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比利时vs摩洛哥足彩 ,
university of california san diego

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special colloquium

aaron lauda

university of columbia

categorifying quantum groups and link invariants

abstract:

\indent the jones polynomial can be understood in terms of the representation theory of the quantum group associated to $sl2$. this description facilitated a vast generalization of the jones polynomial to other quantum link and tangle invariants called reshetikhin-turaev invariants. these invariants, which arise from representations of quantum groups associated to simple lie algebras, subsequently led to the definition of quantum 3-manifold invariants. in this talk we categorify quantum groups using a simple diagrammatic calculus that requires no previous knowledge of quantum groups. these diagrammatically categorified quantum groups not only lead to a representation theoretic explanation of khovanov homology but also inspired webster's recent work categorifying all reshetikhin-turaev invariants of tangles.

january 18, 2011

1:00 pm

ap&m 6402

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