Columbia Geometry & Analysis Seminar

Spring 2023

The Columbia Geometry/Analysis Seminar takes place in 507 Mathematics Hall on Fridays at 1pm - 2pm.

If you want to join the mailing list, please write to Florian Johne,



Next talk:

Friday, March 24: Shuli Chen (Stanford University)

Title of talk: Morse index of minimal hypersurfaces and minimal submanifolds in projective spaces

In this talk we will study the Morse index of minimal hypersurfaces and more generally, minimal submanifolds in projective spaces.
First we look at stable minimal submanifolds. We will talk about works of Simons, Lawson-Simons and Ohnita on the classification of compact stable minimal submanifolds in all compact rank one symmetric spaces, and consider the generalization to product manifolds. We will show that there do not exist odd-dimensional compact stable minimal immersions in the product of two complex projective spaces, and classify the stable minimal submanifolds in the product of a quaternionic projective space (resp. octonionic projective plane) with any other Riemannian manifold. This part is joint work with Alejandra Ramirez Luna (UCSC).
Next, we specialize to minimal hypersurfaces and consider higher Morse index. We will show that for an embedded unstable one-sided minimal hypersurface of the (n+1)-dimensional real projective space, the Morse index is at least n+2, and this bound can be attained by the cubic isoparametric hypersurfaces.
Schedule of talks this semester

Dates marked by an asterix* will be on Zoom
January 27 Thomas Koerber (University of Vienna)

Schoen's conjecture for limits of isoperimetric surfaces

February 03 No seminar


February 10

Christos Mantoulidis (Rice University)

Generic regularity of minimizing hypersurfaces in dimensions 9 and 10
February 17 (*)

Wenkui Du (University of Toronto)

Ancient solutions of mean curvature flow
February 24

Nam Le (Indiana University Bloomington)

Convergence of an inverse iterative scheme for the Hessian eigenvalue
March 03

Daniel Restrepo (University of Texas, Austin)

The Volume Preserving Mean Curvature Flow from the perspective of phase transistions
March 10

Mary Vaughan (University of Texas, Austin)

Regularity theory for fractional elliptic equations in nondivergence form
March 17 No seminar due to spring break


March 24

Shuli Chen (Stanford University)

Morse index of minimal hypersurfaces and minimal submanifolds in projective spaces
March 31

Bernhard Hanke (University of Augsburg)

April 07

Nikos Kapouleas (Brown University, TBC)


April 14


April 21

Pablo Mira (Universidad Politécnica de Cartagena)

April 28

Po-Ning Chen (UC Riverside)