Gromov, Hanke, Sormani, Yu's


Not Only Scalar Curvature

Upcoming talks


October 7, 2026

Liam Mazurowski and Xuan Yao : Quantification of $C^0$-convergence in dimension 3
(16:30 Paris, 10:30 am NYC)
We address Gromov's Quantification of $C^0$-Convergence Conjecture in dimension three. Let $B$ be the unit ball in $R^3$. Let $g$ and $g_0$ be smooth metrics on $B$. We prove there are constants $C$ and $\varepsilon_0$ depending only on $g_0$ so that $\inf_{x \in B} R_g(x) < R_{g_0}(0) + C \|g-g_0\|_{C^0}^{1/2}$ provided $|g-g_0|_{C^0} < \varepsilon_0$. We also construct examples to show that the exponent $1/2$ is sharp. This explicitly quantifies the fact that scalar curvature lower bounds are preserved under $C^0$-convergence of metrics.

The proof is based on an analysis of harmonic functions. We will also briefly discuss some further applications of this method to other problems.

October 21, 2026

Qiaochu Ma: Gromov's Simplicial Volume Vanishing Conjecture for Positive Scalar Curvature
(16:30 Paris, 10:30 am NYC)
Gromov's simplicial volume vanishing conjecture predicts that if a closed oriented manifold admits a positive scalar curvature metric, then its simplicial volume vanishes. In this talk, we present a proof of this conjecture under a spin condition. Our proof is based on a quantitative refinement of the Connes-Moscovici higher index theorem. This is joint work with Jinmin Wang, Zhizhang Xie, Guoliang Yu, and Bo Zhu.

November 4, 2026

Gioacchino Antonelli: Spaces of metrics with positive spectral scalar curvature
(16:30 Paris, 10:30 am NYC)
For a closed $n$-manifold $M$, let $\mathscr{R}^\gamma(M)$ be the space of metrics $g$ for which -$γ \Delta_g + \mathrm{Scal}_g>0$. We prove that $\mathscr{R}^0(M) \hookrightarrow \mathscr{R}^\gamma(M)$ is a homotopy equivalence when $n = 2$ and $\gamma ≥ 0$, or when $n ≥ 3$ and $0 ≤ \gamma ≤ 4(n-1)/(n-2)$, while $\mathscr{R}^\gamma(M)$ is contractible when $n ≥ 3$ and $\gamma > 4(n-1)/(n-2)$. The latter proves a sharp homotopy-theoretic strengthening of a conjecture of Gromov. This is a joint work with G. Frenck and B. Hanke. 

November 18, 2026

Sun-Yung Alice Chang and Ruobing Zhang : tba
(16:30 Paris, 10:30 am NYC)


December 2, 2026

Simon Brendle: tba
(16:30 Paris, 10:30 am NYC)


December 16, 2026

tba
(16:30 Paris, 10:30 am NYC)

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