10:00 AM  10:35 AM


The Intrinsic Flat Metric between Oriented Rectifiable Metric Spaces and Applications"
Christina Sormani (CUNY, Graduate Center)

 Location
 Evans Hall
 Video


 Abstract
 In the past 25 years great advances were made in the study of Riemannian manifolds and metric measure spaces endowed with a notion of lower bound on Ricci curvature by employing the
GromovHausdorff distance and various notions of metric measure convergence. However, in
many settings one does not have such strong curvature controls including, for example, questions concerning manifolds with only lower bounds on scalar curvature or upper bounds on volume and diameter. In joint work with Stefan Wenger building upon work of AmbrosioKirchheim, we introduced the intrinsic flat distance between compact Riemannian manifolds and, more generally, oriented rectifiable metric spaces of finite Hausdorff measure. Wenger proved a compactness theorem requiring only a uniform upper bound on diameter and volume, and in joint work, we proved convergence with respect to this distance agrees with GH convergence on manifolds with nonnegative Ricci curvature. The relationship with smooth convergence away from singularities was explored in joint work with Sajjad Lakzian who then applied this to understanding Ricci flow through a rotationally symmetric neck pinch singularity. In joint work with Dan Lee, this notion has been applied to show asymptotically flat manifolds of nonnegative scalar curvature are close to Euclidean space if they have sufficiently small ADM mass. In current work in progress with Philippe LeFloch, the relationship between weak H^1 convergence of Riemannian metrics with uniform bounds on ADM mass and intrinsic flat convergence is being explored under rotational symmetry. Most recently, Raquel Perales has begun studying the intrinsic flat limits of Riemannian manifolds with boundary that have uniform control on boundary data without any assumptions on rotational symmetry.
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10:40 AM  11:15 AM


A model for random Riemannian metrics
Lior Silberman (University of British Columbia)

 Location
 Evans Hall
 Video


 Abstract
 "I will describe a model for choosing a random deformation of a Riemannian metric, and some preliminary computations in this model.
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11:20 AM  11:40 AM


Break

 Location
 MSRI: Atrium
 Video


 Abstract
 
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11:40 AM  12:15 PM


Convenient Calculus and Differential Geometry in Infinite dimensions, with Applications to Diffeomorphism Groups and Shape Spaces
Peter Michor (University of Vienna)

 Location
 Evans Hall
 Video


 Abstract
 1. A short introduction to convenient calculus in infinite dimensions.
2. Manifolds of mappings (with compact source) and diffeomorphism
groups as convenient manifolds
3. A diagram of actions of diffeomorphism groups 4. Riemannian geometries of spaces of immersions, diffeomorphism groups, and
shape spaces, their geodesic equations with well posedness results and vanishing geodesic
distance.
5. Riemannian geometries on spaces of Riemannian metrics and pulling them
back to diffeomorphism groups.
6. Robust Infinite Dimensional Riemannian manifolds,
and Riemannian homogeneous spaces of diffeomorphism groups.
We will discuss geodesic equations of many different metrics on these spaces and make contact to many well known equations (CammssaHolm, KdV, HunterSaxton, Euler for ideal fluids).
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12:20 PM  02:20 PM


Lunch

 Location
 MSRI: Atrium
 Video


 Abstract
 
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02:20 PM  02:55 PM


Random hyperbolic surfaces of large genus.
Maryam Mirzakhani (Stanford University)

 Location
 Evans Hall
 Video


 Abstract
 
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03:00 PM  03:35 PM


The Cauchy problem for μHS equation: Weak solutions and integrability
Feride Tiglay (Ohio State University)

 Location
 
 Video


 Abstract
 μHS equation has a physical interpretation in the context of liquid crystals and is derived as an EulerArnold equation on the group of circle diffeomorphisms. Like its ''cousins'' in this framework, it has certain manifestations of integrabilitya Lax pair, a biHamiltonian structure and peakon solutions. I will briefly discuss existence of weak solutions and a way of constructing special functions to integrate the equation.
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03:40 PM  04:00 PM


Break

 Location
 MSRI: Atrium
 Video


 Abstract
 
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04:00 PM  04:35 PM


Diffeomorphism groups, infinite dimensional geometry and Ktheory
Guoliang YU (Texas A & M University)

 Location
 Evans Hall
 Video


 Abstract
 I will discuss how geometry of infinite dimensional manifolds can be used to study Ktheory for certain diffeomorphism groups. The main tool is a noncommutative space (C*algebra) naturally associated to the infinite dimensional manifold. I will try to make this talk accessible to nonexperts. This is joint work with Jianchao Wu.
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04:40 PM  05:15 PM


Riemannian constructions in ideal hydrodynamics
Gerard Misiolek (University of Notre Dame)

 Location
 Evans Hall
 Video


 Abstract
 
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05:20 PM  07:00 PM


Reception and Poster Sesssion

 Location
 MSRI: Atrium
 Video


 Abstract
 
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