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DTSTART:20190331T030000
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DTSTAMP:20190319T054053Z
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\, IST Austria
ORGANIZER:tguggenb@ist.ac.at
SUMMARY:Quantum topology from symplectic geometry
URL:https://talks-calendar.app.ist.ac.at/events/1815
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