ICTS

What does geometry look like when branes, rather than points, are taken as the primitive objects? I will describe an emerging categorical framework that gives concrete mathematical form to some of the structures one might expect in such a geometry, drawing together ideas and questions from long-standing programs in several areas of mathematics. Key ingredients are categorical incarnations of boundary RG flows and g-theorem-type monotonicity, Zamolodchikov-type metrics, and BPS conditions. Based on joint work with F. Haiden, L. Katzarkov and M. Kontsevich.