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SUMMARY:Graduate Student Colloquium: Matt McClinton
DESCRIPTION:Harmonize your Fractals\nMatt McClinton\nGraduate Student\nUniversity of Wisconsin-Milwaukee \nThe Sierpinski Gasket (SG) is a known fractal object. A simple observation shows that SG is path connected. Unfortunately\, the infinitely jagged structure of the Gasket prevents these paths from being differentiable. If only there existed a means of smoothing out SG into an object where continuous and differentiable paths existed between pairs of points. As a matter of fact there is! \nI will demonstrate the technique known as “minimizing the graph energy” as described in the late Robert Strichartz’s book “Differential Equations on Fractals”. This technique involves finding the solution to a system of equations where the solution produces a graph that has differentiable paths\, and even better satisfies the Laplacian. Using a homeomorphic mapping defined by Jun Kigami in 1989\, by finding the graph energy minimizing values on level sets of SG\, we produce a fractal object known as the Harmonic Sierpinski Gasket (HSG). \nThis talk is intended for those that are interested in analysis\, algebra\, combinatorics\, topology\, fractal geometry\, and/or graph theory. Any necessary background information will be provided during the talk\, and I will end with some open problems.
URL:https://uwm.edu/math/event/graduate-student-colloquium-matt-mcclinton/
LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States
CATEGORIES:Graduate Student Colloquia
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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