Quantitative topology I

  • Datum:


  • Referent:

    Tam Nguyen Phan

  • Zeit:

    16:00 - 17:30

  • We will focus in this 4-lecture series on the following two

    1. Given a null-homotopic map f from S^m to S^n, what is the best
    Lipschitz constant of a null homotopy of f in terms of the Lipschitz
    constant Lip(f) of f?

    2. If a manifold M is null-cobordant, what is the best lower bound of 
    the geometric complexity of a manifold W bounding M in terms of the
    geometric complexity of M?

    (Give M a metric with bounded local geometry, the geometric complexity
    of M is measured by the volume of M.)

    Gromov found that in general the classical methods give bounds that are
    towers of exponentials (in Lip(f) or Vol(M)) but suggested that the true
    bounds are probably linear. We will attempt to explain a recent break
    through of Chambers, Dotterrer, Manin and Weinberger (CDMW) in getting
    the linear bound for the first question and an almost linear bound for
    the second.


    In the first lecture, we will discuss what was known before CDMW's break through.
    The talk is based on an expository paper by Larry Guth