Hodge theory: a representation theoretic perspective. Lecture notes for the Summer School: Representation theory and flag or quiver varieties, 13-17 June 2022. Lecture 1: an introduction to formal Hodge theory covering polarized Hodge structures; and Hodge groups, representations and domains; and period maps. Lecture 2: Gross's geometric realization problem for Hodge representations of CY type. Lecture 3: characteristic cohomology of the infinitesimal period relation. Lectures 2 and 3 include several open questions. Many exercises are given.
Linear structures of Hodge theory. Lecture notes for the ICERM Introductory Workshop: Combinatorial Algebraic Geometry, 01-05 February 2021. An introduction to Hodge structures and description of the linear structures underlying the Hard Lefschetz Theorem and Hodge–Riemann Bilinear Relations. Many exercises are given.
Q.E.D.: quod erat demonstrandum.
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