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BEGIN:VEVENT
SUMMARY:Francesco Lin (Columbia)
DTSTART:20200416T190000Z
DTEND:20200416T200000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/1
DESCRIPTION:Title: Monopole Floer homology\, eigenform multiplicities and the Seif
ert-Weber dodecahedral space\nby Francesco Lin (Columbia) as part of G
auge theory virtual\n\n\nAbstract\nThis is joint work with M. Lipnowski. W
e show that the Seifert-Weber dodecahedral space SW is an L-space. The pro
of builds on our work relating Floer homology and spectral geometry of hyp
erbolic three-manifolds. A direct application of our previous techniques r
uns into difficulties arising from the computational complexity of the pro
blem. We overcome this by exploiting the large symmetry group and the arit
hmetic and tetrahedral group structure of SW to prove that small eigenvalu
es on coexact 1-forms must have large multiplicity.\n\nThe link to the pap
er on the arxiv is https://arxi
v.org/abs/2003.11165.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Alfieri (University of British Columbia)
DTSTART:20200423T190000Z
DTEND:20200423T200000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/2
DESCRIPTION:Title: Instanton Floer homology of almost-rational plumbings\nby A
ntonio Alfieri (University of British Columbia) as part of Gauge theory vi
rtual\n\n\nAbstract\nPlumbed three-manifolds are those three-manifolds tha
t can be be realized as links of isolated complex surface singularities. I
nspired by Heegaard Floer theory Nemethi introduced a combinatorial invari
ant of complex surface singularities (lattice cohomology) that is conjectu
red to be isomorphic to\nHeegaard Floer\nhomology. I will expose some rece
nt work in collaboration with John Baldwin\, Irving Dai\, and Steven Sivek
showing that the lattice cohomology of an almost-rational singularity is
isomorphic to the framed instanton Floer homology of its link. The proof g
oes through lattice cohomology and makes use of the decomposition along ch
aracteristic vectors of the instanton cobordism maps recently found by Bal
dwin and Sivek.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Kronheimer (Harvard University)
DTSTART:20200430T190000Z
DTEND:20200430T200000Z
DTSTAMP:20260422T225926Z
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 smooth or
iented manifold M contains an embedded codimension-1 sphere\, then one may
define a diffeomorphism of M supported in a neighborhood of that sphere\,
generalizing the familiar Dehn twist along a closed curve in a 2-manifold
. In this talk\, I will explain how Seiberg-Witten theory can be used to s
how that this Dehn twist is not isotopic to the identity in the case that
M is a connected sum K3#K3 (regarded as a smooth 4-manifold). This is join
t work with Tom Mrowka. The talk will include some background and context
for the question\, and can be treated as a prequel to the talk given earli
er in this series by Jianfeng Lin.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gleb Smirnov (ETH Zurich)
DTSTART:20200507T190000Z
DTEND:20200507T200000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/4
DESCRIPTION:Title: The Atiyah flop and diffeomorphism groups\nby Gleb Smirnov
(ETH Zurich) as part of Gauge theory virtual\n\n\nAbstract\nFollowing a sh
ort introduction to the flop surgery\, I will explain how this birational
transformation can be used to detect non-contractible loops in the diffeom
orphism group of the product of 2-spheres and some other algebraic surface
s.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sherry Gong (UCLA)
DTSTART:20201029T190000Z
DTEND:20201029T200000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/5
DESCRIPTION:Title: Non-orientable link cobordisms and torsion order in Floer homol
ogies\nby Sherry Gong (UCLA) as part of Gauge theory virtual\n\n\nAbst
ract\nIn a recent paper\, Juhasz\, Miller and Zemke proved an inequality i
nvolving the number of local maxima and the genus appearing in an oriented
knot cobordism using a version of knot Floer homology. In this talk I wil
l be discussing some similar inequalities for non-orientable knot cobordis
ms using the torsion orders of unoriented versions of knot Floer homology
and instanton Floer homology. This is a joint work with Marco Marengon.\n\
nThe link to the paper on arxiv is https://arxiv.org/abs/2010.06577\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Donghao Wang (MIT)
DTSTART:20201105T200000Z
DTEND:20201105T210000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/6
DESCRIPTION:Title: Monopole Floer homology for 3-manifolds with toroidal boundary<
/a>\nby Donghao Wang (MIT) as part of Gauge theory virtual\n\n\nAbstract\n
The monopole Floer homology of an oriented closed 3-manifold was\ndefined
by Kronheimer-Mrowka around 2007 and has greatly influenced\nthe study of
3-manifold topology since its inception. \nIn this talk\, we will generali
ze their construction and define the\nmonopole Floer homology for any pair
(Y\, ω)\, where Y is a compact\noriented 3-manifold with toroidal bounda
ry and ω is a suitable closed\n2-form. The graded Euler characteristic of
this Floer homology recovers the Milnor-Turaev torsion invariant by a cla
ssical theorem of\nMeng-Taubes. It satisfies a reasonable (3+1) TQFT prope
rty. In the\nend\, we will explain its relation with gauged Landau-Ginzbur
g models\nand point out some future directions.\n\nThe link to the paper i
s https://arxiv.org/pdf/2005.04333.pdf\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhenkun Li (Stanford University)
DTSTART:20201112T200000Z
DTEND:20201112T210000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/7
DESCRIPTION:Title: Instanton Floer homology of (1\,1)-knots\nby Zhenkun Li (St
anford University) as part of Gauge theory virtual\n\n\nAbstract\nInstanto
n knot homology was first introduced by Floer around 1990 and was revisite
d by Kronheimer and Mrowka around 2010. It is built based on the solution
to a set of partial differential equations and is very difficult to comput
e. On the other hand\, Heegaard diagrams are classical tools to describe k
nots and 3-manifolds combinatorially\, and is also the basis of Heegaard F
loer theory\, which was introduced by Ozsváth and Szabó around 2004. In
this talk\, I will explain how to extract some information about instanton
theory from Heegaard diagrams. In particular\, we study the (1\,1)-knots\
, which are known to have simple Heegaard diagrams. We provide an upper bo
und for the dimension of instanton knot homology for all (1\,1)-knots. Als
o\, we prove that\, for some families of (1\,1)-knots\, including all toru
s knots\, the upper bound we obtained is in fact sharp. If time permits\,
I will also discuss on some further applications to the instanton Floer ho
mology of 3-manifolds coming from Dehn surgeries along null-homologous kno
ts. This is a joint work with Fan Ye.\n\nThe link to the paper is https://
arxiv.org/abs/2010.07836\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Fredrickson (University of Oregon)
DTSTART:20201119T200000Z
DTEND:20201119T210000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/8
DESCRIPTION:Title: The asymptotic geometry of the Hitchin moduli space\nby Lau
ra Fredrickson (University of Oregon) as part of Gauge theory virtual\n\n\
nAbstract\nHitchin’s equations are a system of gauge theoretic equations
