Speaker
Chiara Meroni, ETH Zürich
Abstract
Directional convexity is a refined notion of convexity in which convexity is required only along specific directions. This concept arises naturally in the theory of multivariate calculus of variations and has intriguing applications in cryptography. However, constructing directional convex hulls remains a highly challenging problem. In the few cases where explicit constructions are known, the resulting hulls exhibit rich algebraic and combinatorial structures, sometimes polyhedral, other times semialgebraic. In this talk, I will review key results and algorithms related to directional convexity and present recent developments from a joint work with Bogdan Raita.