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BEGIN:VEVENT
SUMMARY:Tudor Dimofte (University of Edinburgh)
DTSTART:20210517T160000Z
DTEND:20210517T170000Z
DTSTAMP:20260404T060946Z
UID:BIRS_21w5105/1
DESCRIPTION:Title: QFT's for non-semisimple TQFT's\nby Tudor Dimofte (Univers
ity of Edinburgh) as part of Perspectives on Knot Homology\n\nAbstract: TB
A\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5105/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Zhang (University of Georgia)
DTSTART:20210517T173000Z
DTEND:20210517T183000Z
DTSTAMP:20260404T060946Z
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\nAbstract\nI will survey link concordance invariants coming from Khovano
v homology\, particularly those similar in spirit to Ozsváth-Stipsicz-Sza
bó's Upsilon\, a 1-parameter family of invariants coming from knot Floer
homology. This is related to my joint work with Linh Truong on annular lin
k concordance invariants as well as ongoing work with Ross Akhmechet.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5105/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ciprian Manolescu (Stanford University)
DTSTART:20210517T190000Z
DTEND:20210517T200000Z
DTSTAMP:20260404T060946Z
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 Ho
mology\n\n\nAbstract\nA well-known strategy to disprove the smooth 4D Poin
care conjecture 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 sug
gested that Rasmussen’s invariant from Khovanov homology could be useful
for this purpose. I will describe how 0-surgery homeomorphisms provide a
large class of potential examples. In particular\, I will show 5 topologic
ally slice knots such that if any of them were slice\, then an exotic 4-sp
here would exist. This is based on joint work with Lisa Piccirillo.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5105/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Ekholm (Uppsala University)
DTSTART:20210518T160000Z
DTEND:20210518T170000Z
DTSTAMP:20260404T060946Z
UID:BIRS_21w5105/4
DESCRIPTION:Title: Skein valued curve counts\, basic holomorphic disks\, and HOMF
LY homology\nby Tobias Ekholm (Uppsala University) as part of Perspect
ives on Knot Homology\n\n\nAbstract\nWe describe invariant counts of holom
orphic curves in a Calabi-Yau 3-fold with boundary in a Lagrangian in the
skein module of that Lagrangian. We show how to turn this into concrete c
ounts for the toric brane in the resolved conifold. This leads to a notion
of basic holomorphic disks for any knot conormal in the resolved conifold
. These basic holomorphic disks seem to generate HOMFLY homology in the ba
sic representation. We give a conjectural description of similar holomorph
ic object generating parts of higher symmetric representation HOMFLY homol
ogy and verify some predictions coming from this conjecture in examples.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5105/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edward Witten (Institute of Advanced Study)
DTSTART:20210518T173000Z
DTEND:20210518T183000Z
DTSTAMP:20260404T060946Z
UID:BIRS_21w5105/5
DESCRIPTION:Title: Knot Homology From Gauge Theory\nby Edward Witten (Institu
te of Advanced Study) as part of Perspectives on Knot Homology\n\n\nAbstra
ct\nIn this talk\, I will motivate the equations of gauge theory in four o
r five dimensions that can be used to give a dual description of the Jones
polynomial by counting solutions of certain elliptic partial differential
equations\, and a construction of Khovanov homology.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5105/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugene Gorsky (UC Davis)
DTSTART:20210518T190000Z
DTEND:20210518T200000Z
DTSTAMP:20260404T060946Z
UID:BIRS_21w5105/6
DESCRIPTION:Title: Tautological classes and symmetry in Khovanov-Rozansky homolog
y\nby Eugene Gorsky (UC Davis) as part of Perspectives on Knot Homolog
y\n\n\nAbstract\nWe define a new family of commuting operators F_k in Khov
anov-Rozansky link homology\, similar to the action of tautological classe
s in cohomology of character varieties. We prove that F_2 satisfies "hard
Lefshetz property" and hence exhibits the symmetry in Khovanov-Rozansky ho
mology conjectured by Dunfield\, Gukov and Rasmussen. This is a joint work
with Matt Hogancamp and Anton Mellit.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5105/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Lipshitz (University of Oregon)
DTSTART:20210519T160000Z
DTEND:20210519T170000Z
DTSTAMP:20260404T060946Z
UID:BIRS_21w5105/7
DESCRIPTION:Title: Khovanov stable homotopy type and friends\nby Robert Lipsh
itz (University of Oregon) as part of Perspectives on Knot Homology\n\n\nA
bstract\nWe will discuss properties of the stable homotopy refinement of K
hovanov homology and some aspects of its construction. We will focus on fe
atures that also appear for other Floer-type invariants\, and on gaps in o
ur understanding. The results are joint with Tyler Lawson and Sucharit Sar
kar (or are due to other people).\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5105/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mina Aganagic (University of Berkeley)
DTSTART:20210519T173000Z
DTEND:20210519T183000Z
DTSTAMP:20260404T060946Z
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://stable.researchseminars.org/talk/BIRS_21w5105/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis-Hadrien Robert (Universite du Luxembourg)
DTSTART:20210520T160000Z
DTEND:20210520T170000Z
DTSTAMP:20260404T060946Z
UID:BIRS_21w5105/9
DESCRIPTION:Title: Foam evaluation\, link homology and Soergel bimodules\nby
Louis-Hadrien Robert (Universite du Luxembourg) as part of Perspectives on
Knot Homology\n\n\nAbstract\nFoams are surfaces with singularities which
can be thought of as\ncobordisms between graphs. Foam evaluation is a comb
inatorial formula\nwhich associates a symmetric polynomial to any closed f
oam. I will\ndescribe this combinatorial formula and explain how it can be
used to\nconstruct link homology theories. Finally I will relate foam eva
luation\nto Soergel bimodules and give a foamy description of their Hochsc
hild\nhomology.\nJoint with Mikhail Khovanov and Emmanuel Wagner.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5105/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Willis (UCLA.)
