Upcoming talks
May 7, 2025
- Andrea Mondino: On manifolds with almost non-negative Ricci curvature and integrally-positive kth-scalar curvature
(16:30 Paris, 10:30 am NYC) - In the talk, I will present a joint work with Alessandro Cucinotta (University of Oxford), where we consider manifolds with almost non-negative Ricci curvature and strictly positive integral lower bounds on the sum of the lowest k eigenvalues of the Ricci tensor. If $(M^n,g)$ is a Riemannian manifold satisfying such curvature bounds for k=2, then we show that $M$ is contained in a neighbourhood of controlled width of an isometrically embedded 1-dimensional submanifold. From this, we deduce several metric and topological consequences: $M$ has at most linear volume growth and at most two ends, the first Betti number of $M$ is bounded above by 1, and there is precise information on elements of infinite order in $π_1(M)$. If $(M^n,g)$ is a Riemannian manifold satisfying such bounds for k≥2 and additionally the Ricci curvature is asymptotically non-negative, then we show that $M$ has at most (k−1)-dimensional behavior at large scales. If k=n=dim($M$), so that the integral lower bound is on the scalar curvature, assuming in addition that the n−2-Ricci curvature is asymptotically non-negative, then we prove that the dimension drop at large scales improves to n−2. From the above results, we deduce topological restrictions, such as upper bounds on the first Betti number. Such results should be read in the broader framework of Gromov’s conjectures about 2-dimensional drop at large scale of manifolds with positive scalar curvature.
Previous talks
Seminar Info
Each session will consist of one or two lectures on a recent advance in geometry. Not all the talks will concern scalar curvature but perhaps many will. Each talk will be followed by a discussion both in person and online. Everyone is welcome to join the session live (zoom) or watch the recorded videos of the talks later.Zoom starts at 16:30 Paris time:
click here to register and receive linkIHES Carmin TV Channel Info:
https://www.carmin.tv/en/collections/not-only-scalar-curvature-seminarOrganizers
Misha Gromov, IHES
Website: https://www.ihes.fr/~gromov/
Bernhard Hanke, University of Augsburg
Website: https://www.uni-augsburg.de/de/fakultaet/mntf/math/prof/diff/team/bernhard-hanke/
Christina Sormani, CUNY Graduate Center and Lehman College
Website: https://sites.google.com/site/professorsormani/home
Gouliang Yu, Texas A&M University
Website: https://www.math.tamu.edu/people/formalpg.php?user=guoliangyu