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PRODID:https://www.calendrier.umontreal.ca/
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UID:603d25942958b
DTSTAMP:20210301T123412
DTSTART:20190902T090000
SEQUENCE:0
TRANSP:OPAQUE
DTEND:20190902T090000
URL:https://www.calendrier.umontreal.ca/detail/876321-serie-de-conferences-
de-la-chaire-aisenstadt-ciprian-manolescu
LOCATION:Université de Montréal - Pavillon André-Aisenstadt\, 2920\, che
min de la Tour\, Montréal\, QC\, Canada\, H3T 1N8
SUMMARY:Série de conférences de la Chaire Aisenstadt Ciprian Manolescu
DESCRIPTION:Première conférence / First Lecture
\n
\nKhovanov homology\,
3-manifolds\, and 4-manifolds
\n
\nKhovanov homology is an invariant of kn
ots in R^3. A major open problem is to extend its definition to knots in o
ther three-manifolds\, and to understand its relation to surfaces in 4-man
ifolds. I will discuss some partial progress in these directions\, from di
fferent perspectives (gauge theory\, representation theory\, sheaf theory)
. In the process I will also review some of the topological applications o
f Khovanov homology.
\nSeconde conférence / Second Lecture
\n
\nKhovanov
homology and surfaces in 4-manifolds
\n
\nBack in 2004\, Rasmussen extract
ed a numerical invariant from Khovanov-Lee homology\, and used it to give
a new proof of Milnorâ€™s conjecture about the slice genus of torus k
nots. In this talk\, I will describe a generalization of Rasmussenâ€™
s invariant to null-homologous knots in S^1 x S^2\, and prove inequalities
that relate it to the genus of surfaces in D^2 x S^2 and in the complex p
rojective space. This is based on joint work with Marco Marengon\, Suchari
t Sarkar\, and Mike Willis.
\nTroisième conférence / Third Lecture
\n
\n
SL(2\,C) Floer homology for knots and 3-manifolds
\n
\nI will explain the
construction of some new homology theories for knots and three-manifolds\,
defined using perverse sheaves on the SL(2\,C) character variety. These i
nvariants are models for an SL(2\,C) version of Floerâ€™s instanton h
omology. I will present a few explicit computations for Brieskorn spheres
and small knots in S^3\, and discuss the connection to the Kapustin-Witten
equations\, Khovanov homology\, skein modules\, and the A-polynomial. The
three-manifold construction is joint work with Mohammed Abouzaid\, and th
e one for knots is joint with Laurent Cote.
\nQuatrième conférence / For
th Lecture
\n
\nGPV invariants and knot complements
\n
\nGukov\, Putrov an
d Vafa predicted (from physics) the existence of some 3-manifold invariant
s that take the form of power series with integer coefficients\, convergin
g in the unit disk. Their radial limits at the roots of unity should recov
er the Witten-Reshetikhin-Turaev invariants. Further\, they should admit a
categorification\, in the spirit of Khovanov homology. Although a mathema
tical definition of the GPV invariants is lacking\, they can be computed i
n many cases. In this talk I will discuss what is known about the GPV inva
riants\, and their behavior with respect to Dehn surgery. The surgery form
ula involves associating to a knot a two-variable series\, obtained by par
ametric resurgence from the asymptotic expansion of the colored Jones poly
nomial. This is based on joint work with Sergei Gukov.
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