DTSTART:20210520T173000Z
DTEND:20210520T183000Z
DTSTAMP:20260404T060946Z
UID:BIRS_21w5105/10
DESCRIPTION:by Michael Willis (UCLA.) as part of Perspectives on Knot Homo
logy\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5105/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Webster (University of Waterloo)
DTSTART:20210520T190000Z
DTEND:20210520T200000Z
DTSTAMP:20260404T060946Z
UID:BIRS_21w5105/11
DESCRIPTION:Title: Knot homology from coherent sheaves on Coulomb branches\n
by Ben Webster (University of Waterloo) as part of Perspectives on Knot Ho
mology\n\n\nAbstract\nRecent work of Aganagic details the construction of
a homological knot invariant categorifying the Reshetikhin-Turaev invarian
ts of miniscule representations of type ADE Lie algebras\, using the geome
try and physics of coherent sheaves on a space which one can alternately d
escribe as a resolved slice in the affine Grassmannian\, a space of G-mono
poles with specified singularities\, or as the Coulomb branch of the corre
sponding 3d quiver gauge theories. We give a construction of this invarian
t using an algebraic perspective on BFN's construction of the Coulomb bran
ch\, and in fact extend it to an invariant of annular knots. This depends
on the theory of line operators in the corresponding quiver gauge theory a
nd their relationship to non-commutative resolutions of these varieties (g
eneralizing Bezrukavnikov's non-commutative Springer resolution).\n
LOCATION:https://stable.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:20260404T060946Z
UID:BIRS_21w5105/12
DESCRIPTION:Title: Invariants of 4-manifolds from Khovanov-Rozansky link homolog
y\nby Paul Wedrich (Max Planck Institute for Mathematics and Universit
y of Bonn) as part of Perspectives on Knot Homology\n\n\nAbstract\nRibbon
categories are 3-dimensional algebraic structures that control quantum lin
k polynomials and that give rise to 3-manifold invariants known as skein m
odules. I will describe how to use Khovanov-Rozansky link homology\, a cat
egorification of the gl(N) quantum link polynomial\, to obtain a 4-dimensi
onal algebraic structure that gives rise to vector space-valued invariants
of smooth 4-manifolds. The technical heart of this construction is the fu
nctoriality of Khovanov-Rozansky homology in the 3-sphere. Based on joint
work with Scott Morrison and Kevin Walker.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5105/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (California Institute of Technology)
DTSTART:20210521T173000Z
DTEND:20210521T183000Z
DTSTAMP:20260404T060946Z
UID:BIRS_21w5105/13
DESCRIPTION:Title: From knot homology to 3-manifold homology\nby Sergei Guko
v (California Institute of Technology) as part of Perspectives on Knot Hom
ology\n\n\nAbstract\nWhat do annular Khovanov homology\, Ozsvath-Szabo's "
correction terms"\, Kapustin-Witten equations\, and enumerative BPS invari
ants have in common? The goal of the talk will be to explain\, from multip
le perspectives\, how this structure makes a somewhat surprising appearanc
e in a problem of generalizing Khovanov homology to homology of knots in a
rbitrary 3-manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5105/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ina Petkova (Dartmouth)
DTSTART:20210521T190000Z
DTEND:20210521T200000Z
DTSTAMP:20260404T060946Z
UID:BIRS_21w5105/14
DESCRIPTION:Title: Annular link Floer homology and gl(1|1)\nby Ina Petkova (
Dartmouth) as part of Perspectives on Knot Homology\n\n\nAbstract\nThe Res
hetikhin-Turaev construction for the quantum group U_q(gl(1|1)) sends tang
les to C(q)-linear maps in such a way that a knot is sent to its Alexander
polynomial. Tangle Floer homology is a combinatorial generalization of kn
ot Floer homology which sends tangles to (homotopy equivalence classes of)
bigraded dg bimodules. In earlier work with Ellis and Vertesi\, we show t
hat tangle Floer homology categorifies a Reshetikhin-Turaev invariant aris
ing naturally in the representation theory of U_q(gl(1|1))\; we further co
nstruct 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 Fl
oer homology 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://stable.researchseminars.org/talk/BIRS_21w5105/14/
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