Geometry and Topology Seminar

The objective of this talk is to explain how symmetric products, macroscopic dimensions, and scalar curvature help in the study of one another. We begin by discussing two distinct notions of macroscopic dimensions arising in the study of manifolds with positive scalar curvature. Then we show that symmetric products of surfaces sharply distinguish between these notions of macroscopic dimensions. Finally, we address versions of the classical Gromov—Lawson and Gromov conjectures that predict obstructions to Kähler metrics of positive scalar curvature on projective varieties in terms of their macroscopic dimensions. This talk is based on joint work with Luca Di Cerbo and Alexander Dranishnikov.