on a Riemann surface that are of interest in many areas including represe
ntation theory\, Teichmuller theory\, and the geometric Langlands correspo
ndence. The Hitchin moduli space carries a natural hyperkahler metric. A c
onjectural description of its asymptotic structure appears in the work of
physicists Gaiotto-Moore-Neitzke and there has been a lot of progress on t
his recently. I will discuss some recent results.\n\nA link to a recent pa
per is https://arxiv.org/abs/2001.03682.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Feehan (Rutgers)
DTSTART:20201210T200000Z
DTEND:20201210T210000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/9
DESCRIPTION:Title: Morse-Bott theory on analytic spaces and applications to to top
ology of smooth 4-manifolds\nby Paul Feehan (Rutgers) as part of 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 gau
ge theory\, such as the moduli space of SO(3) monopoles over 4-manifolds o
r the moduli space of Higgs pairs over Riemann surfaces. We explain how th
is new version of Morse theory\, called virtual Morse-Bott theory\, can po
tentially be used to answer questions arising in the geography of 4-manifo
lds\, such as whether constraints on the topology of compact complex surfa
ces of general type continue to hold for symplectic 4-manifolds or even fo
r smooth 4-manifolds of Seiberg-Witten simple type.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boyu Zhang (Princeton University)
DTSTART:20201203T200000Z
DTEND:20201203T210000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/10
DESCRIPTION:Title: Several detection results for Khovanov homology on links\n
by Boyu Zhang (Princeton University) as part of Gauge theory virtual\n\n\n
Abstract\nIn this talk\, I will present several new detection results of K
hovanov homology on links. In particular\, we show that if L is an n-compo
nent link with Khovanov homology of rank 2^n\, then it is given by the con
nected sums and disjoint unions of unknots and Hopf links. This result giv
es a positive answer to a question asked by Batson-Seed\, and it generaliz
es the unlink detection theorem by Hedden-Ni and Batson-Seed. The proofs o
f this result and the other detection results presented in this talk rely
on a new excision formula for singular instanton Floer homology. This talk
is based on works that are joint with Yi Xie and partially joint with Zhe
nkun Li.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hokuto Konno (University of Tokyo)
DTSTART:20210119T230000Z
DTEND:20210120T000000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/11
DESCRIPTION:Title: Seiberg-Witten theory for families I\nby Hokuto Konno (Uni
versity 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 various compa
risons between the homeomorphism groups and the diffeomorphism groups of 4
-manifolds. I try to sketch basic ideas of this area\, and to describe suc
h applications in detail.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masaki Taniguchi (iTHEMS/RIKEN)
DTSTART:20210121T230000Z
DTEND:20210122T000000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/12
DESCRIPTION:Title: Gauge theory on 4-manifolds with periodic ends I\nby Masak
i Taniguchi (iTHEMS/RIKEN) as part of Gauge theory virtual\n\n\nAbstract\n
We first review the historical backgrounds of Yang-Mills and Seiberg-Witte
n gauge theory for non-compact 4-manifolds having cylindrical\, periodic\,
or conical ends. Then\, we focus on YM-gauge theory on 4-manifolds with p
eriodic ends. As a generalization of Taubes’s compactness theorem of the
ASD-moduli spaces for 4-manifolds with periodic ends\, we show a similar
compactness theorem under some energy condition. As an application\, we co
nstruct an obstruction to a certain type of embeddings of 3-manifolds into
4-manifolds. The obstruction lies in the filtered versions of instanton F
loer cohomology.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hokuto Konno (University of Tokyo)
DTSTART:20210128T230000Z
DTEND:20210129T000000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/13
DESCRIPTION:Title: Seiberg-Witten theory for families II\nby Hokuto Konno (Un
iversity of Tokyo) as part of Gauge theory virtual\n\n\nAbstract\nIn this
latter half I shall focus on recent joint work with Masaki\nTaniguchi (htt
ps://arxiv.org/abs/2010.00340). This is an extension of a part of the last
story to families of 4-manifolds with boundary\, again with applications
to comparisons between the homeomorphism groups and the diffeomorphism gro
ups. 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 Seib
erg-Witten Floer stable homotopy type.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masaki Taniguchi (iTHEMS/RIKEN)
DTSTART:20210202T230000Z
DTEND:20210203T000000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/14
DESCRIPTION:Title: Gauge theory on 4-manifolds with periodic ends II\nby Masa
ki Taniguchi (iTHEMS/RIKEN) as part of Gauge theory virtual\n\n\nAbstract\
nAs a sequel to the first talk “Gauge theory on 4-manifolds with periodi
c ends I”\, we talk about Seiberg-Witten theory for 4-manifolds with per
iodic ends. This is joint work with Hokuto Konno. We show 10/8-type inequa
lities for spin periodic-end-4-manifolds having periodic positive scalar c
urvature metrics on the ends. In the main step of the proof\, we use a cer
tain compactness theorem for the Seiberg-Witten moduli spaces for the peri
odic-end-4-manifolds proved by Jianfeng Lin. As an application\, we give a
new obstruction to positive scalar curvature metric for a certain class o
f homology $S^1\\times S^3$’s.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juanita Pinzón Caicedo (Notre Dame)
DTSTART:20210209T230000Z
DTEND:20210210T000000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/15
DESCRIPTION:Title: Toroidal integer homology spheres have irreducible SU(2)-repre
sentations\nby Juanita Pinzón Caicedo (Notre Dame) as part of Gauge t
heory virtual\n\n\nAbstract\nThe fundamental group is one of the most powe
rful invariants to distinguish closed three-manifolds. One measure of the
non-triviality of a three-manifold is the existence of non-trivial SU(2)-r
epresentations. In this talk I will show that if an integer homology three
-sphere contains an embedded incompressible torus\, then its fundamental g
roup admits irreducible SU(2)-representations. This is joint work with Tye
Lidman and Raphael Zentner.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Baraglia (University of Adelaide)
DTSTART:20210216T230000Z
DTEND:20210217T000000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/16
DESCRIPTION:Title: Tautological classes of definite 4-manifolds\nby David Bar
aglia (University of Adelaide) as part of Gauge theory virtual\n\n\nAbstra
ct\nTautological classes are characteristic classes of manifold bundles. T
hey have been extensively studied for bundles of surfaces\, where they wer
e first introduced by Mumford in the setting of moduli spaces of curves. I
n higher dimensions there are not many examples of manifolds for which the
tautological ring\, the ring generated by tautological classes\, is known
. We will use gauge theory to study tautological classes of 4-manifolds wi
th positive definite intersection form. Amongst other things\, this allows
us to compute the tautological ring for $CP^2$ and the connected sum of $
