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DTSTART;TZID=America/Los_Angeles:20220329T123000
DTEND;TZID=America/Los_Angeles:20220329T132000
DTSTAMP:20260413T151745
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SUMMARY:Peg solitaire in multiple colors on graphs (Tara Davis\, Hawaii Pacific University and Roberto Soto\, Cal State Fullerton)
DESCRIPTION:Peg solitaire is a popular one person board game that has been played in many countries on various board shapes. Recently\, peg solitaire has been studied extensively in two colors on mathematical graphs. We will present our rules for multiple color peg solitaire on graphs. We will present some student and faculty results classifying the solvability of the game on several graceful graphs\, as well as discuss open questions.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-tara-davis-hawaii-pacific-university-and-roberto-soto-cal-state-fullerton/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20220329T150000
DTEND;TZID=America/Los_Angeles:20220329T160000
DTSTAMP:20260413T151745
CREATED:20230913T080151Z
LAST-MODIFIED:20230913T080151Z
UID:3230-1648566000-1648569600@colleges.claremont.edu
SUMMARY:Kauffman Bracket Skein Modules and their Structure (Rhea Palak Bakshi\, ETH Zurich)
DESCRIPTION:Skein modules were introduced by Jozef H. Przytycki as generalisations of the Jones and HOMFLYPT polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. The Kauffman bracket skein module (KBSM) is the most extensively studied of all. However\, computing the KBSM of a 3-manifold is notoriously hard\, especially over the ring of Laurent polynomials. With the goal of finding a definite structure of the KBSM over this ring\, several conjectures and theorems were stated over the years for KBSMs. We show that some of these conjectures\, and even theorems\, are not true. In this talk I will briefly discuss a counterexample to Marche’s generalisation of Witten’s conjecture. I will show that a theorem stated by Przytycki in 1999 about the KBSM of the connected sum of two handlebodies does not hold. I will also give the exact structure of the KBSM of the connected sum of two solid tori.
URL:https://colleges.claremont.edu/ccms/event/kauffman-bracket-skein-modules-and-their-structure-rhea-palak-bakshi-eth-zurich/
LOCATION:Zoom
CATEGORIES:Topology Seminar
ORGANIZER;CN="Sam Nelson":MAILTO:snelson@cmc.edu
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220330T161500
DTEND;TZID=America/Los_Angeles:20220330T173000
DTSTAMP:20260413T151745
CREATED:20220311T141931Z
LAST-MODIFIED:20220328T160742Z
UID:2658-1648656900-1648661400@colleges.claremont.edu
SUMMARY:Voronoi Tessellations:  Optimal Quantization and Modeling Collective Behavior (Prof. Rustum Choksi)
DESCRIPTION:Title: Voronoi Tessellations: Optimal Quantization and Modeling Collective Behavior \nSpeaker: Prof. Rustum Choksi\, Department of Mathematics and Statistics\, McGill University \nAbstract:  Given a set of N distinct points (generators) in a domain (a bounded subset of Euclidean space or a compact Riemannian manifold)\, a Voronoi tessellation is a partition of the domain into N regions (Voronoi cells) with the following property: all points in the interior of the ith Voronoi cell are closer to the ith generating point than to any other generator.  Voronoi tessellations give rise to a wealth of analytic\, geometric\, and computational questions. They are also very useful in mathematical and computational modeling. \nThis talk will consist of three parts: \n\nWe begin by introducing the basic definitions and geometry of Voronoi tessellations\,  centroidal Voronoi tessellations (CVTs)\, and the notion of optimal quantization.\nWe will then address simple\, yet rich\, questions on optimal quantization on the 2D and 3D torus\, and on  the 2-sphere. We will address the geometric nature of the global minimizer (the optimal CVT)\, presenting a few conjectures and a short discussion on rigorous asymptotic results and their proofs.\nWe will then shift gears to address the use Voronoi tessellations in modeling collective behaviors.\n\nCollective behavior in biological systems\, in particular the contrast and connection between individual and collective behavior\, has fascinated researchers for decades. A well-studied paradigm entails the tendency of groups of individual agents to form flocks\, swarms\, herds\, schools\, etc. We will first review some well-known and widely used models for collective behavior.  We will then present a new dynamical model for generic crowds in which individual agents are aware of their local Voronoi environment — i.e.\, neighboring agents and domain boundary features –and may seek static target locations. Our model incorporates features common to many other active matter models like collision avoidance\, alignment among agents\, and homing toward targets. However\, it is novel in key respects: the model combines topological and metrical features in a natural manner based upon the local environment of the agent’s Voronoi diagram. With only two parameters\, it captures a wide range of collective behaviors. The results of many simulations will be shown. \n\nRustum Choksi received the PhD degree in mathematics from Brown University\, in 1994. He held post-doctoral positions with the Center for Nonlinear Analysis\, Carnegie Mellon University and the Courant Institute\, New York University. From 1997 to 2010\, he was a faculty member with the Department of Mathematics\, Simon Fraser University. In 2010\, he joined McGill University where he is currently a full professor with the Department of Mathematics and Statistics. His main research interests include interaction of the calculus of variations and partial differential equations with pattern formation.
URL:https://colleges.claremont.edu/ccms/event/voronoi-tessellations-optimal-quantization-and-modeling-collective-behavior-prof-rustum-choksi/
LOCATION:Zoom
CATEGORIES:Colloquium
ORGANIZER;CN="Andrew Bernoff":MAILTO:ajb@hmc.edu
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