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DTSTART:20190331T030000
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DTSTAMP:20260405T192606Z
UID:5c6a9f2e739d1562021608@ist.ac.at
DTSTART:20190311T100000
DTEND:20190311T110000
DESCRIPTION:Speaker: Vivek Shende\nhosted by Tamas Hausel\nAbstract: The di
 scovery of the Jones polynomial in the early 80's was the beginning of qua
 ntum topology'': the introduction of various invariants which\, in one sen
 se or another\, arise from quantum mechanics and quantum field theory.  Th
 ere are many mathematical constructions of these invariants\, but they all
  share the defect of being first defined in terms of a knot diagram\, and 
 only subsequently shown by calculation to be independent of the presentati
 on.  As a consequence\, the geometric meaning has been somewhat opaque. By
  contrast\, in the physics literature\, there is a geometric story: Witten
  showed that the invariants can be extracted from a 3d quantum field theor
 y\, and he later showed that this quantum field theory can be found as a b
 oundary condition in string theory.  However\, it has been difficult to tr
 anslate these ideas into mathematics\, because they a priori depend on inf
 inite dimensional integrals which have no mathematically rigorous definiti
 on. In the talk I will explain how just enough of the open topological str
 ing theory can be made mathematically precise so as to give a manifestly g
 eometric interpretation of the skein relation: it is a boundary term which
  must be set to zero in order to invariantly count holomorphic curves with
  boundary.  As a consequence one finds that the HOMFLY polynomial (a gener
 alization of the Jones polynomial) is a count of holomorphic curves in a c
 ertain 6-dimensional setting which is invariantly and geometrically constr
 ucted from the three-dimensional topology.  This talk draws from the paper
  Skeins on Branes'' written with Tobias Ekholm.
LOCATION:Mondi Seminar Room 2\, Central Building\, ISTA
ORGANIZER:tguggenb@ist.ac.at
SUMMARY:Vivek Shende: Quantum topology from symplectic geometry
URL:https://talks-calendar.ista.ac.at/events/1815
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