I will explain how certain geometric properties of groups can be used to study rigidity and non-rigidity of manifolds. In particular, I will discuss how a certain secondary invariants of elliptic operators can be used to estimate the degree of non-rigidity of manifolds. Parts of the work are joint with Erik Guentner, Romain Tessera, Shmuel Weinberger, and Zhizhang Xie. This talk will be accessible to graduate students.
Geometry of groups and rigidity of manifolds
Mar. 17, 2016 3pm (MATH 350)
Probability
Asad Lodhia (MIT)
X
We provide an overview of results on the Central Limit Theorem for Linear Statistics of Eigenvalues. We will discuss how the central limit theorem depends on the scale at which the eigenvalues are analyzed and mention various results. We discuss how universality of the behavior of the Law of Large Numbers (e.g. local semicircle law) relates to universality of the Central Limit Theorem for these statistics.
Geometry of groups and rigidity of manifolds