BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Francesco Lin (Columbia)
DTSTART:20200416T190000Z
DTEND:20200416T200000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/1
DESCRIPTION:Title: Monopole Floer homology\, eigenform multiplicities and t
he Seifert-Weber dodecahedral space\nby Francesco Lin (Columbia) as pa
rt of Gauge theory virtual\n\n\nAbstract\nThis is joint work with M. Lipno
wski. We show that the Seifert-Weber dodecahedral space SW is an L-space.
The proof builds on our work relating Floer homology and spectral geometry
of hyperbolic three-manifolds. A direct application of our previous techn
iques runs into difficulties arising from the computational complexity of
the problem. We overcome this by exploiting the large symmetry group and t
he arithmetic and tetrahedral group structure of SW to prove that small ei
genvalues on coexact 1-forms must have large multiplicity.\n\nThe link to
the paper on the arxiv is https
://arxiv.org/abs/2003.11165.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Alfieri (University of British Columbia)
DTSTART:20200423T190000Z
DTEND:20200423T200000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/2
DESCRIPTION:Title: Instanton Floer homology of almost-rational plumbings\nby Antonio Alfieri (University of British Columbia) as part of Gauge th
eory virtual\n\n\nAbstract\nPlumbed three-manifolds are those three-manifo
lds that can be be realized as links of isolated complex surface singulari
ties. Inspired by Heegaard Floer theory Nemethi introduced a combinatorial
invariant of complex surface singularities (lattice cohomology) that is c
onjectured to be isomorphic to\nHeegaard Floer\nhomology. I will expose so
me recent work in collaboration with John Baldwin\, Irving Dai\, and Steve
n Sivek showing that the lattice cohomology of an almost-rational singular
ity is isomorphic to the framed instanton Floer homology of its link. The
proof goes through lattice cohomology and makes use of the decomposition a
long characteristic vectors of the instanton cobordism maps recently found
by Baldwin and Sivek.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Kronheimer (Harvard University)
DTSTART:20200430T190000Z
DTEND:20200430T200000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/3
DESCRIPTION:Title: Dehn twists in dimension four\nby Peter Kronheimer (
Harvard University) as part of Gauge theory virtual\n\n\nAbstract\nIf a sm
ooth oriented manifold M contains an embedded codimension-1 sphere\, then
one may define a diffeomorphism of M supported in a neighborhood of that s
phere\, generalizing the familiar Dehn twist along a closed curve in a 2-m
anifold. In this talk\, I will explain how Seiberg-Witten theory can be us
ed to show that this Dehn twist is not isotopic to the identity in the cas
e that M is a connected sum K3#K3 (regarded as a smooth 4-manifold). This
is joint work with Tom Mrowka. The talk will include some background and c
ontext for the question\, and can be treated as a prequel to the talk give
n earlier in this series by Jianfeng Lin.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gleb Smirnov (ETH Zurich)
DTSTART:20200507T190000Z
DTEND:20200507T200000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/4
DESCRIPTION:Title: The Atiyah flop and diffeomorphism groups\nby Gleb S
mirnov (ETH Zurich) as part of Gauge theory virtual\n\n\nAbstract\nFollowi
ng a short introduction to the flop surgery\, I will explain how this bira
tional transformation can be used to detect non-contractible loops in the
diffeomorphism group of the product of 2-spheres and some other algebraic
surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sherry Gong (UCLA)
DTSTART:20201029T190000Z
DTEND:20201029T200000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/5
DESCRIPTION:Title: Non-orientable link cobordisms and torsion order in Floe
r homologies\nby Sherry Gong (UCLA) as part of Gauge theory virtual\n\
n\nAbstract\nIn a recent paper\, Juhasz\, Miller and Zemke proved an inequ
ality involving the number of local maxima and the genus appearing in an o
riented knot cobordism using a version of knot Floer homology. In this tal
k I will be discussing some similar inequalities for non-orientable knot c
obordisms using the torsion orders of unoriented versions of knot Floer ho
mology and instanton Floer homology. This is a joint work with Marco Maren
gon.\n\nThe link to the paper on arxiv is https://arxiv.org/abs/2010.06577
\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Donghao Wang (MIT)
DTSTART:20201105T200000Z
DTEND:20201105T210000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/6
DESCRIPTION:Title: Monopole Floer homology for 3-manifolds with toroidal bo
undary\nby Donghao Wang (MIT) as part of Gauge theory virtual\n\n\nAbs
tract\nThe monopole Floer homology of an oriented closed 3-manifold was\nd
efined by Kronheimer-Mrowka around 2007 and has greatly influenced\nthe st
udy of 3-manifold topology since its inception. \nIn this talk\, we will g
eneralize their construction and define the\nmonopole Floer homology for a
ny pair (Y\, ω)\, where Y is a compact\noriented 3-manifold with toroidal
boundary and ω is a suitable closed\n2-form. The graded Euler characteri
stic of this Floer homology recovers the Milnor-Turaev torsion invariant b
y a classical theorem of\nMeng-Taubes. It satisfies a reasonable (3+1) TQF
T property. In the\nend\, we will explain its relation with gauged Landau-
Ginzburg models\nand point out some future directions.\n\nThe link to the
paper is https://arxiv.org/pdf/2005.04333.pdf\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhenkun Li (Stanford University)
DTSTART:20201112T200000Z
DTEND:20201112T210000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/7
DESCRIPTION:Title: Instanton Floer homology of (1\,1)-knots\nby Zhenkun
Li (Stanford University) as part of Gauge theory virtual\n\n\nAbstract\nI
nstanton knot homology was first introduced by Floer around 1990 and was r
evisited by Kronheimer and Mrowka around 2010. It is built based on the so
lution to a set of partial differential equations and is very difficult to
compute. On the other hand\, Heegaard diagrams are classical tools to des
cribe knots and 3-manifolds combinatorially\, and is also the basis of Hee
gaard Floer theory\, which was introduced by Ozsváth and Szabó around 20
04. In this talk\, I will explain how to extract some information about in
stanton theory from Heegaard diagrams. In particular\, we study the (1\,1)
-knots\, which are known to have simple Heegaard diagrams. We provide an u
pper bound for the dimension of instanton knot homology for all (1\,1)-kno
ts. Also\, we prove that\, for some families of (1\,1)-knots\, including a
ll torus knots\, the upper bound we obtained is in fact sharp. If time per
mits\, I will also discuss on some further applications to the instanton F
loer homology of 3-manifolds coming from Dehn surgeries along null-homolog
ous knots. This is a joint work with Fan Ye.\n\nThe link to the paper is h
ttps://arxiv.org/abs/2010.07836\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Fredrickson (University of Oregon)
DTSTART:20201119T200000Z
DTEND:20201119T210000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/8
DESCRIPTION:Title: The asymptotic geometry of the Hitchin moduli space\
nby Laura Fredrickson (University of Oregon) as part of Gauge theory virtu
al\n\n\nAbstract\nHitchin’s equations are a system of gauge theoretic eq
uations on a Riemann surface that are of interest in many areas including
representation theory\, Teichmuller theory\, and the geometric Langlands c
orrespondence. The Hitchin moduli space carries a natural hyperkahler metr
ic. A conjectural description of its asymptotic structure appears in the w
ork of physicists Gaiotto-Moore-Neitzke and there has been a lot of progre
ss on this recently. I will discuss some recent results.\n\nA link to a re
cent paper is https://arxiv.org/abs/2001.03682.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Feehan (Rutgers)
DTSTART:20201210T200000Z
DTEND:20201210T210000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/9
