hodge structures. Nilpotent orbit theorem. Limiting Hodge structure over a punctured disk is a polarized mixed Hodge structure. [TTAG Ch V]