Tuesday April 22nd, 2025 | |
| Time: | 4:00 PM - 5:15 PM |
| Title: | Curvature, Macroscopic Dimensions, and Symmetric Products of Surfaces |
| Speaker: | Luca di Cerbo, University of Florida |
| Location: | P-131 |
| Abstract: | |
| Abstract: In this talk, I will present a detailed study of the curvature and symplectic asphericity properties of symmetric products of surfaces. I show that these spaces can be used to answer nuanced questions arising in the study of closed Riemannian manifolds with positive scalar curvature. For example, symmetric products of surfaces sharply distinguish between two distinct notions of macroscopic dimension introduced by Gromov and Dranishnikov. As a natural generalization of this circle of ideas, I will also address the Gromov–Lawson and Gromov conjectures in the Kaehler projective setting and draw new connections between the theories of the minimal model, positivity in algebraic geometry, and macroscopic dimensions. | |