DESCRIPTION:Title: Morse-Bott theory on analytic spaces and applications to
to topology of smooth 4-manifolds\nby Paul Feehan (Rutgers) as part o
f Gauge theory virtual\n\n\nAbstract\nWe describe define a new approach to
Morse theory on singular analytic spaces of the kind that typically arise
in gauge theory\, such as the moduli space of SO(3) monopoles over 4-mani
folds or the moduli space of Higgs pairs over Riemann surfaces. We explain
how this new version of Morse theory\, called virtual Morse-Bott theory\,
can potentially be used to answer questions arising in the geography of 4
-manifolds\, such as whether constraints on the topology of compact comple
x surfaces of general type continue to hold for symplectic 4-manifolds or
even for smooth 4-manifolds of Seiberg-Witten simple type.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boyu Zhang (Princeton University)
DTSTART:20201203T200000Z
DTEND:20201203T210000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/10
DESCRIPTION:Title: Several detection results for Khovanov homology on link
s\nby Boyu Zhang (Princeton University) as part of Gauge theory virtua
l\n\n\nAbstract\nIn this talk\, I will present several new detection resul
ts of Khovanov homology on links. In particular\, we show that if L is an
n-component link with Khovanov homology of rank 2^n\, then it is given by
the connected sums and disjoint unions of unknots and Hopf links. This res
ult gives a positive answer to a question asked by Batson-Seed\, and it ge
neralizes the unlink detection theorem by Hedden-Ni and Batson-Seed. The p
roofs of this result and the other detection results presented in this tal
k rely on a new excision formula for singular instanton Floer homology. Th
is talk is based on works that are joint with Yi Xie and partially joint w
ith Zhenkun Li.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hokuto Konno (University of Tokyo)
DTSTART:20210119T230000Z
DTEND:20210120T000000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/11
DESCRIPTION:Title: Seiberg-Witten theory for families I\nby Hokuto Kon
no (University of Tokyo) as part of Gauge theory virtual\n\n\nAbstract\nI
survey recent development of Seiberg-Witten theory for smooth families of
closed 4-manifolds. Current main applications of this direction are variou
s comparisons between the homeomorphism groups and the diffeomorphism grou
ps of 4-manifolds. I try to sketch basic ideas of this area\, and to descr
ibe such applications in detail.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masaki Taniguchi (iTHEMS/RIKEN)
DTSTART:20210121T230000Z
DTEND:20210122T000000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/12
DESCRIPTION:Title: Gauge theory on 4-manifolds with periodic ends I\nb
y Masaki Taniguchi (iTHEMS/RIKEN) as part of Gauge theory virtual\n\n\nAbs
tract\nWe first review the historical backgrounds of Yang-Mills and Seiber
g-Witten gauge theory for non-compact 4-manifolds having cylindrical\, per
iodic\, or conical ends. Then\, we focus on YM-gauge theory on 4-manifolds
with periodic ends. As a generalization of Taubes’s compactness theorem
of the ASD-moduli spaces for 4-manifolds with periodic ends\, we show a s
imilar compactness theorem under some energy condition. As an application\
, we construct an obstruction to a certain type of embeddings of 3-manifol
ds into 4-manifolds. The obstruction lies in the filtered versions of inst
anton Floer cohomology.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hokuto Konno (University of Tokyo)
DTSTART:20210128T230000Z
DTEND:20210129T000000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/13
DESCRIPTION:Title: Seiberg-Witten theory for families II\nby Hokuto Ko
nno (University of Tokyo) as part of Gauge theory virtual\n\n\nAbstract\nI
n this latter half I shall focus on recent joint work with Masaki\nTaniguc
hi (https://arxiv.org/abs/2010.00340). This is an extension of a part of t
he last story to families of 4-manifolds with boundary\, again with applic
ations to comparisons between the homeomorphism groups and the diffeomorph
ism groups. A main tool in the proofs of main results is a family version
of the relative Bauer-Furuta invariant\, which takes values in Manolescu
’s Seiberg-Witten Floer stable homotopy type.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masaki Taniguchi (iTHEMS/RIKEN)
DTSTART:20210202T230000Z
DTEND:20210203T000000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/14
DESCRIPTION:Title: Gauge theory on 4-manifolds with periodic ends II\n
by Masaki Taniguchi (iTHEMS/RIKEN) as part of Gauge theory virtual\n\n\nAb
stract\nAs a sequel to the first talk “Gauge theory on 4-manifolds with
periodic ends I”\, we talk about Seiberg-Witten theory for 4-manifolds w
ith periodic ends. This is joint work with Hokuto Konno. We show 10/8-type
inequalities for spin periodic-end-4-manifolds having periodic positive s
calar curvature metrics on the ends. In the main step of the proof\, we us
e a certain compactness theorem for the Seiberg-Witten moduli spaces for t
he periodic-end-4-manifolds proved by Jianfeng Lin. As an application\, we
give a new obstruction to positive scalar curvature metric for a certain
class of homology $S^1\\times S^3$’s.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juanita Pinzón Caicedo (Notre Dame)
DTSTART:20210209T230000Z
DTEND:20210210T000000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/15
DESCRIPTION:Title: Toroidal integer homology spheres have irreducible SU(2
)-representations\nby Juanita Pinzón Caicedo (Notre Dame) as part of
Gauge theory virtual\n\n\nAbstract\nThe fundamental group is one of the mo
st powerful invariants to distinguish closed three-manifolds. One measure
of the non-triviality of a three-manifold is the existence of non-trivial
SU(2)-representations. In this talk I will show that if an integer homolog
y three-sphere contains an embedded incompressible torus\, then its fundam
ental group admits irreducible SU(2)-representations. This is joint work w
ith Tye Lidman and Raphael Zentner.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Baraglia (University of Adelaide)
DTSTART:20210216T230000Z
DTEND:20210217T000000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/16
DESCRIPTION:Title: Tautological classes of definite 4-manifolds\nby Da
vid Baraglia (University of Adelaide) as part of Gauge theory virtual\n\n\
nAbstract\nTautological classes are characteristic classes of manifold bun
dles. They have been extensively studied for bundles of surfaces\, where t
hey were first introduced by Mumford in the setting of moduli spaces of cu
rves. In higher dimensions there are not many examples of manifolds for wh
ich the tautological ring\, the ring generated by tautological classes\, i
s known. We will use gauge theory to study tautological classes of 4-manif
olds with positive definite intersection form. Amongst other things\, this
allows us to compute the tautological ring for $CP^2$ and the connected s
um of $CP^2$ with itself.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cliff Taubes (Harvard University)
DTSTART:20210310T193000Z
DTEND:20210310T203000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/17
DESCRIPTION:Title: Morse theory\, configuration spaces and Z/2 eigenfuncti
ons for the Laplacian on 2-sphere.\nby Cliff Taubes (Harvard Universit
y) as part of Gauge theory virtual\n\n\nAbstract\nI once thought that the
Laplacian on the round 2-sphere would have nothing new to offer. As it tur
ns out\, I was wrong. I will describe a set of eigenfunction/eigenvalue pr
oblems on the 2-sphere that Yingying Wu and I are studying that take every
opportunity to do the unexpected. There is a gauge theory tie-in too.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Kotelskiy (Indiana University)
DTSTART:20210303T193000Z
DTEND:20210303T203000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/18
DESCRIPTION:Title: The earring correspondence on the pillowcase.\nby A
rtem Kotelskiy (Indiana University) as part of Gauge theory virtual\n\n\nA
bstract\nGiven a decomposition of a knot K into two four-ended tangles T a
