Gromov, Hanke, Sormani, Yu's


Not Only Scalar Curvature

Upcoming talks


November 19, 2025

Uwe Semmelmann: Quaternion Kähler manifolds of non-negative sectional curvature
(16:30 Paris, 10:30 am NYC)
Quaternion Kähler manifolds, i.e. Riemannian manifolds with holonomy contained in Sp(m)Sp(1), are Einstein. In the case of positive scalar curvature, there is a longstanding conjecture by LeBrun and Salamon stating that all such manifolds should be symmetric. So far, the conjecture has been confirmed only up to dimension 12.

In the first part of my talk I will give an introduction to the geometry of quaternion Kähler manifolds of positive scalar curvature. In the second part I will make a few remarks on the proof of the conjecture under the additional assumption of non-negative sectional curvature. This extends earlier work by Berger, who proved that quaternion Kähler manifolds of positive sectional curvature are isometric to the quaternionic projective space.

My talk is based on a joint article with Simon Brendle and on earlier work by Simon Brendle.

December 3, 2025

Yujie Wu: Application of Curvature Comparison Theorems in Minimal Surfaces
(16:30 Paris, 10:30 am NYC)
We use generalized minimal or capillary hypersurfaces to study comparison theorems of certain class of positively curved manifolds (with boundary); this is also called Gromov's $\mu$-bubble method. We apply these results to obtain useful geometric bounds such as Urysohn width, bandwidth estimates, and study rigidity of (free boundary) minimal hypersurfaces.

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 link


IHES Carmin TV Channel Info:

https://www.carmin.tv/en/collections/not-only-scalar-curvature-seminar

Organizers

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