Wednesday, July 31, 2019
All day 

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07/31/2019  11:00am A metric on a compact manifold M gives rise to a length function on the space of maps of the circle into M, the free loop space LM, whose critical points are the closed geodesics on M in the given metric. Morse theory gives a link between Hamiltonian dynamics and the topology of loop spaces, relating iteration of closed geodesics and the algebraic structure given by the ChasSullivan product and loop coproduct on the homology of LM. We have simplified, chainlevel definitions for the “loop” product and coproduct. The new definitions make possible new links between geometry and loop products. For example, If the kfold coproduct of a homology class X on LM is nontrivial, then every representative of X contains a loop with a (k+1)fold selfintersection. The talk will emphasize geometric motivation and examples. No knowledge of loop products or string topology will be assumed. Joint work with Nathalie Wahl.
Location:
LOM 206
07/31/2019  2:00pm After defining Riemannian manifolds and Integral Current Spaces I will define the Filling Volume of their boundaries. This is a notion first introduced by Gromov and then adapted in joint work with Wenger and with Portegies. I will present sequences of Riemannian manifolds whose volumes remain bounded uniformly away from 0 but whose filling volumes converge to 0.
Location:
LOM 206
07/31/2019  2:00pm After defining Riemannian manifolds and Integral Current Spaces I will define the Filling Volume of their boundaries. This is a notion first introduced by Gromov and then adapted in joint work with Wenger and with Portegies. I will present sequences of Riemannian manifolds whose volumes remain bounded uniformly away from 0 but whose filling volumes converge to 0. Location:
LOM 206
07/31/2019  4:00pm A halfgeodesic is a closed geodesic realizing the distance between any pair of its points. All geodesics in a round sphere are halfgeodesics. Conversely, this talk will establish that Riemannian spheres with all geodesics closed and sufficiently many halfgeodesics are round. This work is joint with Ben Schmidt. Additionally, we will discuss the relationship between these halfgeodesics (more generally 1/kgeodesics) and the GromovHausdorff notion of convergence. Location:
LOM 206