nd T’\, the (holonomy perturbed) traceless-SU(2)-character-variety funct
or produces Lagrangians R(T) and R(T’) in the pillowcase P. Hedden\, Her
ald and Kirk used this to define Pillowcase homology\, conjecturally the s
ymplectic counter-part of the singular instanton homology I(K). Important
in their construction is how R(T) and its restriction to P are affected by
“adding an earring”\, a process used by Kronheimer and Mrowka to avoi
d reducibles. The object that governs this process turns out to be an imme
rsed Lagrangian correspondence from pillowcase to itself. We will describe
this correspondence in detail\, and study its action on Lagrangians. In t
he case of the (4\,5) torus knot\, we will see that a correction term from
the bounding cochains must be added. We will indicate a particular figure
eight bubble which recovers the desired bounding cochain\, as predicted b
y Bottman and Wehrheim. This is joint work with G. Cazassus\, C. Herald an
d P. Kirk.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tadayuki Watanabe (Shimane University)
DTSTART:20210223T230000Z
DTEND:20210224T000000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/19
DESCRIPTION:Title: Trivalent graphs and diffeomorphisms of some 4-manifold
s\nby Tadayuki Watanabe (Shimane University) as part of Gauge theory v
irtual\n\n\nAbstract\nI will explain a geometric method to construct famil
ies of\ndiffeomorphisms of manifolds by using a higher dimensional analogu
e of\nGoussarov-Habiro’s trivalent graph surgery in 3-dimension. This wo
uld\nproduce lots of potentially nontrivial families of diffeomorphisms of
\nmanifolds. In particular\, our construction gives that the homotopy\ngro
ups $\\pi_k \\mathrm{Diff}_{\\partial}(D^4) \\otimes \\mathbb{Q}$ are\nnon
-trivial for many $k$. This is a disproof of the 4-dimensional Smale\nconj
ecture. These non-trivialities can be detected by Kontsevich’s\nconfigur
ation space integrals.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksander Doan (Columbia University)
DTSTART:20210317T183000Z
DTEND:20210317T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/20
DESCRIPTION:Title: Counting pseudo-holomorphic curves in symplectic six-ma
nifolds\nby Aleksander Doan (Columbia University) as part of Gauge the
ory virtual\n\n\nAbstract\nThe signed count of embedded pseudo-holomorphic
curves in a symplectic manifold typically depends on the choice of an alm
ost complex structure on the manifold and so does not lead to a symplectic
invariant. However\, I will discuss two instances in which such naive cou
nting does define a symplectic invariant. The proof of invariance combines
methods of symplectic geometry with results of geometric measure theory.
I will also talk about an idea of defining invariants of symplectic six-ma
nifolds by counting pseudo-holomorphic curves and solutions of gauge-theor
etic equations. The talk is based on joint work with Thomas Walpuski.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dave Auckly (Kansas State University)
DTSTART:20210324T183000Z
DTEND:20210324T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/21
DESCRIPTION:Title: Exotic Families of Diffeomorphisms and Embeddings\n
by Dave Auckly (Kansas State University) as part of Gauge theory virtual\n
\n\nAbstract\nThis will describe joint work with Danny Ruberman demonstrat
ing that the kernel of the map on any homotopy of the diffeomorphism group
to the homotopy group of the homeomorphism group of certain $4$-manifolds
can be very large. We will also discuss an analogous result for smooth an
d continuous families of embeddings. The talk will discuss the constructio
n of these exotic families as well as the computation of the Yang-Mills ba
sed invariant that establishes the non-triviality of the families.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillem Cazassus (University of Oxford)
DTSTART:20210331T183000Z
DTEND:20210331T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/22
DESCRIPTION:Title: Hopf algebras\, equivariant Lagrangian Floer homology\,
and cornered instanton theory\nby Guillem Cazassus (University of Oxf
ord) as part of Gauge theory virtual\n\n\nAbstract\nLet G be a compact Lie
group acting on a symplectic manifold M in a Hamiltonian way. If $L\, L
’$ is a pair of Lagrangians in M\, we show that the Floer complex $CF(L\
,L’)$ is an $A_\\infty$ module over the Morse complex CM(G) (which has
an $A_\\infty$ algebra structure involving the group multiplication). This
permits to define several versions of equivariant Floer homology.\n\nIt a
lso implies that the Fukaya categoy Fuk(M)\, in addition to its own $A_\\i
nfty$ structure\, is an $A_\\infty$ module over CM(G). These two structu
res can be packaged into a single one: CM(G) is an $A_\\infty$ bialgebra\,
and Fuk(M) is a module over it. In fact\, CM(G) should have more structur
e\, it should be a Hopf-infinity algebra\, a structure (still unclear to u
s) that should induce the Hopf algebra structure on $H_*(G)$.\n\nApplied t
o some subsets of Huebschmann-Jeffrey’s extended moduli spaces introduce
d by Manolescu and Woodward\, this construction should permit to define a
cornered instanton theory analogous to Douglas-Lipshitz-Manolescu’s cons
truction in Heegaard-Floer theory. This is work in progress\, joint with P
aul Kirk\, Artem Kotelskiy\, Mike Miller and Wai-Kit Yeung.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Duncan (James Madison University)
DTSTART:20210407T183000Z
DTEND:20210407T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/23
DESCRIPTION:Title: Gluing mASD connections.\nby David Duncan (James Ma
dison University) as part of Gauge theory virtual\n\n\nAbstract\nTaubes’
gluing theorems establish existence for ASD connections on closed 4-manif
olds. We discuss recent extensions of these gluing results to the mASD-con
nections of Morgan–Mrowka–Ruberman on cylindrical end 4-manifolds. Thi
s is joint work with Ian Hambleton.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Wang (Harvard University)
DTSTART:20210414T183000Z
DTEND:20210414T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/24
DESCRIPTION:Title: Floer and Khovanov homologies of band sums\nby Josh
ua Wang (Harvard University) as part of Gauge theory virtual\n\n\nAbstract
\nGiven a nontrivial band sum of two knots\, we may add full twists to the
band to obtain a family of knots indexed by the integers. In this talk\,
I’ll show that the knots in this family have the same Heegaard knot Floe
r homology and the same instanton knot Floer homology but distinct Khovano
v homology\, generalizing a result of M. Hedden and L. Watson. A key compo
nent of the argument is a proof that each of the three knot homologies det
ects the trivial band. The main application is a verification of the gener
alized cosmetic crossing conjecture for split links.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andriy Haydys (Freiburg University)
DTSTART:20210421T183000Z
DTEND:20210421T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/25
DESCRIPTION:Title: Topology of the blow up set for the Seiberg-Witten equa
tions with two spinors\nby Andriy Haydys (Freiburg University) as part
of Gauge theory virtual\n\n\nAbstract\nAn arbitrary sequence of the Seibe
rg-Witten monopoles with two spinors on a three-manifold may well be diver
gent due to the energy concentration along a one-dimensional subset Z\, wh
ich I refer to as a blow up set. It turns out that blow up sets have inter
esting topological properties\, for example in the case the background thr
ee-manifold is a rational homology sphere the Alexander polynomial of Z ev
aluated at $t=-1$ must vanish (under certain conditions\, which I will des
cribe in the talk). I will report about this and other related properties
of blow up sets.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Herald (University of Nevada\, Reno)
DTSTART:20210428T183000Z
DTEND:20210428T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/26
DESCRIPTION:Title: Relative character varieties of tangles in 3-manifolds
and holonomy perturbed flat moduli spaces\nby Chris Herald (University