CP^2$ with itself.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cliff Taubes (Harvard University)
DTSTART:20210310T193000Z
DTEND:20210310T203000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/17
DESCRIPTION:Title: Morse theory\, configuration spaces and Z/2 eigenfunctions for
the Laplacian on 2-sphere.\nby Cliff Taubes (Harvard University) as p
art of Gauge theory virtual\n\n\nAbstract\nI once thought that the Laplaci
an on the round 2-sphere would have nothing new to offer. As it turns out\
, I was wrong. I will describe a set of eigenfunction/eigenvalue problems
on the 2-sphere that Yingying Wu and I are studying that take every opport
unity to do the unexpected. There is a gauge theory tie-in too.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Kotelskiy (Indiana University)
DTSTART:20210303T193000Z
DTEND:20210303T203000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/18
DESCRIPTION:Title: The earring correspondence on the pillowcase.\nby Artem Ko
telskiy (Indiana University) as part of Gauge theory virtual\n\n\nAbstract
\nGiven a decomposition of a knot K into two four-ended tangles T and T’
\, the (holonomy perturbed) traceless-SU(2)-character-variety functor prod
uces Lagrangians R(T) and R(T’) in the pillowcase P. Hedden\, Herald and
Kirk used this to define Pillowcase homology\, conjecturally the symplect
ic counter-part of the singular instanton homology I(K). Important in thei
r construction is how R(T) and its restriction to P are affected by “add
ing an earring”\, a process used by Kronheimer and Mrowka to avoid reduc
ibles. The object that governs this process turns out to be an immersed La
grangian correspondence from pillowcase to itself. We will describe this c
orrespondence in detail\, and study its action on Lagrangians. In the case
of the (4\,5) torus knot\, we will see that a correction term from the bo
unding cochains must be added. We will indicate a particular figure eight
bubble which recovers the desired bounding cochain\, as predicted by Bottm
an and Wehrheim. This is joint work with G. Cazassus\, C. Herald and P. Ki
rk.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tadayuki Watanabe (Shimane University)
DTSTART:20210223T230000Z
DTEND:20210224T000000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/19
DESCRIPTION:Title: Trivalent graphs and diffeomorphisms of some 4-manifolds\n
by Tadayuki Watanabe (Shimane University) as part of Gauge theory virtual\
n\n\nAbstract\nI will explain a geometric method to construct families of\
ndiffeomorphisms of manifolds by using a higher dimensional analogue of\nG
oussarov-Habiro’s trivalent graph surgery in 3-dimension. This would\npr
oduce lots of potentially nontrivial families of diffeomorphisms of\nmanif
olds. In particular\, our construction gives that the homotopy\ngroups $\\
pi_k \\mathrm{Diff}_{\\partial}(D^4) \\otimes \\mathbb{Q}$ are\nnon-trivia
l for many $k$. This is a disproof of the 4-dimensional Smale\nconjecture.
These non-trivialities can be detected by Kontsevich’s\nconfiguration s
pace integrals.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksander Doan (Columbia University)
DTSTART:20210317T183000Z
DTEND:20210317T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/20
DESCRIPTION:Title: Counting pseudo-holomorphic curves in symplectic six-manifolds
\nby Aleksander Doan (Columbia University) as part of Gauge theory vir
tual\n\n\nAbstract\nThe signed count of embedded pseudo-holomorphic curves
in a symplectic manifold typically depends on the choice of an almost com
plex structure on the manifold and so does not lead to a symplectic invari
ant. However\, I will discuss two instances in which such naive counting d
oes define a symplectic invariant. The proof of invariance combines method
s of symplectic geometry with results of geometric measure theory. I will
also talk about an idea of defining invariants of symplectic six-manifolds
by counting pseudo-holomorphic curves and solutions of gauge-theoretic eq
uations. The talk is based on joint work with Thomas Walpuski.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dave Auckly (Kansas State University)
DTSTART:20210324T183000Z
DTEND:20210324T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/21
DESCRIPTION:Title: Exotic Families of Diffeomorphisms and Embeddings\nby Dave
Auckly (Kansas State University) as part of Gauge theory virtual\n\n\nAbs
tract\nThis will describe joint work with Danny Ruberman demonstrating tha
t 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 and conti
nuous families of embeddings. The talk will discuss the construction of th
ese exotic families as well as the computation of the Yang-Mills based inv
ariant that establishes the non-triviality of the families.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillem Cazassus (University of Oxford)
DTSTART:20210331T183000Z
DTEND:20210331T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/22
DESCRIPTION:Title: Hopf algebras\, equivariant Lagrangian Floer homology\, and co
rnered instanton theory\nby Guillem Cazassus (University of Oxford) 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 $CF(L\,L’)$ i
s an $A_\\infty$ module over the Morse complex CM(G) (which has an $A_\\i
nfty$ algebra structure involving the group multiplication). This permits
to define several versions of equivariant Floer homology.\n\nIt also impli
es that the Fukaya categoy Fuk(M)\, in addition to its own $A_\\infty$ st
ructure\, is an $A_\\infty$ module over CM(G). These two structures can b
e 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 structure\, it sh
ould be a Hopf-infinity algebra\, a structure (still unclear to us) that s
hould induce the Hopf algebra structure on $H_*(G)$.\n\nApplied to some su
bsets of Huebschmann-Jeffrey’s extended moduli spaces introduced by Mano
lescu and Woodward\, this construction should permit to define a cornered
instanton theory analogous to Douglas-Lipshitz-Manolescu’s construction
in Heegaard-Floer theory. This is work in progress\, joint with Paul Kirk\
, Artem Kotelskiy\, Mike Miller and Wai-Kit Yeung.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Duncan (James Madison University)
DTSTART:20210407T183000Z
DTEND:20210407T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/23
DESCRIPTION:Title: Gluing mASD connections.\nby David Duncan (James Madison U
niversity) as part of Gauge theory virtual\n\n\nAbstract\nTaubes’ gluing
theorems establish existence for ASD connections on closed 4-manifolds. W
e discuss recent extensions of these gluing results to the mASD-connection
s of Morgan–Mrowka–Ruberman on cylindrical end 4-manifolds. This is jo
int work with Ian Hambleton.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Wang (Harvard University)
DTSTART:20210414T183000Z
DTEND:20210414T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/24
DESCRIPTION:Title: Floer and Khovanov homologies of band sums\nby Joshua 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 t
o 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 Floer homol
ogy and the same instanton knot Floer homology but distinct Khovanov homol
ogy\, generalizing a result of M. Hedden and L. Watson. A key component of
the argument is a proof that each of the three knot homologies detects th
e trivial band. The main application is a verification of the generalized
