Geometric Structures seminar - David Tewodrose, February 24, 2022

[Miruna - Stefana Sorea]

Dear All,

This is to announce the next seminar from the series "Geometric Structures".

Speaker:   David Tewodrose<http://www.google.com/url?q=http%3A%2F%2Fwww.davidtewodrose.com%2FHomepage.F.htm&sa=D&sntz=1&usg=AFQjCNHyBgL9nkBaYi-H_lKoXTWsqyAJzw> (Nantes Université)

Title:          Kato limit spaces

Time:*        February 24, 2022, 2:00 pm (Rome Time)



Venue - hybrid:

  *   at room 134 at SISSA
  *
  *   from remote, on zoom at this link

https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
Passcode: geometry


Abstract:
Consider a sequence of Riemannian manifolds. Assume that this sequence converges, in the measured Gromov-Hausdorff sense, to a possibly non-smooth metric measure space. What are the properties of this limit space? In a series of celebrated works from the nineties, Cheeger and Colding addressed this question under the assumption of a uniform lower bound on the Ricci curvature of the manifolds. This has led to the fruitful development of a synthetic theory of Ricci curvature lower bounds. In this talk, I will present a couple of joint works with Gilles Carron (Nantes Université) and Ilaria Mondello (Université de Créteil) where we relax the uniform Ricci lower bound assumption and work in the context of a weaker uniform Kato-type assumption, namely that the part of the lowest eigenvalue of the Ricci tensor lying under a certain threshold belongs to a given Kato class. Under this assumption which authorizes the Ricci curvature to degenerate to - infinity but in a « heat-kernel controlled » way, we show that most results of Cheeger and Colding are still true, including rectifiability on which I shall focus.



More information can be found here: https://sites.google.com/view/geometric-structures/

Everyone is welcome!


--
Miruna-Stefana Sorea
Postdoctoral Researcher
Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy
https://sites.google.com/view/mirunastefanasorea/