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 Events
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, 3:30pm-5:00pm

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, non-smooth 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 $n+1-k$. 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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Kevin Luli
UC-Davies
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, 3:30pm-4:30pm

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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Nicolau Sarquis Aiex
UBC & PIMS
Tue 16 Jan 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
Tue 16 Jan 2018, 3:30pm-4:30pm

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, 3:30pm-4:30pm

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, 3:30pm-4:30pm

Abstract

 
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