of Nevada\, Reno) as part of Gauge theory virtual\n\n\nAbstract\nThe trac
eless SU(2) character variety of a tangle in a 3-manifold with boundary is
defined to be the set of representations of the tangle complement fundame
ntal group into SU(2) sending tangle meridians to traceless elements\, up
to conjugation. This character variety may be identified with the flat mod
uli space that plays a central role in singular instanton homology. In thi
s gauge theoretic context\, there is a notion of holonomy perturbations\,
which provide a framework to solve transversality problems with flat modul
i spaces\; this notion can be translated back into topological terms to de
fine holonomy perturbed traceless character varieties.\n\nWe’ll show tha
t the restriction map from the holonomy perturbed traceless character vari
ety of a tangle to the traceless character variety of the marked boundary
surface is a Lagrangian immersion at every regular point. The proof avoids
any gauge theoretic analysis\, but makes use of composition in the Weinst
ein category\, the fact that holonomy perturbations in a cylinder induce H
amiltonian isotopies\, and Poincaré duality. This is joint work with Guil
lem Cazassus and Paul Kirk.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Miller (Columbia University)
DTSTART:20210505T183000Z
DTEND:20210505T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/27
DESCRIPTION:Title: Invariance and functoriality in equivariant instanton h
omology\nby Mike Miller (Columbia University) as part of Gauge theory
virtual\n\n\nAbstract\nPreviously\, the author defined an infinite-dimensi
onal SO(3)-equivariant chain complex for rational homology spheres and “
admissible bundles”\, and showed the existence of cobordism maps under s
ome restrictive conditions. This was enough to show that the equivariant i
nstanton homology groups I(Y) depend on at most a small amount of auxiliar
y data (in addition to the choice of 3-manifold): “signature data”\, w
hich is roughly the choice of even integer for every first homology class.
To prove that I(Y) is independent of this choice\, we need cobordism maps
that do not satisfy those restrictive conditions — which involve a fail
ure of equivariant transversality\, a notoriously slippery issue to deal w
ith.\n\nWe will first discuss a new finite-dimensional model for the equiv
ariant instanton chain complex\, and try to get a concrete handle on what
it looks like. We’ll then talk about how obstructed gluing theory allows
us to define a “corrected moduli space”\, satisfying more appropriate
gluing relations\, which allows us to get the “wrong-way” cobordism m
ap needed for invariance above. With invariance handled\, we are able to p
rove that we have cobordism maps under any negative-definite or admissible
cobordism\, with no conditions on signature.\n\nWe will conclude with a d
iscussion of potential applications and future directions. This work is jo
int with Ali Daemi.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Langte Ma (Stonybrook University)
DTSTART:20210512T183000Z
DTEND:20210512T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/28
DESCRIPTION:Title: Torus Signature And Periodic Rho Invariant\nby Lang
te Ma (Stonybrook University) as part of Gauge theory virtual\n\n\nAbstrac
t\nLet T in X be an essentially embedded torus in a homology $S^1 \\times
S^3$. There are two approaches defining an equivariant signature invariant
for\nthe pair (X\, T): one introduced by Echeverria as the signed count o
f degree zero singular instantons\; the other given by Ruberman as the the
rho invariant of the cross-section of the 0-surgered manifold of X along
T. Both invariants\nrecover the Levine-Tristram signature in the case of a
product $S^1 \\times (Y\, K)$ with K a knot in an integral homology spher
e Y. We show that these two invariants are equivalent. The proof is to rel
ate both invariants to the periodic\nrho invariant of the ASD DeRham opera
tor. The relation with a conjecture of Furuta-Ohta will also be discussed.
\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariano Echeverria (Rutgers University)
DTSTART:20210519T183000Z
DTEND:20210519T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/29
DESCRIPTION:Title: The SO(3) vortex equations over orbifold Riemann surfac
es\nby Mariano Echeverria (Rutgers University) as part of Gauge theory
virtual\n\n\nAbstract\nWe study the general properties of the moduli spac
es of SO(3) vortices over orbifold Riemann surfaces and use these to chara
cterize the solutions of the SO(3) monopole equations on Seifert manifolds
following in the footsteps of Mrowka\, Ozsváth and Yu.\n\nWe also study
the solutions to the SO(3) monopole equations on the product of a circle a
nd a surface in order to motivate the construction of a version of monopol
e Floer homology\, which we call framed monopole Floer homology\, in analo
gy with the construction given by Kronheimer and Mrowka for the case of in
stanton Floer homology.\n\nFinally\, the SO(3) vortex moduli spaces provid
e a nice toy model for recent work due to Feehan and Leness regarding the
study of a natural Morse-Bott function on the moduli space of SO(3) monopo
les over Kahler manifolds. In particular\, we compute the Morse-Bott indic
es of this function.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Rasmussen (University of Cambridge)
DTSTART:20210526T183000Z
DTEND:20210526T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/30
DESCRIPTION:Title: An $SL_2(R)$ Casson-Lin Invariant\nby Jacob Rasmuss
en (University of Cambridge) as part of Gauge theory virtual\n\n\nAbstract
\nIn the early 90’s X.S. Lin defined an invariant of a knot K in $S^3$\,
which counts irreducible representations of the knot group into $SU(2)$\n
which have fixed meridinal holonomy. I’ll discuss an analogous construct
ion\, but with $SL_2(R)$ in place of $SU(2)$. The sum of the two invariant
s turns out to be independent of the choice of the meridinal\nholonomy. Th
is fact has applications to a number of problems\, including the construct
ion of left-orders on 3-manifolds obtained from the knot complement and th
e existence of real parabolic representations on the\nknot complement.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Marengon (Max Planck Institute)
DTSTART:20210602T183000Z
DTEND:20210602T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/31
DESCRIPTION:Title: Relative genus bounds in indefinite 4-manifolds\nby
Marco Marengon (Max Planck Institute) as part of Gauge theory virtual\n\n
\nAbstract\nGiven a closed 4-manifold X with an indefinite intersection fo
rm\, we consider smoothly embedded surfaces in X-int($B^4$)\, with boundar
y a given knot K in the 3-sphere.\nWe give several methods to bound the ge
nus of such surfaces in a fixed homology class. Our techniques include adj
unction inequalities from Heegaard Floer homology and the Bauer-Furuta inv
ariants\, and the 10/8 theorem.\nIn particular\, we present obstructions t
o a knot being H-slice (that is\, bounding a null-homologous disc) in a 4-
manifold and show that the set of H-slice knots can detect exotic smooth s
tructures on closed 4-manifolds.\n\nThis is joint work with Ciprian Manole
scu and Lisa Piccirillo.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Baldwin (Boston College)
DTSTART:20211007T173000Z
DTEND:20211007T183000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/32
DESCRIPTION:Title: Fixed points\, Khovanov homology\, and Dehn surgery
\nby John Baldwin (Boston College) as part of Gauge theory virtual\n\n\nAb
stract\nWe partially characterize L-space knots of genus 2\, in both the H
eegaard and instanton Floer settings\, using relationships between these t
heories and the symplectic Floer cohomology of surface diffeomorphisms. We
combine this with gauge theory and deep results in Khovanov homotopy to p
rove that Khovanov homology detects the cinquefoil. In another application
\, we prove that the fundamental group of 3-surgery on a nontrivial knot a
lways admits an irreducible SU(2)-representation\, answering an old questi
on of Kronheimer and Mrowka from their work on the Property P conjecture.
