Thursday, August 1, 2019
Time  Items 

All day 

10am 
08/01/2019  10:00am In this talk I will define the notion of Generalized Tetrahedral Property which extends Sormani’s Tetrahedral Property. This definition retains all the results of the original TP proven by PortegiesSormani: it provides a lower bound on the sliced filling volume and a lower bound on the volumes of balls. Hence, sequences with uniform GTP have subsequences which converge in both GromovHausdorff and SormaniWenger Intrinsic Flat sense to the same noncollapsed metric space. Through some examples we will see that the main motivation to extend the TP is to include Euclidean cones over metric spaces with small diameter. (Joint work with Jesús NuñezZimbrón) Location:
LOM 206

1pm 
08/01/2019  1:00pm Intuition drawn from quantum mechanics and geometric optics raises the following longstanding problem: is the length spectrum of a closed Riemannian manifold encoded in its Laplace spectrum? That is, can you hear the length spectrum of a manifold? The answer to this question is known to be positive for a generic (i.e. sufficiently “bumpy”) manifold; however, little seems to be known in general. This is especially true for spaces with large symmetry groups. In this talk we’ll report on the progress we’ve made answering this question for symmetric spaces of the compact type and other homogeneous spaces. Location:
LOM 206

4pm 
08/01/2019  4:00pm In a 1978 paper, Gromov explained how the Lipschitz constant of a map S^n > Y, where Y is a simply connected compact Riemannian manifold, restricts its homotopy class. He later conjectured that the bounds obtained there are asymptotically sharp. For example, this would imply that if Y is a closed oriented nmanifold with a disk cut out, then one could always find a C(Y)LLipschitz map which is homotopic to L^n times the puncture, even though you can only get Location:
LOM 206
