ChainletTheory and Dynamics.
Connections for Women: Dynamical Systems
January 18, 2007 01:30 PM to 02:30 PM
Speakers:
Harrison, Jenny
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Summary: |
Using chainlets, and elegant calculas is built enabling the study of a wide variety of applications including discrete and continuous domains, soap fils, fractals, vector fields and charged particles. |
Abstract: |
In this lecture we describe a class of objects called 'chainlets', a particularly well-behaved subspace of de Rham currents. Chainlets are a generalization of $k$-surfaces in $n$-space, but with algebraic information encoded both locally and globally. Equipped with a new, 'natural' norm, we discard many cumbersome methods used in geometric measure theory, instead building an elegant calculus from the ground up on domains that include, but are not limited to, discrete and continuous domains, soap films, fractals, vector fields and charged particle. Applications arise in a vast array of applications, from analysis to differential and algebraic topology, calculus of variations, PDEs, dynamical systems, and physics. |
Keywords: |
de Rham currents; Chainlets; Calculus |
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