cosmetic crossing conjecture for split links.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andriy Haydys (Freiburg University)
DTSTART:20210421T183000Z
DTEND:20210421T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/25
DESCRIPTION:Title: Topology of the blow up set for the Seiberg-Witten equations w
ith two spinors\nby Andriy Haydys (Freiburg University) as part of Gau
ge theory virtual\n\n\nAbstract\nAn arbitrary sequence of the Seiberg-Witt
en monopoles with two spinors on a three-manifold may well be divergent du
e to the energy concentration along a one-dimensional subset Z\, which I r
efer to as a blow up set. It turns out that blow up sets have interesting
topological properties\, for example in the case the background three-mani
fold is a rational homology sphere the Alexander polynomial of Z evaluated
at $t=-1$ must vanish (under certain conditions\, which I will describe i
n the talk). I will report about this and other related properties of blow
up sets.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Herald (University of Nevada\, Reno)
DTSTART:20210428T183000Z
DTEND:20210428T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/26
DESCRIPTION:Title: Relative character varieties of tangles in 3-manifolds and hol
onomy perturbed flat moduli spaces\nby Chris Herald (University of Nev
ada\, Reno) as part of Gauge theory virtual\n\n\nAbstract\nThe traceless S
U(2) character variety of a tangle in a 3-manifold with boundary is define
d to be the set of representations of the tangle complement fundamental gr
oup into SU(2) sending tangle meridians to traceless elements\, up to conj
ugation. This character variety may be identified with the flat moduli spa
ce that plays a central role in singular instanton homology. In this gauge
theoretic context\, there is a notion of holonomy perturbations\, which p
rovide a framework to solve transversality problems with flat moduli space
s\; this notion can be translated back into topological terms to define ho
lonomy perturbed traceless character varieties.\n\nWe’ll show that the r
estriction map from the holonomy perturbed traceless character variety 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 ga
uge theoretic analysis\, but makes use of composition in the Weinstein cat
egory\, the fact that holonomy perturbations in a cylinder induce Hamilton
ian isotopies\, and Poincaré duality. This is joint work with Guillem Caz
assus and Paul Kirk.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Miller (Columbia University)
DTSTART:20210505T183000Z
DTEND:20210505T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/27
DESCRIPTION:Title: Invariance and functoriality in equivariant instanton homology
\nby Mike Miller (Columbia University) as part of Gauge theory virtual
\n\n\nAbstract\nPreviously\, the author defined an infinite-dimensional SO
(3)-equivariant chain complex for rational homology spheres and “admissi
ble bundles”\, and showed the existence of cobordism maps under some res
trictive conditions. This was enough to show that the equivariant instanto
n homology groups I(Y) depend on at most a small amount of auxiliary data
(in addition to the choice of 3-manifold): “signature data”\, which is
roughly the choice of even integer for every first homology class. To pro
ve that I(Y) is independent of this choice\, we need cobordism maps that d
o not satisfy those restrictive conditions — which involve a failure of
equivariant transversality\, a notoriously slippery issue to deal with.\n\
nWe will first discuss a new finite-dimensional model for the equivariant
instanton chain complex\, and try to get a concrete handle on what it look
s 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 map need
ed for invariance above. With invariance handled\, we are able to prove th
at we have cobordism maps under any negative-definite or admissible cobord
ism\, with no conditions on signature.\n\nWe will conclude with a discussi
on of potential applications and future directions. This work is joint wit
h Ali Daemi.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Langte Ma (Stonybrook University)
DTSTART:20210512T183000Z
DTEND:20210512T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/28
DESCRIPTION:Title: Torus Signature And Periodic Rho Invariant\nby Langte Ma (
Stonybrook University) as part of Gauge theory virtual\n\n\nAbstract\nLet
T in X be an essentially embedded torus in a homology $S^1 \\times S^3$. T
here are two approaches defining an equivariant signature invariant for\nt
he pair (X\, T): one introduced by Echeverria as the signed count of degre
e zero singular instantons\; the other given by Ruberman as the the rho in
variant 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 produc
t $S^1 \\times (Y\, K)$ with K a knot in an integral homology sphere Y. We
show that these two invariants are equivalent. The proof is to relate bot
h invariants to the periodic\nrho invariant of the ASD DeRham operator. Th
e relation with a conjecture of Furuta-Ohta will also be discussed.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariano Echeverria (Rutgers University)
DTSTART:20210519T183000Z
DTEND:20210519T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/29
DESCRIPTION:Title: The SO(3) vortex equations over orbifold Riemann surfaces\
nby Mariano Echeverria (Rutgers University) as part of Gauge theory virtua
l\n\n\nAbstract\nWe study the general properties of the moduli spaces of S
O(3) vortices over orbifold Riemann surfaces and use these to characterize
the solutions of the SO(3) monopole equations on Seifert manifolds follow
ing in the footsteps of Mrowka\, Ozsváth and Yu.\n\nWe also study the sol
utions to the SO(3) monopole equations on the product of a circle and a su
rface in order to motivate the construction of a version of monopole Floer
homology\, which we call framed monopole Floer homology\, in analogy with
the construction given by Kronheimer and Mrowka for the case of instanton
Floer homology.\n\nFinally\, the SO(3) vortex moduli spaces provide a nic
e toy model for recent work due to Feehan and Leness regarding the study o
f a natural Morse-Bott function on the moduli space of SO(3) monopoles ove
r Kahler manifolds. In particular\, we compute the Morse-Bott indices of t
his function.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Rasmussen (University of Cambridge)
DTSTART:20210526T183000Z
DTEND:20210526T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/30
DESCRIPTION:Title: An $SL_2(R)$ Casson-Lin Invariant\nby Jacob Rasmussen (Uni
versity of Cambridge) as part of Gauge theory virtual\n\n\nAbstract\nIn th
e 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 $SU(2)$\nwhich h
ave fixed meridinal holonomy. I’ll discuss an analogous construction\, b
ut with $SL_2(R)$ in place of $SU(2)$. The sum of the two invariants turns
out to be independent of the choice of the meridinal\nholonomy. This fact
has applications to a number of problems\, including the construction of
left-orders on 3-manifolds obtained from the knot complement and the exist
ence of real parabolic representations on the\nknot complement.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Marengon (Max Planck Institute)
DTSTART:20210602T183000Z
DTEND:20210602T193000Z
DTSTAMP:20260422T225926Z
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\nAbstr
act\nGiven a closed 4-manifold X with an indefinite intersection form\, we
