Project Grant 2151946

This three-year Project Grant from the National Science Foundation Division of Mathematical Sciences, totaling $540,974, will fund collaborative research applying recent developments in higher category theory and condensed mathematics to longstanding questions in algebraic geometry and the introduction of new questions in analytic algebraic geometry. Specifically, the principal investigators and their collaborators at the University of California, Berkeley will pursue four main research challenges: developing complete noncommutative categorical invariants and a bridge between topological and categorical invariants; clarifying the role of commutative objects inside noncommutative objects in an attempt to settle Orlov's geometricity conjecture; studying p-adic cohomology of algebraic varieties via higher categorical invariants such as topological Hochschild homology; and constructing the correct noncommutative invariants of a rigid analytic variety and generalizing the first three projects to the more general analytic context. In addition to research, the award will support graduate student and postdoctoral training as well as workshops for early-career mathematicians. This Project Grant is funded through the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049), which supports increasing the store of scientific knowledge and understanding of major problems through mathematical and physical sciences research and education.