Activities This Week

We will consider some basic optimization problems and how they relate to optics. We then define an index of refraction to any given distribution. We conjecture an estimate for the index and explain how its related to some natural operations research questions. We also consider lenses and ask questions about the probabilistic behavior of discrete geodesics in a lens setting.

Several functional analogs of fundamental geometric inequalities have appeared in recent decades, beginning with the works of Prekopa and Leindler in the 1970’s. In this talk I will, after discussing the method of functionalization of geometry, present new functional extensions of the Brunn Minkowski inequality and their consequences.

In this second talk we prove that the localizations of the categories of dg categories, of cohomologically unital and strictly unital A_\inftycategories with respect to the corresponding classes of quasi-equivalences are all equivalent. As an application, we give a complete proof of a claim by Kontsevich stating that the category of internal Homs for two dg categories can be described as the category of strictly unital A_\inftyfunctors between them. This is a joint work with Prof. A. Canonaco and Prof. P. Stellari arXiv:1811.07830.