consider smoothly embedded surfaces in X-int($B^4$)\, with boundary a giv
en knot K in the 3-sphere.\nWe give several methods to bound the genus of
such surfaces in a fixed homology class. Our techniques include adjunction
inequalities from Heegaard Floer homology and the Bauer-Furuta invariants
\, and the 10/8 theorem.\nIn particular\, we present obstructions to a kno
t being H-slice (that is\, bounding a null-homologous disc) in a 4-manifol
d and show that the set of H-slice knots can detect exotic smooth structur
es on closed 4-manifolds.\n\nThis is joint work with Ciprian Manolescu and
Lisa Piccirillo.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Baldwin (Boston College)
DTSTART:20211007T173000Z
DTEND:20211007T183000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/32
DESCRIPTION:Title: Fixed points\, Khovanov homology\, and Dehn surgery\nby Jo
hn Baldwin (Boston College) as part of Gauge theory virtual\n\n\nAbstract\
nWe partially characterize L-space knots of genus 2\, in both the Heegaard
and instanton Floer settings\, using relationships between these theories
and the symplectic Floer cohomology of surface diffeomorphisms. We combin
e this with gauge theory and deep results in Khovanov homotopy to prove th
at Khovanov homology detects the cinquefoil. In another application\, we p
rove that the fundamental group of 3-surgery on a nontrivial knot always a
dmits an irreducible SU(2)-representation\, answering an old question of K
ronheimer and Mrowka from their work on the Property P conjecture. All of
this is joint with Steven Sivek. The first application is also joint with
Ying Hu\, and the second is also joint with Zhenkun Li and Fan Ye.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sudipta Ghosh (Louisiana State University)
DTSTART:20211021T173000Z
DTEND:20211021T183000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/33
DESCRIPTION:Title: Connected sums and directed systems in knot Floer homologies\nby Sudipta Ghosh (Louisiana State University) as part of Gauge theory
virtual\n\n\nAbstract\nKnot Floer homology is an invariant of knot which w
as first introduced in the context of Heegaard Floer homology and later ex
tended to other Floer theories. In this talk\, we discuss a new approach t
o the connected sum formula using direct limits. Our methods apply to vers
ions of knot Floer homology arising in the context of Heegaard\, instanton
and monopole Floer homology. This is joint work with Ian Zemke.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anubhav Mukherjee (Georgia Tech)
DTSTART:20211104T173000Z
DTEND:20211104T183000Z
DTSTAMP:20260422T225926Z
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\nAbst
ract\nAn important principle in 4-dimesional topology\, as discovered by W
all in the 1960s\, states that all exotic phenomena are eliminated by suff
iciently many stabilizations (i.e.\, taking connected sum with $S^2 \\time
s S^2$’s). Since then\, it has been a fundamental problem to search for
exotic phenomena that survives one stabilization. In this talk\, we will e
stablish the first pair of orientable exotic surfaces (in a puctured K3) w
hich are not smoothly isotopic even after one stabilization. A key ingredi
ent in our argument is a vanishing theorem for the family Bauer-Furuta inv
ariant\, proved using equivariant stable homotopy theory. This theorem app
lies to a large family of spin 4-manifolds and has some interesting applic
ations in Smale’s conjecture (about exotic diffeomorphisms on $S^4$). In
particular\, it implies that the $S^1$-equivariant or non-equivariant fam
ily Bauer-Furuta invariant do not detect an exotic diffeomorphism on $S^4$
and it suggests that the Pin(2)-symmetry could be a game changer. \n\nThi
s is a joint work with Jianfeng Lin.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Ye (University of Cambridge)
DTSTART:20211118T183000Z
DTEND:20211118T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/35
DESCRIPTION:Title: A large surgery formula for instanton Floer homology\nby F
an Ye (University of Cambridge) as part of Gauge theory virtual\n\n\nAbstr
act\nFor a knot K in the 3-sphere\, Ozsváth-Szabó and Rasmussen introduc
ed a large surgery formula which computes the Heegaard Floer homology 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 ana
logous formula for instanton Floer homology. More precisely\, I construct
two differentials on the instanton knot homology of K and use them to comp
ute the framed instanton homology of m-surgery for any large integer m. As
an application\, I show that if the coefficients of the Alexander polynom
ial of K are not in {-1\,0\,1}\, then there exists an irreducible represen
tation from the fundamental group of $S^3_r(K)$ to SU(2) for all but finit
ely many rational numbers r. In particular\, all hyperbolic alternating kn
ots satisfy this condition. Also by this large surgery formula\, I show in
stanton and Heegaard knot Floer homology agree for any Berge knot\, and th
at the framed instanton homology of $S^3_r(K)$ agrees with the Heegaard Fl
oer homology for any genus-one alternating knot K. This is a joint work wi
th Zhenkun Li.\n\nRelated preprints:\n\nhttps://arxiv.org/abs/2107.11005\n
\nhttps://arxiv.org/abs/2107.10490\n\nhttps://arxiv.org/abs/2101.05169\n\n
https://arxiv.org/abs/2010.07836\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minh Nguyen (University of Arkansas)
DTSTART:20211202T183000Z
DTEND:20211202T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/36
DESCRIPTION:Title: Finite dimensional approximation and Pin(2)-equivariant proper
ties for the Rarita-Schwinger-Seiberg-Witten equations\nby Minh Nguyen
(University of Arkansas) as part of Gauge theory virtual\n\n\nAbstract\nT
he Rarita-Schwinger operator Q was initially proposed in the 1941 paper by
Rarita and Schwinger to study wave functions of particles of spin 3/2\, a
nd there is a vast amount of physics literature on its properties. Roughly
speaking\, 3/2−spinors are spinor-valued 1-forms that also happen to be
in the kernel of the Clifford multiplication. Let X be a Riemannian spin
4−manifold. Associated to\na fixed spin structure on X\, we define a Sei
berg-Witten-like system of non-linear\nPDEs using Q and the Hodge-Dirac op
erator after suitable gauge-fixing.\nThe moduli space of solutions M conta
ins (3/2-spinors\, purely imaginary 1-forms).\nUnlike in the case of Seibe
rg-Witten equations\, solutions are hard to find or construct. However\, b
y adapting the finite-dimensional technique of Furuta\, we provide a topol
ogical condition of X to ensure that M is non-compact\; and thus\, contain
s\ninfinitely many elements.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linh Truong (University of Michigan)
DTSTART:20220210T193000Z
DTEND:20220210T203000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/37
DESCRIPTION:Title: Homology concordance and knot Floer homology\nby Linh Truo
ng (University of Michigan) as part of Gauge theory virtual\n\n\nAbstract\
nHomology concordance and knot Floer homology\n\nAbstract: Two knots in ho
mology 3-spheres are homology concordant if they are smoothly concordant i
n a homology cobordism. I will explain how to construct integer-valued hom
omorphisms from this group of knots up to homology concordance. This const
ruction uses knot Floer homology and generalizes concordance homomorphisms
