BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Matthew Hedden
DTSTART:20200608T150000Z
DTEND:20200608T160000Z
DTSTAMP:20260404T060944Z
UID:BIRS_20w5088/1
DESCRIPTION:Title: Relative adjunction inequalities and their applications\nb
y Matthew Hedden as part of Interactions of gauge theory with contact and
symplectic topology in dimensions 3 and 4\n\n\nAbstract\nI'll discuss ongo
ing joint work with Katherine Raoux that uses knot Floer homology to estab
lish relative adjunction inequalities. These inequalities bound the Euler
characteristics of properly embedded smooth cobordisms between links in th
e boundary of certain smooth 4-manifolds. The inequalities generalize the
slice genus bound for the "tau" invariant studied by Ozsvath-Szabo and Ras
mussen. I will use our inequalities to define concordance invariants of li
nks\, prove new results about contact structures\, motivate a 4-dimensiona
l interpretation of tightness\, and to show that knots with simple Floer h
omology in lens spaces (or L-spaces) minimize rational slice genus amongst
all curves in their homology class\, upgrading a remarkable result of Ni
and Wu pertaining to the rational Seifert genus.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5088/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Lipshitz
DTSTART:20200608T160000Z
DTEND:20200608T170000Z
DTSTAMP:20260404T060944Z
UID:BIRS_20w5088/2
DESCRIPTION:Title: Khovanov homology detects split links\nby Robert Lipshitz
as part of Interactions of gauge theory with contact and symplectic topolo
gy in dimensions 3 and 4\n\n\nAbstract\nWe will use the Ozsváth-Szabó an
d Kronheimer-Mrowka spectral sequences to show that the module structure o
n Khovanov homology detects split links. This is joint work with Sucharit
Sarkar.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5088/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vera Vertesi
DTSTART:20200609T150000Z
DTEND:20200609T160000Z
DTSTAMP:20260404T060944Z
UID:BIRS_20w5088/3
DESCRIPTION:Title: Bordered contact invariants\nby Vera Vertesi as part of In
teractions of gauge theory with contact and symplectic topology in dimensi
ons 3 and 4\n\n\nAbstract\nThe relationship between contact topology and v
arious Floer homologies has been a fundamental tool to settle open questio
n in low dimensional topology. The contact invariant in Heegaard Floer hom
ology was one of the main instrument in these applications. In this talk I
will extend the definition of the contact invariant for bordered Floer ho
mology. The bordered contact invariant satisfies a gluing formula and reco
vers the contact invariant for closed and sutured manifolds. The main tool
s for this extension are foliated open books\, and I will spend most of th
e time explaining these\, and another application concerning the additivit
y of the support norm for tight contact structures. Parts of this talk is
joint work with Alishahi\, Foldvari\, Hendricks\, Licata\, and Petkova.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5088/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Lambert-Cole
DTSTART:20200609T160000Z
DTEND:20200609T170000Z
DTSTAMP:20260404T060944Z
UID:BIRS_20w5088/4
DESCRIPTION:by Peter Lambert-Cole as part of Interactions of gauge theory
with contact and symplectic topology in dimensions 3 and 4\n\nAbstract: TB
A\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5088/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Hanselman
DTSTART:20200611T140000Z
DTEND:20200611T150000Z
DTSTAMP:20260404T060944Z
UID:BIRS_20w5088/5
DESCRIPTION:Title: Knot Floer homology as immersed curves\nby Jonathan Hansel
man as part of Interactions of gauge theory with contact and symplectic to
pology in dimensions 3 and 4\n\n\nAbstract\nI will describe how the knot F
loer homology of a knot K can be represented by a decorated collection of
immersed curves in the marked torus. The surgery formula for knot Floer ho
mology translates nicely to this setting: the Heegaard Floer homology HF^-
of p/q surgery on K is given by the Lagrangian Floer homology of these im
mersed curves with a line of slope p/q. For a simplified “UV = 0” vers
ion of knot Floer homology\, the analogous statements follow from earlier
work with Rasmussen and Watson by passing through the bordered Floer homol
ogy of the knot complement\, but a more direct approach allows us to captu
re the stronger “minus” invariant by adding decorations to the curves.