All of this is joint with Steven Sivek. The first application is also join
t with Ying Hu\, and the second is also joint with Zhenkun Li and Fan Ye.\
n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sudipta Ghosh (Louisiana State University)
DTSTART:20211021T173000Z
DTEND:20211021T183000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/33
DESCRIPTION:Title: Connected sums and directed systems in knot Floer homol
ogies\nby Sudipta Ghosh (Louisiana State University) as part of Gauge
theory virtual\n\n\nAbstract\nKnot Floer homology is an invariant of knot
which was first introduced in the context of Heegaard Floer homology and l
ater extended to other Floer theories. In this talk\, we discuss a new app
roach to the connected sum formula using direct limits. Our methods apply
to versions of knot Floer homology arising in the context of Heegaard\, in
stanton and monopole Floer homology. This is joint work with Ian Zemke.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anubhav Mukherjee (Georgia Tech)
DTSTART:20211104T173000Z
DTEND:20211104T183000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/34
DESCRIPTION:Title: Exotic surfaces and the family Bauer-Furuta invariant\nby Anubhav Mukherjee (Georgia Tech) as part of Gauge theory virtual\n\
n\nAbstract\nAn important principle in 4-dimesional topology\, as discover
ed by Wall in the 1960s\, states that all exotic phenomena are eliminated
by sufficiently many stabilizations (i.e.\, taking connected sum with $S^2
\\times S^2$’s). Since then\, it has been a fundamental problem to sear
ch for exotic phenomena that survives one stabilization. In this talk\, we
will establish the first pair of orientable exotic surfaces (in a pucture
d K3) which are not smoothly isotopic even after one stabilization. A key
ingredient in our argument is a vanishing theorem for the family Bauer-Fur
uta invariant\, proved using equivariant stable homotopy theory. This theo
rem applies to a large family of spin 4-manifolds and has some interesting
applications in Smale’s conjecture (about exotic diffeomorphisms on $S^
4$). In particular\, it implies that the $S^1$-equivariant or non-equivari
ant family Bauer-Furuta invariant do not detect an exotic diffeomorphism o
n $S^4$ and it suggests that the Pin(2)-symmetry could be a game changer.
\n\nThis is a joint work with Jianfeng Lin.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Ye (University of Cambridge)
DTSTART:20211118T183000Z
DTEND:20211118T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/35
DESCRIPTION:Title: A large surgery formula for instanton Floer homology\nby Fan Ye (University of Cambridge) as part of Gauge theory virtual\n\n
\nAbstract\nFor a knot K in the 3-sphere\, Ozsváth-Szabó and Rasmussen i
ntroduced a large surgery formula which computes the Heegaard Floer homolo
gy of m-surgery on K for any large integer m\, in terms of bent complexes
defined using the knot Floer complex of K. In this talk\, I’ll introduce
an analogous formula for instanton Floer homology. More precisely\, I con
struct two differentials on the instanton knot homology of K and use them
to compute the framed instanton homology of m-surgery for any large intege
r m. As an application\, I show that if the coefficients of the Alexander
polynomial of K are not in {-1\,0\,1}\, then there exists an irreducible r
epresentation from the fundamental group of $S^3_r(K)$ to SU(2) for all bu
t finitely many rational numbers r. In particular\, all hyperbolic alterna
ting knots satisfy this condition. Also by this large surgery formula\, I
show instanton and Heegaard knot Floer homology agree for any Berge knot\,
and that the framed instanton homology of $S^3_r(K)$ agrees with the Heeg
aard Floer homology for any genus-one alternating knot K. This is a joint
work with Zhenkun Li.\n\nRelated preprints:\n\nhttps://arxiv.org/abs/2107.
11005\n\nhttps://arxiv.org/abs/2107.10490\n\nhttps://arxiv.org/abs/2101.05
169\n\nhttps://arxiv.org/abs/2010.07836\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minh Nguyen (University of Arkansas)
DTSTART:20211202T183000Z
DTEND:20211202T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/36
DESCRIPTION:Title: Finite dimensional approximation and Pin(2)-equivariant
properties for the Rarita-Schwinger-Seiberg-Witten equations\nby Minh
Nguyen (University of Arkansas) as part of Gauge theory virtual\n\n\nAbst
ract\nThe Rarita-Schwinger operator Q was initially proposed in the 1941 p
aper by Rarita and Schwinger to study wave functions of particles of spin
3/2\, and there is a vast amount of physics literature on its properties.
