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SUMMARY:Noah Snyder (Indiana University)
DTSTART:20200420T200000Z
DTEND:20200420T210000Z
DTSTAMP:20260423T005657Z
UID:ADM-Davis/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ADM-Davis/1/
 ">The exceptional knot polynomial</a>\nby Noah Snyder (Indiana University)
  as part of UC Davis algebra & discrete math seminar\n\n\nAbstract\nMany L
 ie algebras fit into discrete families like $\\operatorname{GL}_n$\, $\\op
 eratorname{O}_n$\, $\\operatorname{Sp}_n$. By work of Brauer\, Deligne and
  others\, the corresponding planar algebras fit into continuous familes $\
 \operatorname{GL}_t$ and $\\operatorname{OSp}_t$. A similar story holds fo
 r quantum groups\, so we can speak of two parameter families $(\\operatorn
 ame{GL}_t)_q$ and $(\\operatorname{OSp}_t)_q$. These planar algebras are t
 he ones attached to the HOMFLY and Kauffman polynomials.  There are a few 
 remaining Lie algebras which don't fit into any of the classical families:
  $G_2$\, $F_4$\, $E_6$\, $E_7$\, and $E_8$. By work of Deligne\, Vogel\, a
 nd Cvitanovic\, there is a conjectural 1-parameter continuous family of pl
 anar algebras which interpolates between these exceptional Lie algebras. S
 imilarly to the classical families\, there ought to be a 2-paramter family
  of planar algebras which introduces a variable q\, and yields a new excep
 tional knotpolynomial. In joint work with Scott Morrison and Dylan Thursto
 n\, we give a skein theoretic description of what this knot polynomial wou
 ld have to look like. In particular\, we show that any braided tensor cate
 gory whose box spaces have the appropriate dimension and which satisfies s
 ome mild assumptions must satisfy these exceptional skein relations.\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/1/
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