Differential Geometry Seminar

Past Seminar Schedules and Abstracts:

Spring 2008. Fall 2007. Spring-Summer 2007. Fall 2006. Spring-Summer 2006. Fall 2005. Spring 2005 Fall 2004, Spring 2004, Fall 2003, Spring 2003, Fall 2002, Spring 2002, Fall 2001 Spring 2001.

Schedule, Fall 2008

See also the CUNY Geometry and Topology Seminar.
• Friday August 15: CUNY Isoperimetric Inequalities Workshop
  Speakers: M. Lucia, G. LaNave, M. Ludwig
• Tuesday September 16 (3-4 pm): Kei Kondo (Tokai University)
  Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below
  Abstract: Cohn-Vossen is one of pioneers in global differential geometry. About 70 years ago, he investigated the relationship between the total curvature and the Riemannian structure of complete open surfaces. Some of his results were generalized to any dimensional manifolds : The splitting theorem ([Toponogov, 1959], [Cheeger--Gromoll, 1971]), The classic structure theorems for complete open Riemannian manifolds ([Gromoll--Meyer, 1969], [Cheeger--Gromoll, 1972]). Note that all these results above are assumed to have non-negative curvatures. Here we want to generalize some results of complete open surfaces to higher-dimensional manifolds from radial curvature geometry's standpoint, where the curvature may change signs wildly. In this talk, I would like to talk about the relationship between total curvatures and Busemann functions due to K. Shiohama and our results from recent collaborative works with Professor Minoru Tanaka.
• Tuesday September 23: Jason Behrstock (Lehman College, CUNY)
  "Geometry and Rigidity of Mapping Class Groups"
  Abstract: In this talk accessible to the general geometry/topology audience, we will discuss the geometry of the mapping class group and applications to quasi-isometric rigidity. This will include the recent result that any quasi-isometry of the mapping class group is a bounded distance away from any isometry induced by left multiplication. This has the consequence that any finitely generated group which is quasi-isometric to the mapping class groups is, up to a finite group, isomorphic to it. This talk will cover all relevant definitions and survey the relevant history as well as joint work with B. Kleiner, Y. Minsky, and L. Mosher.
• Tuesday September 30: No meeting
  CUNY holiday
• Tuesday October 7: Michael Puls (John Jay, CUNY)
  "The first reduced l^p- cohomology of finitely generated infinite groups"
  Abstract: We will define the first reduced l^p- cohomology space of a finitely generated infinite group, where p is a real number greater than one. We will then give some results concerning the vanishing and non-vanishing of this space. We will also give links between the first reduced l^p-cohomology space of a group with the p-harmonic functions on the group and various boundaries of the group. This will be an expository talk.
• Tuesday October 14: no meeting
  CUNY on a Monday Schedule
• Tuesday October 21: no meeting
  Conflict with committee meetings
• Friday October 24 (11:00 am -12:00 pm): Reading Seminar
  Mass Transport
  Michael Munn (City Tech, CUNY) presenting
• Tuesday October 28: Dan Lee (Queens College, CUNY)
  Title: The Riemannian Penrose Inequality in dimensions less than 8.
  Abstract: The Riemannian Penrose Inequality was first proved in three dimensions in 1997 by G. Huisken and T. Ilmanen for the case of a single black hole. In 1999, H. Bray extended this result to the general case of multiple black holes using a different technique. I will discuss joint work with H. Bray on extending Bray's technique to dimensions less than 8.
• Tuesday November 4 (1:30-3:00 pm): Reading Seminar (Election Day)
  Title: Mass Transport II
  Michael Munn (City Tech, CUNY) presenting
• Tuesday November 11: no meeting
  Veteran's Day
• Tuesday November 18 (1:30-3:00 pm, 4419): Reading Seminar
  Isoperimetric Inequalities and Mass Transport: Introduction
  Isaac Chavel presenting
• Friday November 21 (11-12:00 Room 3309): Steve Ferry (Rutgers)
  Title: "Gromov-Hausdorff convergence to non-manifolds"
  Abstract: We will discuss families of Riemannian manifolds with a common contractibility function that converge in Gromov-Hausdorff space to non-manifolds. It turns out that these limits have many properties of manifolds, including (at least) simple-homotopy types and rational characteristic classes.
• Friday December 5: Two seminars
  • (11-12:00 Room 3309): Bianca Santoro (Duke)
    Title: "Complete Ricci flat Kahler manifolds with topology at infinity"
    Abstract: In this talk, we plan to explain some existence results for complete Ricci-flat \kahler metrics on special types of manifolds with prescribed behavior at infinity. This result provides an interesting corollary: we are able to construct new examples of Kahler Ricci-flat metrics with richer asymptotic topology.
  • (2-3:00 Room 3309): Fernando Marquez (IMPA)
    Title: The space of positive scalar curvature metrics on the three sphere
    Abstract: We will discuss a proof of the path connectedness of the space of positive scalar curvature metrics on the three sphere. The proof uses Ricci flow with surgery and the connected sum construction of Gromov and Lawson. The work of Perelman on Hamilton's Ricci flow is fundamental.
• Tuesday December 9 (1:30-3:00 pm): Reading Seminar
  Isaac Chavel presents
  isoperimetric inequalities and mass transport
• Tuesday December 16: no meeting
  committee conflict
• Tuesday December 23 (1:30-3:00 pm): Reading Seminar
  Title TBA
  Abstract: TBA