Roughly speaking\, 3/2−spinors are spinor-valued 1-forms that also happe
n to be in the kernel of the Clifford multiplication. Let X be a Riemannia
n spin 4−manifold. Associated to\na fixed spin structure on X\, we defin
e a Seiberg-Witten-like system of non-linear\nPDEs using Q and the Hodge-D
irac operator after suitable gauge-fixing.\nThe moduli space of solutions
M contains (3/2-spinors\, purely imaginary 1-forms).\nUnlike in the case o
f Seiberg-Witten equations\, solutions are hard to find or construct. Howe
ver\, by adapting the finite-dimensional technique of Furuta\, we provide
a topological condition of X to ensure that M is non-compact\; and thus\,
contains\ninfinitely many elements.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linh Truong (University of Michigan)
DTSTART:20220210T193000Z
DTEND:20220210T203000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/37
DESCRIPTION:Title: Homology concordance and knot Floer homology\nby Li
nh Truong (University of Michigan) as part of Gauge theory virtual\n\n\nAb
stract\nHomology concordance and knot Floer homology\n\nAbstract: Two knot
s in homology 3-spheres are homology concordant if they are smoothly conco
rdant in a homology cobordism. I will explain how to construct integer-val
ued homomorphisms from this group of knots up to homology concordance. Thi
s construction uses knot Floer homology and generalizes concordance homomo
rphisms for knots in the 3-sphere.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clayton McDonald (UC Davis)
DTSTART:20220217T183000Z
DTEND:20220217T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/38
DESCRIPTION:Title: Surface slices and homology spheres\nby Clayton McD
onald (UC Davis) as part of Gauge theory virtual\n\n\nAbstract\nIn this ta
lk\, we develop the theory of the diagrammatics of surface cross sections
to prove that there are an infinite number of homology 3-spheres smoothly
embeddable in a homology 4-sphere but not in a homotopy 4-sphere. Our prim
ary obstruction comes from work of Daemi.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Zemke (Princeton University)
DTSTART:20220303T183000Z
DTEND:20220303T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/39
DESCRIPTION:Title: The link surgery formula and plumbed 3-manifolds\nb
y Ian Zemke (Princeton University) as part of Gauge theory virtual\n\n\nAb
stract\nLattice homology is a combinatorial invariant of plumbed 3-manifol
ds due to Némethi. The definition is a formalization of Ozsváth and Szab
ó’s computation of the Heegaard Floer homology of plumbed 3-manifolds.
Nemethi conjectured that lattice homology is isomorphic to Heegaard Floer
homology. For a restricted class of plumbings\, this isomorphism is known
to hold\, due to work of Ozsváth-Szabó\, Némethi\, and Ozsváth-Stipsic
z-Szabó. By using the Manolescu-Ozsváth link surgery formula for Heegaar
d Floer homology\, we prove the conjectured isomorphism in general. In thi
s talk\, we will talk about aspects of the proof\, as well as some other p
erspectives in terms of bordered 3-manifolds with torus boundary.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayato Imori (Kyoto University)
DTSTART:20220317T173000Z
DTEND:20220317T183000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/40
DESCRIPTION:Title: Instanton knot invariants with rational holonomy parame
ters and an application for torus knot groups\nby Hayato Imori (Kyoto
University) as part of Gauge theory virtual\n\n\nAbstract\nSeveral knot in
variants from instantons provide powerful tools to study the topology of k
nots in terms of representations of knot groups. In this talk\, we introdu
ce a generalization of Daemi-Scaduto’s equivariant singular instanton Fl
oer theory to rational holonomy parameters. As an application\, it enables
us to show that any SU(2)-representation of torus knot groups can be exte
nded to the complement of any concordance from the torus knot to another k
not. This result gives further evidence to a version of slice-ribbon conje
cture to torus knots.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Kirk (Indiana University)
DTSTART:20220414T173000Z
DTEND:20220414T183000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/41
DESCRIPTION:Title: Holonomy perturbed SU(2) character varieties of tangles
\nby Paul Kirk (Indiana University) as part of Gauge theory virtual\n\
n\nAbstract\nOne approach to produce topological invariants of low-dimensi
onal manifolds by a 2-step process\, the first step applies the SU(2) char
acter variety functor\, which converts surfaces into (singular) symplectic
manifolds\, and converts 3-manifolds with boundary into Lagrangian immers
ions. The second step applies Lagragian Floer homology to the resulting La
grangian immersion. The Atiyah-Floer conjecture posits an identification o
f the resulting theory with instanton homology. In order to be sensible\,
the first step requires the use of holonomy perturbations of Taubes and Do
naldson to make flat moduli spaces smooth. This talk will describe several
explicit calculations of holonomy perturbed character varieties\, and how
to extract topological information from them\, summarizing ideas worked o
ut in several articles co-authored with Cazassus\, Kotelskiy\, Herald\, He
dden\, and Hogancamp.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gard Olav Helle
DTSTART:20220331T173000Z
DTEND:20220331T183000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/42
DESCRIPTION:Title: Calculations of equivariant instanton Floer groups for
binary polyhedral spaces.\nby Gard Olav Helle as part of Gauge theory
virtual\n\n\nAbstract\nBinary polyhedral spaces are the quotient manifolds
obtained\nfrom the canonical action of the finite subgroups of SU(2) on t
he\n3-sphere. In this talk I will discuss calculations of the equivariant\
ninstanton Floer groups\, in the sense of Miller Eismeier\, for the\ntrivi
al SU(2)-bundle over this family of manifolds.\nDue to work of Austin and
Kronheimer one may obtain very precise\ninformation about the instanton mo
duli spaces over the cylinders\nassociated with these manifolds. If one re
quires 2 to be invertible\nin the ring of coefficients\, this is sufficien
t to explicitly identify\nthe complexes calculating equivariant instanton
Floer homology. From\nthere it is a matter of algebra to extract explicit
calculations\nin all cases.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Daemi (Washington University in St Louis)
DTSTART:20221003T183000Z
DTEND:20221003T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/43
DESCRIPTION:Title: The knot complement problem for nullhomotopic knots
\nby Ali Daemi (Washington University in St Louis) as part of Gauge theory
virtual\n\nLecture held in Simons Auditorium\, MSRI.\n\nAbstract\nIn thei
r celebrated work\, Gordon and Luecke proved that knots\nin the three-dime
nsional sphere are determined by their complements.\nSubsequently\, Boilea
u asked whether the same result holds for null-homotopic\nknots in arbitra
ry 3-manifolds. In this talk\, I will discuss a program to\nanswer this qu
estion. In particular\, I will explain how one can give an\naffirmative an
swer to Boileau's question for arbitrary knots in some families\nof 3-mani
folds including any connected sum of Brieskorn homology spheres.\nThis is
joint work with Tye Lidman.\n\nTalks will be broadcast live from the Simon
s Auditorium at SLMath/MSRI\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Hutchings (University of California\, Berkeley)
DTSTART:20221017T183000Z
DTEND:20221017T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/44
DESCRIPTION:Title: Floer theory of families of equivalent objects\nby
Michael Hutchings (University of California\, Berkeley) as part of Gauge t
heory virtual\n\nLecture held in Simons Auditorium\, MSRI.\n\nAbstract\nWe
review a general scheme for extending Floer theoretic invariants to invar
iants of families of equivalent objects for which the Floer theory is defi
ned (e.g. families of three-manifolds\, families of Hamiltonian isotopic s
ymplectomorphisms\, etc.). We discuss how this kind of construction has be
en used\, and potentially could be used\, for various kinds of Floer theor
y\, with applications to symplectic geometry and (maybe) gauge theory.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tye Lidman (North Carolina State University)
DTSTART:20221031T183000Z
DTEND:20221031T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/45
DESCRIPTION:Title: Instantons and handle decompositions.\nby Tye Lidma
n (North Carolina State University) as part of Gauge theory virtual\n\nLec
ture held in Simons Auditorium\, MSRI.\n\nAbstract\nWe show that there are
homology three-spheres for which any bounding definite four-manifold requ
ires lots of handles. The proof uses instanton Floer homology to show that
lots of representations on the boundary must extend over the four-manifol
d. This is joint work with Paolo Aceto\, Ali Daemi\, Jen Hom\, and JungHwa
n Park.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masaki Taniguchi
DTSTART:20221121T193000Z
DTEND:20221121T203000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/46
DESCRIPTION:Title: Relative genus bounds from Floer K-theory\nby Masak
i Taniguchi as part of Gauge theory virtual\n\nLecture held in Simons Audi
torium\, MSRI.\n\nAbstract\nWe provide a relative genus bound obtained as
a version of 10/8-inequality for knots. The 10/8-inequality will be proven
by observing “the real part” of Seiberg-Witten Floer homotopy type fo
r branched covers. This work is joint work with Hokuto Konno and Jin Miyaz
awa.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Lotay (Oxford University)
DTSTART:20221212T193000Z
DTEND:20221212T203000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/47
DESCRIPTION:Title: Stability and neck pinches in Lagrangian mean curvature
flow\nby Jason Lotay (Oxford University) as part of Gauge theory virt
ual\n\nLecture held in Simons Auditorium\, MSRI.\n\nAbstract\nThe famous r
elation between stability of holomorphic vector bundles and existence of H
ermitian Yang-Mills connections can be demonstrated using Yang-Mills flow.
