{"id":14160,"date":"2024-04-15T13:09:13","date_gmt":"2024-04-15T18:09:13","guid":{"rendered":"https:\/\/uwm.edu\/math\/?post_type=tribe_events&p=14160"},"modified":"2024-04-15T13:09:13","modified_gmt":"2024-04-15T18:09:13","slug":"graduate-student-colloquium-matt-mcclinton","status":"publish","type":"tribe_events","link":"https:\/\/uwm.edu\/math\/event\/graduate-student-colloquium-matt-mcclinton\/","title":{"rendered":"Graduate Student Colloquium: Matt McClinton"},"content":{"rendered":"

\"\"<\/h1>\n

Harmonize your Fractals<\/h1>\n

Matt McClinton
\nGraduate Student<\/em>
\nUniversity of Wisconsin-Milwaukee<\/p>\n

The 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!<\/p>\n

I 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).<\/p>\n

This 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.<\/p>\n","protected":false},"excerpt":{"rendered":"

Harmonize your Fractals Matt McClinton Graduate Student University of Wisconsin-Milwaukee The 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 …<\/p>\n","protected":false},"author":4217,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":"","uwm_wg_additional_authors":[]},"tags":[],"tribe_events_cat":[70],"class_list":["post-14160","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-graduate-student-colloquia","cat_graduate-student-colloquia"],"yoast_head":"\nMathematical Sciences<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/uwm.edu\/math\/event\/graduate-student-colloquium-matt-mcclinton\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Graduate Student Colloquium: Matt McClinton\" \/>\n<meta property=\"og:description\" content=\"Harmonize your Fractals Matt McClinton Graduate Student University of Wisconsin-Milwaukee The Sierpinski Gasket (SG) is a known fractal object. A simple observation shows that SG is path connected. 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