for knots in the 3-sphere.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clayton McDonald (UC Davis)
DTSTART:20220217T183000Z
DTEND:20220217T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/38
DESCRIPTION:Title: Surface slices and homology spheres\nby Clayton McDonald (
UC Davis) as part of Gauge theory virtual\n\n\nAbstract\nIn this talk\, we
develop the theory of the diagrammatics of surface cross sections to prov
e that there are an infinite number of homology 3-spheres smoothly embedda
ble in a homology 4-sphere but not in a homotopy 4-sphere. Our primary obs
truction comes from work of Daemi.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Zemke (Princeton University)
DTSTART:20220303T183000Z
DTEND:20220303T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/39
DESCRIPTION:Title: The link surgery formula and plumbed 3-manifolds\nby Ian Z
emke (Princeton University) as part of Gauge theory virtual\n\n\nAbstract\
nLattice homology is a combinatorial invariant of plumbed 3-manifolds due
to Némethi. The definition is a formalization of Ozsváth and Szabó’s
computation of the Heegaard Floer homology of plumbed 3-manifolds. Nemethi
conjectured that lattice homology is isomorphic to Heegaard Floer homolog
y. For a restricted class of plumbings\, this isomorphism is known to hold
\, due to work of Ozsváth-Szabó\, Némethi\, and Ozsváth-Stipsicz-Szab
ó. By using the Manolescu-Ozsváth link surgery formula for Heegaard Floe
r homology\, we prove the conjectured isomorphism in general. In this talk
\, we will talk about aspects of the proof\, as well as some other perspec
tives in terms of bordered 3-manifolds with torus boundary.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayato Imori (Kyoto University)
DTSTART:20220317T173000Z
DTEND:20220317T183000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/40
DESCRIPTION:Title: Instanton knot invariants with rational holonomy parameters an
d an application for torus knot groups\nby Hayato Imori (Kyoto Univers
ity) as part of Gauge theory virtual\n\n\nAbstract\nSeveral knot invariant
s from instantons provide powerful tools to study the topology of knots in
terms of representations of knot groups. In this talk\, we introduce a ge
neralization of Daemi-Scaduto’s equivariant singular instanton Floer the
ory to rational holonomy parameters. As an application\, it enables us to
show that any SU(2)-representation of torus knot groups can be extended to
the complement of any concordance from the torus knot to another knot. Th
is result gives further evidence to a version of slice-ribbon conjecture t
o torus knots.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Kirk (Indiana University)
DTSTART:20220414T173000Z
DTEND:20220414T183000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/41
DESCRIPTION:Title: Holonomy perturbed SU(2) character varieties of tangles\nb
y Paul Kirk (Indiana University) as part of Gauge theory virtual\n\n\nAbst
ract\nOne approach to produce topological invariants of low-dimensional ma
nifolds by a 2-step process\, the first step applies the SU(2) character v
ariety functor\, which converts surfaces into (singular) symplectic manifo
lds\, and converts 3-manifolds with boundary into Lagrangian immersions. T
he second step applies Lagragian Floer homology to the resulting Lagrangia
n immersion. The Atiyah-Floer conjecture posits an identification of the r
esulting theory with instanton homology. In order to be sensible\, the fir
st step requires the use of holonomy perturbations of Taubes and Donaldson
to make flat moduli spaces smooth. This talk will describe several explic
it calculations of holonomy perturbed character varieties\, and how to ext
ract topological information from them\, summarizing ideas worked out in s
everal articles co-authored with Cazassus\, Kotelskiy\, Herald\, Hedden\,
and Hogancamp.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gard Olav Helle
DTSTART:20220331T173000Z
DTEND:20220331T183000Z
DTSTAMP:20260422T225926Z
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 obtain
ed\nfrom the canonical action of the finite subgroups of SU(2) on the\n3-s
phere. In this talk I will discuss calculations of the equivariant\ninstan
ton Floer groups\, in the sense of Miller Eismeier\, for the\ntrivial SU(2
)-bundle over this family of manifolds.\nDue to work of Austin and Kronhei
mer one may obtain very precise\ninformation about the instanton moduli sp
aces over the cylinders\nassociated with these manifolds. If one requires
2 to be invertible\nin the ring of coefficients\, this is sufficient to ex
plicitly identify\nthe complexes calculating equivariant instanton Floer h
omology. From\nthere it is a matter of algebra to extract explicit calcula
tions\nin all cases.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Daemi (Washington University in St Louis)
DTSTART:20221003T183000Z
DTEND:20221003T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/43
DESCRIPTION:Title: The knot complement problem for nullhomotopic knots\nby Al
i Daemi (Washington University in St Louis) as part of Gauge theory virtua
l\n\nLecture held in Simons Auditorium\, MSRI.\n\nAbstract\nIn their celeb
rated work\, Gordon and Luecke proved that knots\nin the three-dimensional
sphere are determined by their complements.\nSubsequently\, Boileau asked
whether the same result holds for null-homotopic\nknots in arbitrary 3-ma
nifolds. In this talk\, I will discuss a program to\nanswer this question.
In particular\, I will explain how one can give an\naffirmative answer to
Boileau's question for arbitrary knots in some families\nof 3-manifolds i
ncluding any connected sum of Brieskorn homology spheres.\nThis is joint w
ork with Tye Lidman.\n\nTalks will be broadcast live from the Simons Audit
orium at SLMath/MSRI\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Hutchings (University of California\, Berkeley)
DTSTART:20221017T183000Z
DTEND:20221017T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/44
DESCRIPTION:Title: Floer theory of families of equivalent objects\nby Michael
Hutchings (University of California\, Berkeley) as part of Gauge theory v
irtual\n\nLecture held in Simons Auditorium\, MSRI.\n\nAbstract\nWe review
a general scheme for extending Floer theoretic invariants to invariants o
f families of equivalent objects for which the Floer theory is defined (e.
g. families of three-manifolds\, families of Hamiltonian isotopic symplect
omorphisms\, etc.). We discuss how this kind of construction has been used
\, and potentially could be used\, for various kinds of Floer theory\, wit
h applications to symplectic geometry and (maybe) gauge theory.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tye Lidman (North Carolina State University)
DTSTART:20221031T183000Z
DTEND:20221031T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/45
DESCRIPTION:Title: Instantons and handle decompositions.\nby Tye Lidman (Nort
h Carolina State University) as part of Gauge theory virtual\n\nLecture he
ld in Simons Auditorium\, MSRI.\n\nAbstract\nWe show that there are homolo
gy three-spheres for which any bounding definite four-manifold requires lo
ts of handles. The proof uses instanton Floer homology to show that lots o
f representations on the boundary must extend over the four-manifold. This
is joint work with Paolo Aceto\, Ali Daemi\, Jen Hom\, and JungHwan Park.
