Columbia Geometry & Analysis Seminar

Fall 2022


The Columbia Geometry/Analysis Seminar takes place in 312 Mathematics Hall on Fridays at 1pm - 2pm.

If you want to join the mailing list, please write to Florian Johne, johne@math.columbia.edu.

 

 

Next talk:

Friday, November 18: Simone Cecchini (Texas A&M University)  

Title of talk: Metric inequalities with positive scalar curvature

Abstract:

We will discuss various situations where a certain perturbation of the Dirac operator on spin manifolds can be used to obtain distance estimates from lower scalar curvature bounds. A first situation consists in an area non-decreasing map from a Riemannian spin manifold with boundary X into the round sphere under the condition that the map is locally constant near the boundary and has nonzero degree. Here a positive lower bound of the scalar curvature is quantitatively related to the distance from the support of the differential of f and the boundary of X. A second situation consists in estimating the distance between the boundary components of Riemannian “bands” M×[−1,1] where M is a closed manifold that does not carry positive scalar curvature. Both situations originated from questions asked by Gromov.
In the final part, I will compare the Dirac method with the minimal hypersurface method and show that if N is a closed manifold such that the cylinder NxR carries a complete metric of positive scalar curvature, then N also carries a metric of positive scalar curvature. This answers a question asked by Rosenberg and Stolz. Some of the results using the Dirac method are joint work with Rudolf Zeidler. The results using the minimal hypersurface method are joint work with Daniel Räde and Rudolf Zeidler.
 
 
 
Schedule of talks this semester

Dates marked by an asterix* will be on Zoom
 
September 23 Keaton Naff (MIT)
The prescribed-point area estimate in space forms
September 30 Paula Burkhardt-Guim (NYU)

ADM mass for $C^0$ metrics and distortion under Ricci-DeTurck flow

October 07 Antonio De Rosa (University of Maryland)
Mix-max construction of anisotropic CMC surfaces
October 14 Hector Chang (Básicas del CIMAT Guanajuato) A non-variational approach for porous media type equations
October 21 Nikola Kamburov (Pontificia Universidad Católica de Chile)
Nondegeneracy and curvature bounds for stable free boundaries
October 28* Jun-cheng Wei (UBC Vancouver)
Nonexistence of Type II blowups  for an energy critical nonlinear heat equation in large dimensions 
November 04 Douglas Stryker (Princeton) Stable minimal hypersurfaces in 4-manifolds
November 11 Manuel del Pino (University of Bath)

Dynamics of concentrated vorticities in 2D and 3D Euler flows

November 18 Simone Cecchini (Texas A&M University)
Metric inequalities with positive scalar curvature
November 25 No seminar due to Thanksgiving  
December 02 Stephen Lynch (Imperial College London) TBA
December 09 Kasia Wyczesany (Brown University)
Optimal transport with respect to costs attaining infinite values