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DTSTART:20070311T020000
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DTSTAMP:20230918T145559
DTSTART;TZID=America/Detroit:20230927T160000
DTEND;TZID=America/Detroit:20230927T170000
SUMMARY:Lecture / Discussion:Math Undergraduate Seminar: Constructing equivalence relations between the Spider Category and the Kauffman-Vogel Category
DESCRIPTION:The diagrammatic relations appearing in categories naturally allow us to obtain knot invariants by interpreting knot diagrams within the framework of ribbon categories arising from representation theory. Furthermore\, these categories yield invariants of 3-manifolds which are important topological tools. \n\nIn this talk\, we first introduce the category coming from the representation theory of the quantum group associated to $\mathfrak{sl}_4$ with diagrammatic presentations\, also known as $SL_4$-spider categories. In particular\, we then relate the 3-valent $SL_4$-spider category defined by Cautis-Kamnitzer-Morrison\, to a 4-valent spider category defined using the Kauffman-Vogel relations. By building up the map between these two categories\, we show the equivalence relation between these two categories.
UID:112606-21829175@events.umich.edu
URL:https://events.umich.edu/event/112606
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics,Talk,Undergraduate Students
LOCATION:East Hall - 3096
CONTACT:
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