public 44:51

Gary Zhou : Elliptic Curves Over Dedekind Domains

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public 29:56
public 02:34:31

Ashleigh Thomas : Invariants and Metrics for Multiparameter Persistent Homology

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public 43:08

James Colliander : Crowdmark presentation

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public 00:04

M. Lipnowski : M. Lipnowski (Room Reservation)

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public 02:33:52

Thomas Witelski : Math 551 Review session

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public 01:34:43

Yingyi Shen : A study of edge toric ideals using associated graphs

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public 01:34:55

Ben Bellis : Local Computation of the Signature of a Manifold

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public 01:34:50

James Bremer : Improved methods for discretizing integral operators

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Integral equation methods are frequently used in the numerical solution of elliptic boundary value problems. After giving a brief overview of the advantages and disadvantages of such methods vis-a-vis more direct techniques like finite element methods, I will discuss two problems which arise in integral equation methods. In both cases, I take a contrarian position. The first is the discretization of integral operators on singular domains (e.g., surfaces with edges and curves with corners). The consensus opinion holds that integral equations given on such domains are exceedingly difficult to discretize and that sophisticated analysis, often specific to a particular boundary value problem, is required. I will explain that, in fact, the efficient solution of a broad class of such problems can be effected using an elementary approach. Exterior scattering problems given on planar domains with tens of thousands of corner points can be solved to 12 digit accuracy on my two year old desktop computer in a matter of hours. The second problem I will discuss is the evaluation of the singular integrals which arise form the discretization of weakly singular integral operators given on surfaces. Exponentially convergent algorithms for evaluating these integrals have been described in the literature and it is widely regarded as a "solved" problem. I will explain why this is not so and describe an approach which yields only algebraic convergence, but nonetheless performs better in practice than standard exponentially convergent methods.

public 01:34:51

Thomas Witelski : Grant Writing Workshop

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