Metric-S14

Metric Geometry Reading Seminar Spring 2014

Scalar Curvature and Convergence

This Spring semester, Professor Sormani's Metric Geometry Reading Seminar organized jointly with Dr. Sinaei will be held Thursday afternoons 12:35-1:20 pm right before Gromov's Special Topics Course (which is 1:25-3:15 pm in the same classroom 1302 WWH at NYU). We met January- March and will take a break until after our top level students have defended their dissertations.

Gromov's course concerns:

  • "Schoen-Yau's Incompresible Minimal Surfaces and Positive Scalar Curvature" [Schoen-Yau-Inc] *

  • "Spin, Dirac Operators, A hat genus and Scalar Curvature" c.f. [Gromov-sign] [Spin Geometry]

  • "Gromov-Lawson's work on Scalar Curvature, Enlargeability and Tori" [GL-Annals-80-1] c.f. [Gromov-sign]

  • "Gromov-Lawson's Classification of Simply Connected Manifolds" [GL-Annals-80-2]

  • "Gromov-Lawson's Positive Scalar Curvature and the Dirac Operator on Complete Manifolds" [GL-IHES-83]

and Gromov's recent preprints: "Plateau Stein Manifolds" and "Dirac and Plateau Billiards in Domains with Corners".

Our seminar focused on the convergence of Riemannian manifolds including Gromov Hausdorff Convergence and Intrinsic Flat Convergence. See "How Manifolds Converge" for a survey. At this time there is no known notion of convergence which is well suited to nonnegative scalar curvature. Gromov's recent preprints suggest that intrinsic flat convergence may be a useful notion in this setting.

Before the semester begins we will have two meetings in which senior visiting participants will be presenting their own recent research:

  • Tu 1/21: 4214:03 CUNYGC 12:30-1:30 pm: "Bartnik's Conjecure of Prescibed Scalar Curvature"

    • presented by Chen-Yun Lin [Lin]

  • Th 1/23: 4214:03 CUNYGC 12:30-1:30 pm: "Almost Rigidity of the Positive Mass Theorem"

  • presented by Dan Lee, [Schoen-Yau-PMT] [Lee-Sormani]

Spring 2014 Schedule [Thursdays 12:35-1:20 1304 WWH at NYU]

  • Th 1/30: "Gromov-Hausdorff Convergence"

    • presented by Christina Sormani (CUNY) [G][BBI]

  • Th 2/06: "Gromov's Compactness Theorem"

    • presented by Raquel Perales (SUNYSB) [G][BBI] (2/13 no meeting due to storm)

  • Th 2/20: "Schoen-Yau's Structures of Manifolds with Positive Scalar Curvature"

  • presented by Pei-Ken Hung (Columbia) [Schoen-Yau-Str] c.f. [Gromov-sign] [Spin Geometry]

  • Th 2/27: "Ambrosio-Kirchheim's Currents and Minimal Surfaces on Metric Spaces"

  • presented by Jacobus Portegies (Courant) [AK]

  • Th 3/06*: NO MEETING

  • because Professors Gromov and Sormani are out of town

  • Th 3/13: "Intrinsic Flat Convergence"

    • presented by Christina Sormani (CUNY) [SW]

  • Th 3/20: NO MEETING

  • because it is NYU's Spring Break

  • Th 3/27: "Schoen-Yau's Incompresible Minimal Surfaces and Positive Scalar Curvature"

  • presented by Zahra Sinaei (Courant) [Schoen-Yau-Inc] *

Prior Semesters:

Metric Geometry Spring-Summer 2012, at CUNY GC

Metric Geometry Fall 2012, at CUNY GC

Metric Geometry Spring 2013 at CUNY GC

Metric Geometry Fall 2013 at MSRI

This Summer:

CUNY Converging Metric Spaces Workshop 8/7/2014-8/8/2014