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 Events
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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IBM TJ Watson Research Center
Mon 2 Feb 2015, 4:00pm
Department Colloquium
LSK 200
TBA
LSK 200
Mon 2 Feb 2015, 4:00pm-5:00pm

Abstract

Refreshments will be served at 3:40pm in the Math Lounge area, MATH 125 before the colloquium.
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NYU
Tue 3 Feb 2015, 4:00pm
Department Colloquium
MATH 100
TBA
MATH 100
Tue 3 Feb 2015, 4:00pm-5:00pm

Abstract


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UT Austin
Thu 5 Feb 2015, 12:30pm
Department Colloquium
MATX 1100
Applications and Numerical Methods for Optimal Transportation
MATX 1100
Thu 5 Feb 2015, 12:30pm-1:30pm

Abstract

The problem of optimal transportation, which involves finding the most cost-efficient mapping between two measures, arises in many different applications. However, the numerical solution of this problem remains extremely challenging. After surveying several current applications, we describe a numerical method for the widely-studied case when the cost is quadratic. The solution is obtained by solving the Monge-Ampere equation, a fully nonlinear elliptic partial differential equation (PDE), coupled to anon-standard implicit boundary condition. Expressing this problem in terms of weak (viscosity) solutions enables us to construct a monotone finite difference approximation that provably converges to the correct solution. A range of challenging computational examples demonstrate the effectiveness of this method.
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Los Alamos National Laboratory
Thu 5 Feb 2015, 4:00pm
Department Colloquium
ESB 2012 (note changed time and place)
Low Reynolds number flows through shaped and deformable conduits
ESB 2012 (note changed time and place)
Thu 5 Feb 2015, 4:00pm-5:00pm

Abstract

Unconventional fossil energy resources are revolutionizing the US energy market. While the techniques developed over the last 50 years lead to viable and profitable extraction of, e.g., trapped gas and hydrocarbons from almost-impermeable rock formations via hydraulic fracturing, the abysmal extraction rates (typically 15%) suggest the fluid mechanics of these processes is not well understood. In this talk, I will describe three basic theoretical fluid mechanics problems inspired by unconventional fossil fuel extraction. The first problem is flow in a deformable microchannel. Fluid-structure interaction couples the shape of the conduit to the flow through it, drastically altering the flow rate--pressure drop relation. Using perturbation methods, we show that the flow rate is a quartic polynomial of pressure drop for shallow channels, in contrast to the linear relation for rigid conduits. The second problem involves two-phase (gas-liquid) displacement in a horizontal Hele-Shaw cell with an elastic membrane as the top boundary. This problem arises at the pore-scale in enhanced oil recovery for large injection pressures. Once again, fluid-structure interaction alters the problem, leading to stabilization of the Saffman--Taylor (viscous fingering) instability below a critical flow rate. Using lubrication theory, we derive the stability threshold and show that it agrees well with recent experiments. The third problem involves the spread of a viscous liquid in a vertical Hele-Shaw cell with a variable thickness in the flow-wise direction, as a model for the spread of a plume of supercritical carbon dioxide through the non-uniform passages created by hydraulic fracturing. We show that the propagation regimes in such a shaped conduit are set by the direction of propagation. While the rate of spread in the direction of increasing gap thickness (and, hence, permeability) can be obtained by standard scaling techniques, the reverse scenario requires the construction of a so-called second-kind self-similar solution, leading to nontrivial exponents in the rate of spread.

Note for Attendees

Refreshments will be served at 2:40pm in the Math Lounge area, MATH 125 before the colloquium.
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McGill University
Wed 11 Feb 2015, 3:00pm
Department Colloquium
ESB 2012
TBA
ESB 2012
Wed 11 Feb 2015, 3:00pm-4:00pm

Abstract


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Anthony Wachs
IFP Energies nouvelles
Thu 12 Feb 2015, 4:00pm
Department Colloquium
ESB 2012
TBA
ESB 2012
Thu 12 Feb 2015, 4:00pm-5:00pm

Abstract


Note for Attendees

Refreshments will be served at 2:40pm in the Math Lounge area, MATH 125 before the colloquium.
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Stanford U. and UC Irvine
Mon 16 Feb 2015, 3:30pm
Department Colloquium
ESB 2012 (PIMS) (Tentative)
TBA Special PIMS colloquium
ESB 2012 (PIMS) (Tentative)
Mon 16 Feb 2015, 3:30pm-4:30pm

Abstract


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Northwestern University
Mon 23 Feb 2015, 4:00pm
Department Colloquium
LSK 200
TBA
LSK 200
Mon 23 Feb 2015, 4:00pm-5:00pm

Abstract


Note for Attendees

Refreshments will be served at 3:40pm in the Math Lounge area, MATH 125 before the colloquium.
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Caltech
Fri 27 Feb 2015, 3:00pm
Department Colloquium
ESB 2012 (PIMS)
PIMS-UBC distinguished colloquium
ESB 2012 (PIMS)
Fri 27 Feb 2015, 3:00pm-4:00pm

Abstract


Note for Attendees

Coffee, tea and cookies served at 2:30pm in the PIMS Lounge, ESB 4133.
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UCLA
Fri 6 Mar 2015, 3:00pm
Department Colloquium
LSK 200 (Note the special location)
TBA
LSK 200 (Note the special location)
Fri 6 Mar 2015, 3:00pm-4:00pm

Abstract


Note for Attendees

Refreshments will be served at 2:40pm in the Math Lounge area, MATH 125 before the colloquium.
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Brown University
Fri 13 Mar 2015, 3:00pm
Department Colloquium
ESB 2012 (PIMS)
The mathematics of lattice-based cryptography (PIMS-UBC Distinguished Colloquium)
ESB 2012 (PIMS)
Fri 13 Mar 2015, 3:00pm-4:00pm

Abstract


Note for Attendees

Coffee, tea and cookies served at 2:30pm in the PIMS Lounge, ESB 4133.
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UBC
Fri 20 Mar 2015, 3:00pm
Department Colloquium
LSK 200 (Note the special location)
Graduate Research Award Lecture
LSK 200 (Note the special location)
Fri 20 Mar 2015, 3:00pm-4:00pm

Abstract


Note for Attendees

Refreshments will be served at 2:40pm in the Math Lounge area, MATH 125 before the colloquium.
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TBA
Fri 27 Mar 2015, 3:00pm
Department Colloquium
ESB 2012
CRM-Fields-PIMS prize lecture
ESB 2012
Fri 27 Mar 2015, 3:00pm-4:00pm

Abstract


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Fri 11 Sep 2015, 3:00pm
Department Colloquium
reserved
Fri 11 Sep 2015, 3:00pm-4:00pm

Abstract


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Yakov Sinai
Princeton University
Fri 23 Oct 2015, 3:00pm SPECIAL
Department Colloquium / PIMS Seminars and PDF Colloquiums
ESB2012
TBA-PIMS/UBC Distinguished Colloquium
ESB2012
Fri 23 Oct 2015, 3:00pm-4:00pm
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