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 Events
Mon 26 Jan 2015, 1:00pm
Math Education Research Reading
MATX1118
"Student learning and perceptions in a flipped linear algebra course" by Betty Love, Angie Hodgea, Neal Grandgenettb & Andrew W. Swifta
MATX1118
Mon 26 Jan 2015, 1:00pm-2:00pm

Abstract


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DWAVE
Mon 26 Jan 2015, 3:00pm
Institute of Applied Mathematics
LSK 460
Quantum computation: from DWAVE to sheaves
LSK 460
Mon 26 Jan 2015, 3:00pm-4:00pm

Abstract

I start with DWAVE, a successful BC company building and selling quantum computers. I go through the math, the chip and the controversies. I explain how one can program DWAVE machines and solve NP hard problems. I then talk about measurement based quantum computation (MBQC, also a BC product), lots of math, no controversies but no machines. I explain how it relates to Einstein–Podolsky–Rosen paradox and topos theory.

Note for Attendees

 Tea and cookies beforehand in the IAM lounge, LSK 306
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Stanford University
Mon 26 Jan 2015, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127
Picard Groups of K3 Moduli Spaces
ESB 4127
Mon 26 Jan 2015, 3:00pm-4:00pm

Abstract

  Polarized K3 surfaces of genus g can be thought of as families of canonical curves.  As such, their moduli space K_g has similar properties to M_g.  For instance, both are unirational for low values of g, and both have discrete Picard group.  In this talk, we will use the explicit unirationality of K_g to compute its Picard number in a few cases, which verifies the Noether-Lefschetz conjecture for genus up to 10.
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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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U. of Pennsylvania
Thu 29 Jan 2015, 3:30pm
Probability Seminar
MATH 104
Harnack inequalities for degenerate diffusions
MATH 104
Thu 29 Jan 2015, 3:30pm-5:00pm

Abstract


Abstract: We will present probabilistic and analytic properties of a class of degenerate diffusion operators arising in population genetics, the so-called generalized Kimura diffusion operators. Such processes arise as models for the evolution of gene frequencies. We will start by highlighting the main questions of interest and the mathematical difficulties in addressing them. Our main results are a stochastic representation of weak solutions to a degenerate parabolic equation with singular lower-order coefficients, and the proof of the scale-invariant Harnack inequality for nonnegative solutions to the Kimura parabolic equation. The stochastic representation of solutions that we establish is a considerable generalization of the classical results on Feynman-Kac formulas concerning the assumptions on the degeneracy of the diffusion matrix, the boundedness of the drift coefficients, and on the a priori regularity of the weak solutions.

This is joint work with Charles Epstein.
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SFU
Thu 29 Jan 2015, 3:30pm
Number Theory Seminar
room ASB 10940 (SFU - IRMACS)
Genus 2 curves with (3, 3)-isogenies and 3-torsion in Sha
room ASB 10940 (SFU - IRMACS)
Thu 29 Jan 2015, 3:30pm-4:30pm

Abstract

We parametrize genus 2 curves with a maximal isotropic (Z/3)2 in their Jacobian, together with an explicit description of the associated isogeny. This allows us to perform (3, 3)-isogeny descent on various simple principally polarized abelian surfaces and exhibit non-trivial 3-part in their Tate-Shafarevich groups. This is joint work with Victor Flynn and Damiano Testa.
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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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