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SUMMARY:Graduate Student Colloquium: Kimberly Hadaway
DESCRIPTION:On Combinatorial Problems of Generalized Parking Functions\nKimberly Hadaway\nPhD Student\nIowa State University \nIn this talk\, we study combinatorial problems related to generalized parking functions. Our work is motivated by two different research questions posed to us by Dr. Ken Fan and Dr. Shanise Walker. First\, we reframe Dr. Fan’s probabilistic question in terms of defective parking functions\, which enumerate the number of cars unable to park in the classical parking function problem\, thereby providing a partial answer to his question. Second\, we answer Dr. Walker’s question establishing a bijection between unit interval parking functions and the Fubini rankings\, which get their name as they are enumerated by the Fubini numbers.
URL:/math/event/graduate-student-colloquium-kimberly-hadaway/
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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DTSTART;TZID=America/Chicago:20240419T123000
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DTSTAMP:20260423T040932
CREATED:20240415T180913Z
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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:/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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DTSTART;TZID=America/Chicago:20240426T123000
DTEND;TZID=America/Chicago:20240426T133000
DTSTAMP:20260423T040932
CREATED:20240422T160442Z
LAST-MODIFIED:20240422T160442Z
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SUMMARY:Graduate Student Colloquium: Alex Moon
DESCRIPTION:Counting Orbits of Defective Parking Functions\nAlex Moon\nPhD Student\nUniversity of Wisconsin-Milwaukee \nParking functions are well-studied objects in combinatorics and representation theory which constitute tuples of preferred parking spots for cars under a linear parking scheme. This talk will generalize to defective parking functions. I will enumerate the orbits of defective parking functions under the action of the symmetric group by characterizing them as nondecreasing tuples and sketching a bijection to standard nondecreasing parking functions. I will also introduce the concept of the conjugate of a nondecreasing parking function in order to simplify the case where the number of cars and spots differ. \nThis is a joint with Pamela E. Harris\, Aaron Ortiz\, Lauren J. Quesada\, Cynthia Marie Rivera Sánchez\, and Dwight A. Williams II.
URL:/math/event/graduate-student-colloquium-alex-moon/
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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