Motivated by this theory and Mirror Symmetry\, Thomas-Yau conjectured a
stability condition for Lagrangian mean curvature flow which detects when
the flow wants to break up the Lagrangian. When such break up occurs in t
he flow it is expected to be a singularity called a neck pinch. I will re
port on joint work with F. Schulze and G. Szekelyhidi which shows that\, f
or Lagrangian surfaces\, Thomas-Yau stability does indeed rule out neck pi
nch singularities breaking up the Lagrangian along the flow.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiajun Yan (University of Virginia)
DTSTART:20230210T183000Z
DTEND:20230210T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/48
DESCRIPTION:Title: A New Gauge-Theoretic Construction of 4-dimensional Hyp
erkähler ALE Spaces\nby Jiajun Yan (University of Virginia) as part o
f Gauge theory virtual\n\n\nAbstract\nNon-compact hyperkähler spaces aris
e frequently in gauge theory. The 4-dimensional hyperkähler ALE spaces ar
e a special class of non-compact hyperkähler spaces. They are in one-to-o
ne correspondence with the finite subgroups of SU(2) and have interesting
connections with representation theory and singularity theory captured by
the McKay Correspondence.\n\nIn this talk\, we first review the finite-dim
ensional construction of the 4-dimensional hyperkähler ALE spaces given b
y Peter Kronheimer in his PhD thesis. Then we give a new construction of t
hese spaces via gauge theory.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bob Gompf
DTSTART:20230224T183000Z
DTEND:20230224T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/49
DESCRIPTION:Title: Transverse Tori in Engel Manifolds\nby Bob Gompf as
part of Gauge theory virtual\n\n\nAbstract\nEngel manifolds are closely r
elated to contact manifolds\, but only occur in dimension 4. They are much
less well understood than contact manifolds. For example\, it is still un
known if “tight” Engel structures exist. A primary tool for understand
ing such issues for contact 3-manifolds is transverse knot theory. Every k
not in a contact 3-manifold is isotopic to transverse knots\, realizing in
finitely many values of the associated homotopy invariant (self-linking nu
mber) when it is defined. At a 2017 AIM conference\, Eliashberg suggested
the analogous problem of understanding transverse (closed\, oriented) surf
aces in Engel manifolds. It is easy to see that such transverse surfaces a
re necessarily tori with trivial normal bundles\, but no further results w
ere obtained at the time\, beyond a few examples. It now turns out that th
ese conditions are also sufficient: Every torus with trivial normal bundle
is isotopic to infinitely many transverse tori\, analogously to knots in
contact 3-manifolds. This could potentially turn into a powerful tool for
understanding Engel manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Hedenlund
DTSTART:20230310T183000Z
DTEND:20230310T193000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/50
DESCRIPTION:Title: Seiberg-Witten Floer Theory and Twisted Parametrised Sp
ectra\nby Alice Hedenlund as part of Gauge theory virtual\n\n\nAbstrac
t\nSeiberg-Witten theory has played a central role in the study of smooth
low-dimensional manifolds since their introduction in the 90s. Parallel to
this\, Cohen\, Jones\, and Segal asked the question of whether various ty
pes of Floer homology could be upgraded to the homotopy level by construct
ing (stable) homotopy types encoding Floer data. In 2003\, Manolescu const
ructed Seiberg-Witten Floer stable homotopy types for rational homology 3-
spheres\, and in particular used these to settle the triangulation conject
ure once and for all.\n\nIn this talk\, I will report on joint work in pro
gress with S. Behrens and T. Kragh in which we construct “twisted parame
trised spectra” from Seiberg-Witten Floer data. These are the main mathe
matical objects in twisted stable homotopy theory and were introduced by D
ouglas in his PhD thesis. We give an introduction to twisted parametrised
spectra and explain how Seiberg-Witten Floer data naturally gives rise to
such objects. This is work in progress joint with S. Behrens and T. Kragh.
