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 Events
UBC
Mon 26 Jan 2015, 4:00pm
Department Colloquium
LSK 200
Azumaya Algebras and Obstruction Theory
LSK 200
Mon 26 Jan 2015, 4:00pm-5:00pm

Abstract

Azumaya Algebras are a generalization of central simple algebras over fields, and have been studied since the 1950s. In this talk, I shall explain how topological obstruction theory for PGLn bundles can be used to answer questions about Azumaya Algebras over rings.

Note for Attendees

Refreshments will be served at 3:40pm in the Math Lounge area, MATH 125 before the colloquium.
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Oxford Mathematical Institute
Thu 29 Jan 2015, 12:30pm
Department Colloquium
MATX 1100
Stable and Consistent Algorithms for Numerical Computation on Curved Surfaces
MATX 1100
Thu 29 Jan 2015, 12:30pm-2:00pm

Abstract

The Closest Point Method is a set of mathematical principles and associated numerical techniques for solving partial differential equations (PDEs) posed on curved surfaces or other general domains. The method works by embedding the surface in a higher-dimensional space and solving the PDE in that space using simple finite difference and interpolation schemes.

This presentation outlines how a chance encounter with instability improved our understanding of the method and is leading to new formulations with proven convergence properties.

We will also briefly survey some applications in thin-film flows, reaction-diffusion equations, bulk-surface coupling, point clouds, and image processing.

Note for Attendees

 Sushi will be served at the talk. 
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University of Pennsylvania
Fri 30 Jan 2015, 3:00pm
Department Colloquium
LSK 200
The fractional Laplacian operator and its gradient perturbations
LSK 200
Fri 30 Jan 2015, 3:00pm-4:00pm

Abstract

The fractional Laplacian operator plays the same paradigmatic role in the theory of nonlocal operators that the Laplacian plays in the theory of local operators. We will present regularity results for solutions to problems defined by the fractional Laplacian operator with gradient perturbations. Our main results are the regularity of solutions in Sobolev spaces to the linear equation in the supercritical regime, when the operator is not elliptic, and the optimal regularity of solutions to the stationary obstacle problem in the supercritical regime.

This is joint work with Charles Epstein and Arshak Petrosyan.

Note for Attendees

Refreshments will be served at 2:40pm in the Math Lounge area, MATH 125 before the colloquium.
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