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DTSTART;TZID=America/Chicago:20241004T123000
DTEND;TZID=America/Chicago:20241004T133000
DTSTAMP:20260420T064212
CREATED:20240925T143928Z
LAST-MODIFIED:20240925T143928Z
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SUMMARY:Graduate Student Colloquium: Jillian Cervantes
DESCRIPTION:(t\,r) Broadcast Domination of the Truncated Square Tiling Graph\nJillian Cervantes\nGraduate Student\nUniversity of Wisconsin – Milwaukee \nThis talk will introduce graph domination theory and a generalization called (t\,r) broadcast domination. We study a family of graphs that arise as a finite subgraph of the truncated square tiling\, which utilizes regular squares and octagons to tile the Euclidean plane. For positive integers m and n\, we let Hm\,n be the graph consisting of m rows of n octagons (cycle graph on 8 vertices). For all t ≥ 2\, we provide lower and upper bounds for the (t\, 1) broadcast domination number for Hm\,n for all m\, n ≥ 1. We give exact (2\, 1) broadcast domination numbers for Hm\,n when (m\, n) ∈ {(1\, 1)\, (1\, 2)\, (1\, 3)\, (1\, 4)\, (2\, 2)}. We also consider the infinite truncated square tiling\, and we provide constructions of infinite (t\, r) broadcasts for (t\, r) ∈ {(2\, 1)\, (2\, 2)\, (3\, 1)\, (3\, 2)\, (3\, 3)\, (4\, 1)}. Using these constructions we give upper bounds on the density of these broadcasts i.e.\, the proportion of vertices needed to (t\, r) broadcast dominate this infinite graph. We end with some directions for future study
URL:/math/event/graduate-student-colloquium-jillian-cervantes/
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:20241011T123000
DTEND;TZID=America/Chicago:20241011T133000
DTSTAMP:20260420T064212
CREATED:20241008T163200Z
LAST-MODIFIED:20241008T163200Z
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SUMMARY:Graduate Student Colloquium: Kelsey Brouwer
DESCRIPTION:Combinatorial Models for Some Generalized McMullen Maps in the Case of Two Bounded Critical Orbits\nKelsey Brouwer\nPhD Student\nUniversity of Wisconsin – Milwaukee \nThe family of generalized McMullen maps R(z)= z^n + b + a/z^n has two independent critical orbits. We consider the case in which one critical value lies in the immediate basin of an attracting cycle and the other critical value eventually lands in that immediate basin. Computer-generated images of the dynamical plane suggest the presence of both baby quadratic Julia sets and some sets which appear to be modifications of those. We present combinatorial models of the dynamics which help to explain this phenomena.
URL:/math/event/graduate-student-colloquium-kelsey-brouwer/
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:20241018T123000
DTEND;TZID=America/Chicago:20241018T133000
DTSTAMP:20260420T064212
CREATED:20241008T150918Z
LAST-MODIFIED:20241008T150918Z
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SUMMARY:Graduate Student Colloquium: Gregory Mwamba
DESCRIPTION:Blowup of the Nonlinear Klein-Gordon Equation in FLRW Spacetimes\nGregory Mwamba\nGraduate Student\nUniversity of California – Merced \nThe nonlinear Klein-Gordon equations are a class of important evolution equations that describe the movement of spinless relativistic particles\, which can lend understanding in many physical applications. In this talk we will demonstrate a sufficient condition for blowup of the nonlinear Klein-Gordon equation\, with arbitrarily positive initial energy in Friedmann-Lemaître-Robertson-Walker spacetimes. This is accomplished using an established concavity method that has been employed for similar PDEs in Minkowski space. This proof relies on the energy inequality associated with this equation. \nThis talk will be online at the following zoom link: https://wisconsin-edu.zoom.us/j/94983351854 and will also be streamed in EMS E495.
URL:/math/event/graduate-student-colloquium-gregory-mwamba/
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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