Mathematical Conversations

What do graph matchings and independent vertex sets have to do with the cohomology of products of projective lines? I will share with you an example in the study of “equivariant log-concavity”, which enriches the notion of log-concavity. By keeping in mind the symmetry while playing with the underlying combinatorial objects, we will rediscover log-concavity using the hard Lefschetz theorem in Hodge theory. Non-technical talk; nothing is assumed beyond linear algebra and basic graph theory.