University of Toronto

Thu 4 Jan 2018, 3:30pm
SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
TBA

Free Discontinuities in Optimal Transport

TBA
Thu 4 Jan 2018, 3:30pm5:00pm
Abstract
Optimal maps in $R^n$ to disconnected targets necessarily contain discontinuities (i.e.~tears). But how smooth are these tears? When the target components are suitably separated by hyperplanes, nonsmooth versions of the implicit function theorem can be developed which show the tears are hypersurfaces given as differences of convex functions  DC for short. If in addition the targets are convex the tears are actually $C^{1,\alpha}$. Similarly, under suitable affine independence assumptions, singularities of multiplicity $k$ lie on DC rectifiable submanifolds of dimension $n+1k$. These are stable with respect to $W_\infty$ perturbations of the target measure. Moreover, there is at most one singularity of multiplicity $n$. This represents joint work with Jun Kitagawa.
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UCDavies

Tue 9 Jan 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Variational Problems on Arbitrary Sets

ESB 2012
Tue 9 Jan 2018, 3:30pm4:30pm
Abstract
: Let E be an arbitrary subset of R^n. Given real valued functions f defined on E and g defined on R^n, the classical obstacle problem asks for a minimizer of the Dirichlet energy subject to the following two constraints: (1) F = f on E and (2) F lies above g on R^n. In this talk, we will discuss how to use extension theory to construct (almost) solutions directly. We will also explain several recent results that will help lay the foundation for building a complete theory revolving around the belief that any variational problems that can be solved using PDE theory can also be dealt with using extension theory.
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UBC & PIMS

Tue 16 Jan 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar


Tue 16 Jan 2018, 3:30pm4:30pm
Abstract
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University of California, Davis

Tue 20 Mar 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

TBA

ESB 2012
Tue 20 Mar 2018, 3:30pm4:30pm
Abstract
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Eberhard Karls University, Tuebingen

Tue 3 Apr 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

TBA

ESB 2012
Tue 3 Apr 2018, 3:30pm4:30pm
Abstract
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