\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masaki Taniguchi
DTSTART:20221121T193000Z
DTEND:20221121T203000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/46
DESCRIPTION:Title: Relative genus bounds from Floer K-theory\nby Masaki Tanig
uchi as part of Gauge theory virtual\n\nLecture held in Simons Auditorium\
, MSRI.\n\nAbstract\nWe provide a relative genus bound obtained as a versi
on of 10/8-inequality for knots. The 10/8-inequality will be proven by obs
erving “the real part” of Seiberg-Witten Floer homotopy type for branc
hed covers. This work is joint work with Hokuto Konno and Jin Miyazawa.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Lotay (Oxford University)
DTSTART:20221212T193000Z
DTEND:20221212T203000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/47
DESCRIPTION:Title: Stability and neck pinches in Lagrangian mean curvature flow\nby Jason Lotay (Oxford University) as part of Gauge theory virtual\n\n
Lecture held in Simons Auditorium\, MSRI.\n\nAbstract\nThe famous relation
between stability of holomorphic vector bundles and existence of Hermitia
n Yang-Mills connections can be demonstrated using Yang-Mills flow. Motiv
ated by this theory and Mirror Symmetry\, Thomas-Yau conjectured a stabili
ty condition for Lagrangian mean curvature flow which detects when the flo
w wants to break up the Lagrangian. When such break up occurs in the flow
it is expected to be a singularity called a neck pinch. I will report on
joint work with F. Schulze and G. Szekelyhidi which shows that\, for Lagr
angian surfaces\, Thomas-Yau stability does indeed rule out neck pinch sin
gularities breaking up the Lagrangian along the flow.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiajun Yan (University of Virginia)
DTSTART:20230210T183000Z
DTEND:20230210T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/48
DESCRIPTION:Title: A New Gauge-Theoretic Construction of 4-dimensional Hyperkähl
er ALE Spaces\nby Jiajun Yan (University of Virginia) as part of Gauge
theory virtual\n\n\nAbstract\nNon-compact hyperkähler spaces arise frequ
ently in gauge theory. The 4-dimensional hyperkähler ALE spaces are a spe
cial class of non-compact hyperkähler spaces. They are in one-to-one corr
espondence with the finite subgroups of SU(2) and have interesting connect
ions with representation theory and singularity theory captured by the McK
ay Correspondence.\n\nIn this talk\, we first review the finite-dimensiona
l construction of the 4-dimensional hyperkähler ALE spaces given by Peter
Kronheimer in his PhD thesis. Then we give a new construction of these sp
aces via gauge theory.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bob Gompf
DTSTART:20230224T183000Z
DTEND:20230224T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/49
DESCRIPTION:Title: Transverse Tori in Engel Manifolds\nby Bob Gompf as part o
f Gauge theory virtual\n\n\nAbstract\nEngel manifolds are closely related
to contact manifolds\, but only occur in dimension 4. They are much less w
ell understood than contact manifolds. For example\, it is still unknown i
f “tight” Engel structures exist. A primary tool for understanding suc
h issues for contact 3-manifolds is transverse knot theory. Every knot in
a contact 3-manifold is isotopic to transverse knots\, realizing infinitel
y many values of the associated homotopy invariant (self-linking number) w
hen it is defined. At a 2017 AIM conference\, Eliashberg suggested the ana
logous problem of understanding transverse (closed\, oriented) surfaces in
Engel manifolds. It is easy to see that such transverse surfaces are nece
ssarily tori with trivial normal bundles\, but no further results were obt
ained at the time\, beyond a few examples. It now turns out that these con
ditions are also sufficient: Every torus with trivial normal bundle is iso
topic to infinitely many transverse tori\, analogously to knots in contact
3-manifolds. This could potentially turn into a powerful tool for underst
anding Engel manifolds.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Hedenlund
DTSTART:20230310T183000Z
DTEND:20230310T193000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/50
DESCRIPTION:Title: Seiberg-Witten Floer Theory and Twisted Parametrised Spectra\nby Alice Hedenlund as part of Gauge theory virtual\n\n\nAbstract\nSeib
erg-Witten theory has played a central role in the study of smooth low-dim
ensional manifolds since their introduction in the 90s. Parallel to this\,
Cohen\, Jones\, and Segal asked the question of whether various types of
Floer homology could be upgraded to the homotopy level by constructing (st
able) homotopy types encoding Floer data. In 2003\, Manolescu constructed
Seiberg-Witten Floer stable homotopy types for rational homology 3-spheres
\, and in particular used these to settle the triangulation conjecture onc
e and for all.\n\nIn this talk\, I will report on joint work in progress w
ith S. Behrens and T. Kragh in which we construct “twisted parametrised
spectra” from Seiberg-Witten Floer data. These are the main mathematical
objects in twisted stable homotopy theory and were introduced by Douglas
in his PhD thesis. We give an introduction to twisted parametrised spectra
and explain how Seiberg-Witten Floer data naturally gives rise to such ob
jects. This is work in progress joint with S. Behrens and T. Kragh.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Mark (University of Virginia)
DTSTART:20230324T173000Z
DTEND:20230324T183000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/51
DESCRIPTION:Title: Fillable contact structures from positive surgery\nby Thom
as Mark (University of Virginia) as part of Gauge theory virtual\n\n\nAbst
ract\nFor a Legendrian knot $K$ in a closed contact 3-manifold\, we descri
be a necessary and sufficient condition for contact $n$-surgery along $K$
to yield a weakly symplectically fillable contact manifold\, for some inte
ger $n>0$. When specialized to knots in the standard 3-sphere this gives a
n effective criterion for the existence of a fillable positive surgery\, a
long with various obstructions. These are sufficient to determine\, for ex
ample\, whether such a surgery exists for all knots of up to 10 crossings.
The result also has certain purely topological consequences\, such as the
fact that a knot admitting a lens space surgery must have slice genus equ
al to its 4-dimensional clasp number. We will mainly explore these topolog
ically-flavored aspects\, but will give some hints of the general proof if
time allows.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhenkun Li
DTSTART:20230407T173000Z
DTEND:20230407T183000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/52
DESCRIPTION:Title: A surgery formula in instanton Floer theory\nby Zhenkun Li
as part of Gauge theory virtual\n\n\nAbstract\nInstanton Floer homology i
s introduced by Floer in 1980s. It is a powerful invariants for 3-manifold
s and knots and links inside them. There have been many important applicat
ions of Instanton Floer homology\, such as the approval of Property P conj
ecture. It has been conjectured that the instanton Floer homology is isomo
rphic to other versions of Floer theory. Though this conjecture is still w
idely open\, one could ask whether some important properties that has been
known to be true in other Floer theory also hold for instanton theory. On
e such property is the surgery formula\, which relates the instanton Floer
homology of a 3-manifold coming from Dehn surgeries along a knot with the
instanton Floer homology of the knot. In this talk\, we will present a su
rgery formula for instanton theory\, and describe how this formula can be
applied in computing instanton Floer homology and study the SU(2)-represen
tations of fundamental groups of 3-manifolds.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akram Alishahi
DTSTART:20230428T173000Z
DTEND:20230428T183000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/53
DESCRIPTION:Title: Khovanov homology and involutive Heegaard Floer homology\n
by Akram Alishahi as part of Gauge theory virtual\n\n\nAbstract\nFor any k
not K in the 3-sphere\, Ozsváth and Szabó construct a spectral sequence
from the Khovanov homology of K to the Heegaard Floer homology of the bran
ched double cover of K. This spectral sequence is the first of many intere
sting works studying the interactions of Heegaard Floer homology and Khova
nov homology over the past two decades. In 2017\, Hendricks and Manolescu
incorporated the conjugation action on Heegaard Floer homology to produce
a richer 3-manifold invariant\, called involutive Heegaard Floer homology.
