Politechic University of Catalonia

Tue 13 Oct 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

On singular solutions for the fractional Yamabe problem

ESB 2012
Tue 13 Oct 2015, 3:30pm4:30pm
Abstract
Abstract: We construct some ODE solutions for the fractional Yamabe problem in conformal geometry. The fractional curvature, a generalization of the usual scalar curvature, is defined from the conformal fractional Laplacian, which is a nonlocal operator constructed on the conformal infinity of a conformally compact Einstein manifold.
These ODE solutions are a generalization of the usual Delaunay and, in particular, solve the fractional Yamabe problem
$$ (\Delta)^\gamma u= c_{n, {\gamma}}u^{\frac{n+2\gamma}{n2\gamma}}, u>0 \ \mbox{in} \ \r^n \backslash \{0\},$$
with an isolated singularity at the origin.
This is a fractional order ODE for which new tools need to be developed. The key of the proof is the computation of the fractional Laplacian in polar coordinates.
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University of Tennessee, Knoxville

Tue 27 Oct 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

TBA

ESB 2012
Tue 27 Oct 2015, 3:30pm4:30am
Abstract
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University of Toronto

Tue 5 Jan 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB2012

Vortex filaments in the Euler equation

ESB2012
Tue 5 Jan 2016, 3:30pm4:30pm
Abstract
Abstract: Classical fluid dynamics arguments suggest that in certain
limits, the evolution of thin vortex filaments in an ideal incompressible
fluid should roughly be governed by an equation called the binormal
curvature flow. However, these classical arguments rely on assumptions
that are so unrealistic that it would be hard even to extract from them a
precise conjecture that admits any realistic possibility of a proof. We
present a different approach to this question that yields a reasonable
formulation of a conjecture and strong supporting evidence, and that
clarifies the very substantial obstacles to a full proof. Parts of the
talk are based on joint work with Didier Smets and with Christian Seis
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