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BEGIN:VEVENT
SUMMARY:Tudor Dimofte (University of Edinburgh)
DTSTART:20210517T160000Z
DTEND:20210517T170000Z
DTSTAMP:20260422T185127Z
UID:BIRS_21w5105/1
DESCRIPTION:Title: QFT's for non-semisimple TQFT's\nby Tudor Dimofte (University of
Edinburgh) as part of Perspectives on Knot Homology\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5105/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Zhang (University of Georgia)
DTSTART:20210517T173000Z
DTEND:20210517T183000Z
DTSTAMP:20260422T185127Z
UID:BIRS_21w5105/2
DESCRIPTION:Title: Upsilon-like invariants from Khovanov homology\nby Melissa Zhang
(University of Georgia) as part of Perspectives on Knot Homology\n\n\nAbst
ract\nI will survey link concordance invariants coming from Khovanov homol
ogy\, particularly those similar in spirit to Ozsváth-Stipsicz-Szabó's U
psilon\, a 1-parameter family of invariants coming from knot Floer homolog
y. This is related to my joint work with Linh Truong on annular link conco
rdance invariants as well as ongoing work with Ross Akhmechet.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5105/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ciprian Manolescu (Stanford University)
DTSTART:20210517T190000Z
DTEND:20210517T200000Z
DTSTAMP:20260422T185127Z
UID:BIRS_21w5105/3
DESCRIPTION:Title: Khovanov homology and the search for exotic 4-spheres\nby Ciprian
Manolescu (Stanford University) as part of Perspectives on Knot Homology\
n\n\nAbstract\nA well-known strategy to disprove the smooth 4D Poincare co
njecture is to find a knot that bounds a disk in a homotopy 4-ball but not
in the standard 4-ball. Freedman\, Gompf\, Morrison and Walker suggested
that Rasmussen’s invariant from Khovanov homology could be useful for th
is purpose. I will describe how 0-surgery homeomorphisms provide a large c
lass of potential examples. In particular\, I will show 5 topologically sl
ice knots such that if any of them were slice\, then an exotic 4-sphere wo
uld exist. This is based on joint work with Lisa Piccirillo.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5105/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Ekholm (Uppsala University)
DTSTART:20210518T160000Z
DTEND:20210518T170000Z
DTSTAMP:20260422T185127Z
UID:BIRS_21w5105/4
DESCRIPTION:Title: Skein valued curve counts\, basic holomorphic disks\, and HOMFLY homo
logy\nby Tobias Ekholm (Uppsala University) as part of Perspectives on
Knot Homology\n\n\nAbstract\nWe describe invariant counts of holomorphic
curves in a Calabi-Yau 3-fold with boundary in a Lagrangian in the skein m
odule of that Lagrangian. We show how to turn this into concrete counts f
or the toric brane in the resolved conifold. This leads to a notion of bas
ic holomorphic disks for any knot conormal in the resolved conifold. These
basic holomorphic disks seem to generate HOMFLY homology in the basic rep
resentation. We give a conjectural description of similar holomorphic obje
ct generating parts of higher symmetric representation HOMFLY homology and
verify some predictions coming from this conjecture in examples.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5105/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edward Witten (Institute of Advanced Study)
DTSTART:20210518T173000Z
DTEND:20210518T183000Z
DTSTAMP:20260422T185127Z
UID:BIRS_21w5105/5
DESCRIPTION:Title: Knot Homology From Gauge Theory\nby Edward Witten (Institute of A
dvanced Study) as part of Perspectives on Knot Homology\n\n\nAbstract\nIn
this talk\, I will motivate the equations of gauge theory in four or five
dimensions that can be used to give a dual description of the Jones polyno
mial by counting solutions of certain elliptic partial differential equati
ons\, and a construction of Khovanov homology.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5105/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugene Gorsky (UC Davis)
DTSTART:20210518T190000Z
DTEND:20210518T200000Z
DTSTAMP:20260422T185127Z
UID:BIRS_21w5105/6
DESCRIPTION:Title: Tautological classes and symmetry in Khovanov-Rozansky homology\n
by Eugene Gorsky (UC Davis) as part of Perspectives on Knot Homology\n\n\n
Abstract\nWe define a new family of commuting operators F_k in Khovanov-Ro
zansky link homology\, similar to the action of tautological classes in co
homology of character varieties. We prove that F_2 satisfies "hard Lefshet
z property" and hence exhibits the symmetry in Khovanov-Rozansky homology
conjectured by Dunfield\, Gukov and Rasmussen. This is a joint work with M
att Hogancamp and Anton Mellit.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5105/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Lipshitz (University of Oregon)
DTSTART:20210519T160000Z
DTEND:20210519T170000Z
DTSTAMP:20260422T185127Z
UID:BIRS_21w5105/7
DESCRIPTION:Title: Khovanov stable homotopy type and friends\nby Robert Lipshitz (Un
iversity of Oregon) as part of Perspectives on Knot Homology\n\n\nAbstract
\nWe will discuss properties of the stable homotopy refinement of Khovanov
homology and some aspects of its construction. We will focus on features
that also appear for other Floer-type invariants\, and on gaps in our unde
rstanding. The results are joint with Tyler Lawson and Sucharit Sarkar (or
are due to other people).\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5105/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mina Aganagic (University of Berkeley)
DTSTART:20210519T173000Z
DTEND:20210519T183000Z
DTSTAMP:20260422T185127Z
UID:BIRS_21w5105/8
DESCRIPTION:by Mina Aganagic (University of Berkeley) as part of Perspecti
ves on Knot Homology\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5105/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis-Hadrien Robert (Universite du Luxembourg)
DTSTART:20210520T160000Z
DTEND:20210520T170000Z
DTSTAMP:20260422T185127Z
UID:BIRS_21w5105/9
DESCRIPTION:Title: Foam evaluation\, link homology and Soergel bimodules\nby Louis-H
adrien Robert (Universite du Luxembourg) as part of Perspectives on Knot H
omology\n\n\nAbstract\nFoams are surfaces with singularities which can be
thought of as\ncobordisms between graphs. Foam evaluation is a combinatori
al formula\nwhich associates a symmetric polynomial to any closed foam. I
will\ndescribe this combinatorial formula and explain how it can be used t
o\nconstruct link homology theories. Finally I will relate foam evaluation
\nto Soergel bimodules and give a foamy description of their Hochschild\nh
omology.\nJoint with Mikhail Khovanov and Emmanuel Wagner.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5105/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Willis (UCLA.)