In this talk\, we will discuss an involutive version of Ozsváth-Szabó
’s spectral sequence that converges to the involutive Heegaard Floer hom
ology of the branched double cover of the knot. This is a joint work with
Linh Truong and Melissa Zhang.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianfeng Lin
DTSTART:20230918T140000Z
DTEND:20230918T150000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/54
DESCRIPTION:Title: Configuration space integrals and formal smooth structures.\nby Jianfeng Lin as part of Gauge theory virtual\n\n\nAbstract\nWatanabe
disproved the 4-dimensional Smale conjecture by establishing many disk bu
ndles which are topologically trivial but not smoothly so. Amazingly\, Wat
anabe used Kontsevich’s characteristic classes\, which are very differen
t from previous invariants that can detect exoticness in dimension 4 (e.g.
the Seiberg-Witten invariants and the Donaldson invariants). So one may w
onder what’s the role played by the smooth structure in this story. In t
his talk\, I will sketch our proof that Kontsevich’s characteristic clas
ses only depend on a formal smooth structure (i.e. a vector bundle structu
re on the topological tangent bundle). This makes the invariant more flexi
ble and allows several new applications. For example\, we show that the ho
meomorphism group of the 4-dimensional sphere or Euclidian space has nontr
ivial rational homotopy/homology group in infinitely many dimensions. And
we show that for any compact orientable 4-manifold\, the natural inclusion
from the diffeomorphism group to the homeomorphism group is not a homotop
y equivalence. Furthermore\, we discovered a new MMM (Morita-Miller-Mumfor
d) class\, which can obstruct the smoothing of 4-dimensional topological
bundles. The talk is based on a joint work with Yi Xie.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Miller Eismeier (University of Vermont)
DTSTART:20231016T140000Z
DTEND:20231016T150000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/55
DESCRIPTION:Title: Filtered instanton Floer homology and cosmetic surgery\nby
Mike Miller Eismeier (University of Vermont) as part of Gauge theory virt
ual\n\n\nAbstract\nIf Y is a closed oriented 3-manifold\, its Chern-Simons
function is a function on a certain infinite-dimensional space\, and the
instanton Floer homology I_*(Y) is constructed as the Morse homology of th
is function. What's special about the Chern-Simons function is that it dep
ends only on the topology of Y\, not any other geometric input or auxiliar
y data. As a result\, we can define filtered Floer homologies F_r I_*(Y) w
hich are roughly the Morse homology of the sublevel set cs^{-1}(-infty\, r
]\, and these give topological invariants of Y with good structural proper
ties.\n\nThere is a long history of using the Chern-Simons function to pro
ve results about homology cobordism of 3-manifolds. It was used in Furuta'
s 1990 proof that the homology cobordism group is infinitely generated\; r
ecently\, Nozaki-Sato-Taniguchi used the CS filtration to give examples of
integer homology spheres Y so that any 4-manifold bounding Y must be inde
finite (there must be some essential surface Sigma with self-intersection
number zero).\n\nI will discuss applications of a different sort: distingu
ishing the diffeomorphism types of two 3-manifolds using their filtered Fl
oer homology\, with applications to cosmetic surgery problems. This work i
s joint with Tye Lidman.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luya Wang (Stanford University)
DTSTART:20231030T140000Z
DTEND:20231030T150000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/56
DESCRIPTION:Title: Deformation inequivalent symplectic structures and Donaldson
’s four-six question.\nby Luya Wang (Stanford University) as part of
Gauge theory virtual\n\n\nAbstract\nStudying symplectic structures up to
deformation equivalences is a fundamental question in symplectic geometry.
Donaldson asked: given two homeomorphic closed symplectic four-manifolds\
, are they diffeomorphic if and only if their stabilized symplectic six-ma
nifolds\, obtained by taking products with CP^1 with the standard symplect
ic form\, are deformation equivalent? I will discuss joint work with Amand
a Hirschi on showing how deformation inequivalent symplectic forms remain
deformation inequivalent when stabilized\, under certain algebraic conditi
ons. This gives the first counterexamples to one direction of Donaldson’
s “four-six” question and the related Stabilizing Conjecture by Ruan.\
n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Zemke (Princeton University)
DTSTART:20231113T150000Z
DTEND:20231113T160000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/57
DESCRIPTION:Title: A general Heegaard Floer surgery formula.\nby Ian Zemke (P
rinceton University) as part of Gauge theory virtual\n\n\nAbstract\nIn thi
s talk\, we will describe a very flexible version of the Manolescu-Ozsvath
-Szabo surgery formula which is purely “local” and holds for any link
in any 3 manifold. Reinterpreted\, the construction gives a bordered invar
iant for any 3-manifold with torus boundaries. In this talk\, we will focu
s on basic examples and illustrations of the construction\, such as defini
tion of the chain complex for the unknot or an S^1 fiber in S^1 x S^2. Tim
e 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://researchseminars.org/talk/GaugeTheoryVirtual/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Ladu
DTSTART:20231127T150000Z
DTEND:20231127T160000Z
DTSTAMP:20260422T225926Z
UID:GaugeTheoryVirtual/58
DESCRIPTION:Title: Non-smoothable homeomorphisms of 4-manifolds with boundary.\nby Roberto Ladu as part of Gauge theory virtual\n\n\nAbstract\nIn 1988
Friedman and Morgan used Donaldson polynomial invariants to show that seve
ral simply connected algebraic surfaces possess self-homeomorphisms which
are non-smoothable i.e. are not C^0-isotopic to any self-diffeomorphism. S
ince then many other pairs (X\,phi) with X a simply-connected 4-manifold a
nd phi:X->X a non-smoothable homeomorphism have been found. In all known e
xamples phi acts non-trivially in homology\; when X is closed\, this is a
necessary condition for non-smoothability for otherwise phi would be isoto
pic to the identity (Perron-Quinn). I will show that this is not necessary
anymore when X has non-empty boundary. More precisely\, I will show how t
o construct simply connected 4-manifolds with non-empty boundary possessin
g non-smoothable self-homeomorphisms which fix the boundary pointwise and
act trivially in homology. This is a joint work with Daniel Galvin.\n
LOCATION:https://researchseminars.org/talk/GaugeTheoryVirtual/58/
END:VEVENT
END:VCALENDAR