Karim Adiprasito, Semigroup algebras, Parseval identities and twists

I will provide some deeper insights into the proof of unimodality of the (local) h* vector for certain lattice polytopes, and give a combinatorial interpretation for one of the key algebraic identities, the Parseval identity. Finally, I will discuss a new proof using classical Hodge theory and a twisted version of the semigroup algebra.