DTSTART:20210520T173000Z
DTEND:20210520T183000Z
DTSTAMP:20260422T185127Z
UID:BIRS_21w5105/10
DESCRIPTION:by Michael Willis (UCLA.) as part of Perspectives on Knot Homo
logy\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5105/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Webster (University of Waterloo)
DTSTART:20210520T190000Z
DTEND:20210520T200000Z
DTSTAMP:20260422T185127Z
UID:BIRS_21w5105/11
DESCRIPTION:Title: Knot homology from coherent sheaves on Coulomb branches\nby Ben
Webster (University of Waterloo) as part of Perspectives on Knot Homology\
n\n\nAbstract\nRecent work of Aganagic details the construction of a homol
ogical knot invariant categorifying the Reshetikhin-Turaev invariants of m
iniscule representations of type ADE Lie algebras\, using the geometry and
physics of coherent sheaves on a space which one can alternately describe
as a resolved slice in the affine Grassmannian\, a space of G-monopoles w
ith specified singularities\, or as the Coulomb branch of the correspondin
g 3d quiver gauge theories. We give a construction of this invariant using
an algebraic perspective on BFN's construction of the Coulomb branch\, an
d in fact extend it to an invariant of annular knots. This depends on the
theory of line operators in the corresponding quiver gauge theory and thei
r relationship to non-commutative resolutions of these varieties (generali
zing Bezrukavnikov's non-commutative Springer resolution).\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5105/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Wedrich (Max Planck Institute for Mathematics and University
of Bonn)
DTSTART:20210521T160000Z
DTEND:20210521T170000Z
DTSTAMP:20260422T185127Z
UID:BIRS_21w5105/12
DESCRIPTION:Title: Invariants of 4-manifolds from Khovanov-Rozansky link homology\n
by Paul Wedrich (Max Planck Institute for Mathematics and University of Bo
nn) as part of Perspectives on Knot Homology\n\n\nAbstract\nRibbon categor
ies are 3-dimensional algebraic structures that control quantum link polyn
omials and that give rise to 3-manifold invariants known as skein modules.
I will describe how to use Khovanov-Rozansky link homology\, a categorifi
cation of the gl(N) quantum link polynomial\, to obtain a 4-dimensional al
gebraic structure that gives rise to vector space-valued invariants of smo
oth 4-manifolds. The technical heart of this construction is the functoria
lity of Khovanov-Rozansky homology in the 3-sphere. Based on joint work wi
th Scott Morrison and Kevin Walker.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5105/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (California Institute of Technology)
DTSTART:20210521T173000Z
DTEND:20210521T183000Z
DTSTAMP:20260422T185127Z
UID:BIRS_21w5105/13
DESCRIPTION:Title: From knot homology to 3-manifold homology\nby Sergei Gukov (Cali
fornia Institute of Technology) as part of Perspectives on Knot Homology\n
\n\nAbstract\nWhat do annular Khovanov homology\, Ozsvath-Szabo's "correct
ion terms"\, Kapustin-Witten equations\, and enumerative BPS invariants ha
ve in common? The goal of the talk will be to explain\, from multiple pers
pectives\, how this structure makes a somewhat surprising appearance in a
problem of generalizing Khovanov homology to homology of knots in arbitrar
y 3-manifolds.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5105/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ina Petkova (Dartmouth)
DTSTART:20210521T190000Z
DTEND:20210521T200000Z
DTSTAMP:20260422T185127Z
UID:BIRS_21w5105/14
DESCRIPTION:Title: Annular link Floer homology and gl(1|1)\nby Ina Petkova (Dartmou
th) as part of Perspectives on Knot Homology\n\n\nAbstract\nThe Reshetikhi
n-Turaev construction for the quantum group U_q(gl(1|1)) sends tangles to
C(q)-linear maps in such a way that a knot is sent to its Alexander polyno
mial. Tangle Floer homology is a combinatorial generalization of knot Floe
r homology which sends tangles to (homotopy equivalence classes of) bigrad
ed dg bimodules. In earlier work with Ellis and Vertesi\, we show that tan
gle Floer homology categorifies a Reshetikhin-Turaev invariant arising nat
urally in the representation theory of U_q(gl(1|1))\; we further construct
bimodules \\E and \\F corresponding to E\, F in U_q(gl(1|1)) that satisfy
appropriate categorified relations. After a brief summary of this earlier
work\, I will discuss how the horizontal trace of the \\E and \\F actions
on tangle Floer homology gives a gl(1|1) action on annular link Floer hom
ology that has an interpretation as a count of certain holomorphic curves.
This is based on joint work in progress with Andy Manion and Mike Wong.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5105/14/
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