MathSciNet listing of published research papers
Research preprints on arXiv
Hodge theory and degenerations of projective manifolds. Notes from a course (Math 690, Spring 2024) with the goal to obtain a working understanding of the relationship between degenerations of projective manifolds (to singular projective varieties) and mixed Hodge structures. Many exercises are included.
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.
Moduli, Hodge theory, and completions. Slides from Stockholm U colloquium, May 2025. The aim of the talk was give a sample of how Hodge theory can be used to study projective manifolds and their moduli, and use this to motivate a program to construct completions of period maps.