Toric and tropical compactifications of hyperplane complements
These lecture notes survey and compare various compactifications of complex hyperplane arrangement complements. In particular, we review the Gelfand-MacPherson construction, Kapranov’s visible contours compactification, and De Concini and Procesi’s wonderful compactification. We explain how these constructions are unified by some ideas from the modern origins of tropical geometry.
Variations of Hodge structure considered as an exterior differential system: old and new results.