\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Mark (University of Virginia)
DTSTART:20230324T173000Z
DTEND:20230324T183000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/51
DESCRIPTION:Title: Fillable contact structures from positive surgery\n
by Thomas Mark (University of Virginia) as part of Gauge theory virtual\n\
n\nAbstract\nFor a Legendrian knot $K$ in a closed contact 3-manifold\, we
describe a necessary and sufficient condition for contact $n$-surgery alo
ng $K$ to yield a weakly symplectically fillable contact manifold\, for so
me integer $n>0$. When specialized to knots in the standard 3-sphere this
gives an effective criterion for the existence of a fillable positive surg
ery\, along with various obstructions. These are sufficient to determine\,
for example\, whether such a surgery exists for all knots of up to 10 cro
ssings. The result also has certain purely topological consequences\, such
as the fact that a knot admitting a lens space surgery must have slice ge
nus equal to its 4-dimensional clasp number. We will mainly explore these
topologically-flavored aspects\, but will give some hints of the general p
roof if time allows.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhenkun Li
DTSTART:20230407T173000Z
DTEND:20230407T183000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/52
DESCRIPTION:Title: A surgery formula in instanton Floer theory\nby Zhe
nkun Li as part of Gauge theory virtual\n\n\nAbstract\nInstanton Floer hom
ology is introduced by Floer in 1980s. It is a powerful invariants for 3-m
anifolds and knots and links inside them. There have been many important a
pplications of Instanton Floer homology\, such as the approval of Property
P conjecture. It has been conjectured that the instanton Floer homology i
s isomorphic to other versions of Floer theory. Though this conjecture is
still widely open\, one could ask whether some important properties that h
as been known to be true in other Floer theory also hold for instanton the
ory. One such property is the surgery formula\, which relates the instanto
n Floer homology of a 3-manifold coming from Dehn surgeries along a knot w
ith the instanton Floer homology of the knot. In this talk\, we will prese
nt a surgery formula for instanton theory\, and describe how this formula
can be applied in computing instanton Floer homology and study the SU(2)-r
epresentations of fundamental groups of 3-manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akram Alishahi
DTSTART:20230428T173000Z
DTEND:20230428T183000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/53
DESCRIPTION:Title: Khovanov homology and involutive Heegaard Floer homolog
y\nby Akram Alishahi as part of Gauge theory virtual\n\n\nAbstract\nFo
r any knot K in the 3-sphere\, Ozsváth and Szabó construct a spectral se
quence from the Khovanov homology of K to the Heegaard Floer homology of t
he branched double cover of K. This spectral sequence is the first of many
interesting works studying the interactions of Heegaard Floer homology an
d Khovanov homology over the past two decades. In 2017\, Hendricks and Man
olescu incorporated the conjugation action on Heegaard Floer homology to p
roduce a richer 3-manifold invariant\, called involutive Heegaard Floer ho
mology. In this talk\, we will discuss an involutive version of Ozsváth-S
zabó’s spectral sequence that converges to the involutive Heegaard Floe
r homology of the branched double cover of the knot. This is a joint work
with Linh Truong and Melissa Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianfeng Lin
DTSTART:20230918T140000Z
DTEND:20230918T150000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/54
DESCRIPTION:Title: Configuration space integrals and formal smooth structu
res.\nby Jianfeng Lin as part of Gauge theory virtual\n\n\nAbstract\nW
atanabe disproved the 4-dimensional Smale conjecture by establishing many
disk bundles which are topologically trivial but not smoothly so. Amazingl
y\, Watanabe used Kontsevich’s characteristic classes\, which are very d
ifferent from previous invariants that can detect exoticness in dimension
4 (e.g. the Seiberg-Witten invariants and the Donaldson invariants). So on
e may wonder what’s the role played by the smooth structure in this stor
y. In this talk\, I will sketch our proof that Kontsevich’s characterist
ic classes only depend on a formal smooth structure (i.e. a vector bundle
structure on the topological tangent bundle). This makes the invariant mor
e flexible and allows several new applications. For example\, we show that
the homeomorphism group of the 4-dimensional sphere or Euclidian space ha
s nontrivial rational homotopy/homology group in infinitely many dimension
s. And we show that for any compact orientable 4-manifold\, the natural in
clusion from the diffeomorphism group to the homeomorphism group is not a
homotopy equivalence. Furthermore\, we discovered a new MMM (Morita-Miller
-Mumford) class\, which can obstruct the smoothing of 4-dimensional topolo
gical bundles. The talk is based on a joint work with Yi Xie.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Miller Eismeier (University of Vermont)
DTSTART:20231016T140000Z
DTEND:20231016T150000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/55
DESCRIPTION:Title: Filtered instanton Floer homology and cosmetic surgery<
/a>\nby Mike Miller Eismeier (University of Vermont) as part of Gauge theo
ry virtual\n\n\nAbstract\nIf Y is a closed oriented 3-manifold\, its Chern
-Simons function is a function on a certain infinite-dimensional space\, a
nd the instanton Floer homology I_*(Y) is constructed as the Morse homolog
y of this function. What's special about the Chern-Simons function is that
it depends only on the topology of Y\, not any other geometric input or a
uxiliary data. As a result\, we can define filtered Floer homologies F_r I
_*(Y) which are roughly the Morse homology of the sublevel set cs^{-1}(-in
fty\, r]\, and these give topological invariants of Y with good structural
properties.\n\nThere is a long history of using the Chern-Simons function
to prove results about homology cobordism of 3-manifolds. It was used in
Furuta's 1990 proof that the homology cobordism group is infinitely genera
ted\; recently\, Nozaki-Sato-Taniguchi used the CS filtration to give exam
ples of integer homology spheres Y so that any 4-manifold bounding Y must
be indefinite (there must be some essential surface Sigma with self-inters
ection number zero).\n\nI will discuss applications of a different sort: d
istinguishing the diffeomorphism types of two 3-manifolds using their filt
ered Floer homology\, with applications to cosmetic surgery problems. This
work is joint with Tye Lidman.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luya Wang (Stanford University)
DTSTART:20231030T140000Z
DTEND:20231030T150000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/56
DESCRIPTION:Title: Deformation inequivalent symplectic structures and Dona
ldson’s four-six question.\nby Luya Wang (Stanford University) as pa
rt of Gauge theory virtual\n\n\nAbstract\nStudying symplectic structures u
p to deformation equivalences is a fundamental question in symplectic geom
etry. Donaldson asked: given two homeomorphic closed symplectic four-manif
olds\, are they diffeomorphic if and only if their stabilized symplectic s
ix-manifolds\, obtained by taking products with CP^1 with the standard sym
plectic form\, are deformation equivalent? I will discuss joint work with
Amanda Hirschi on showing how deformation inequivalent symplectic forms re
main deformation inequivalent when stabilized\, under certain algebraic co
nditions. This gives the first counterexamples to one direction of Donalds
on’s “four-six” question and the related Stabilizing Conjecture by R
uan.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Zemke (Princeton University)
DTSTART:20231113T150000Z
DTEND:20231113T160000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/57
DESCRIPTION:Title: A general Heegaard Floer surgery formula.\nby Ian Z
emke (Princeton University) as part of Gauge theory virtual\n\n\nAbstract\
nIn this talk\, we will describe a very flexible version of the Manolescu-
Ozsvath-Szabo surgery formula which is purely “local” and holds for an
y link in any 3 manifold. Reinterpreted\, the construction gives a bordere
d invariant for any 3-manifold with torus boundaries. In this talk\, we wi
ll focus on basic examples and illustrations of the construction\, such as
definition of the chain complex for the unknot or an S^1 fiber in S^1 x S
^2. Time permitting we may mention some applications of the theory\, such
as the computation of link Floer homology of all plumbed L-space links in
S^3.\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Ladu
DTSTART:20231127T150000Z
DTEND:20231127T160000Z
DTSTAMP:20260404T111321Z
UID:GaugeTheoryVirtual/58
DESCRIPTION:Title: Non-smoothable homeomorphisms of 4-manifolds with bound
ary.\nby Roberto Ladu as part of Gauge theory virtual\n\n\nAbstract\nI
n 1988 Friedman and Morgan used Donaldson polynomial invariants to show th
at several simply connected algebraic surfaces possess self-homeomorphisms
which are non-smoothable i.e. are not C^0-isotopic to any self-diffeomorp
hism. Since then many other pairs (X\,phi) with X a simply-connected 4-man
ifold and phi:X->X a non-smoothable homeomorphism have been found. In all
known examples phi acts non-trivially in homology\; when X is closed\, thi
s is a necessary condition for non-smoothability for otherwise phi would b
e isotopic to the identity (Perron-Quinn). I will show that this is not ne
cessary anymore when X has non-empty boundary. More precisely\, I will sho
w how to construct simply connected 4-manifolds with non-empty boundary po
ssessing non-smoothable self-homeomorphisms which fix the boundary pointwi
se and act trivially in homology. This is a joint work with Daniel Galvin.
\n
LOCATION:https://stable.researchseminars.org/talk/GaugeTheoryVirtual/58/
END:VEVENT
END:VCALENDAR