Often recasting algebraic structures in terms of geometric objects in thi
s way leads to new insights and results\; I will mention some applications
of this immersed curves framework\, including obstructions to cosmetic su
rgeries.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5088/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristen Hendricks
DTSTART:20200612T140000Z
DTEND:20200612T150000Z
DTSTAMP:20260404T060944Z
UID:BIRS_20w5088/6
DESCRIPTION:Title: Rank inequalities for the Heegaard Floer homology of branched
covers\nby Kristen Hendricks as part of Interactions of gauge theory w
ith contact and symplectic topology in dimensions 3 and 4\n\n\nAbstract\nI
n joint work with T. Lidman and R. Lipshitz\, we show that for K a nullhom
ologous knot in a 3-manifold Y and Sigma(Y\,K) a double cover of Y branche
d along K\, there exists a spectral sequence related the Heegaard Floer ho
mology of Sigma(Y\,K) and Y\, and a corresponding rank inequality for HFha
t. This extends recent work of T. Large and previous work of R. Lipshitz\,
and S. Sarkar\, and I.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5088/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josh Greene
DTSTART:20200611T150000Z
DTEND:20200611T160000Z
DTSTAMP:20260404T060944Z
UID:BIRS_20w5088/7
DESCRIPTION:Title: The rectangular peg problem\nby Josh Greene as part of Int
eractions of gauge theory with contact and symplectic topology in dimensio
ns 3 and 4\n\n\nAbstract\nI will discuss the context and solution of the r
ectangular peg problem: for every smooth Jordan curve and rectangle in the
Euclidean plane\, one can place four points on the curve at the vertices
of a rectangle similar to the one given. The solution involves symplectic
geometry in a surprising way. ‘Joint work with Andrew Lobb.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5088/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aliakbar Daemi
DTSTART:20200611T160000Z
DTEND:20200611T170000Z
DTSTAMP:20260404T060944Z
UID:BIRS_20w5088/8
DESCRIPTION:Title: Lagrangians\, SO(3)-instantons and the Atiyah-Floer Conjecture
\nby Aliakbar Daemi as part of Interactions of gauge theory with conta
ct and symplectic topology in dimensions 3 and 4\n\n\nAbstract\nA useful t
ool to study a 3-manifold is the space of representations of its fundament
al group into a Lie group. Any 3-manifold can be decomposed as the union o
f two handlebodies. Thus representations of the 3-manifold group into a Li
e group can be obtained by intersecting representation varieties of the tw
o handlebodies. Casson utilized this observation to define his celebrated
invariant. Later Taubes introduced an alternative approach to define Casso
n invariant using more geometric objects. By building on Taubes' work\, Fl
oer refined Casson invariant into a 3-manifold invariant which is known as
instanton Floer homology. The Atiyah-Floer conjecture states that Casson'
s original approach can be also used to define a graded vector space and t
he resulting invariant of 3-manifolds is isomorphic to instanton Floer hom
ology. In this talk\, I will discuss a variation of the Atiyah-Floer conje
cture\, which states that framed Floer homology (defined by Kronheimer and
Mrowka) is isomorphic to symplectic framed Floer homology (defined by Weh
rheim and Woodward). I will also discuss how techniques from symplectic to
pology could be useful to study framed Floer homology. This talk is based
on a joint work with Kenji Fukaya and Maksim Lipyanskyi.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5088/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juanita Pinzon-Caicedo
DTSTART:20200612T150000Z
DTEND:20200612T160000Z
DTSTAMP:20260404T060944Z
UID:BIRS_20w5088/9
DESCRIPTION:Title: Instanton and Heegaard Floer homologies of surgeries on torus
knots\nby Juanita Pinzon-Caicedo as part of Interactions of gauge theo
ry with contact and symplectic topology in dimensions 3 and 4\n\n\nAbstrac
t\nThe Instanton Floer chain complex is generated by flat connections on a
principal SU(2)-bundle over\, and the differential counts solutions to th
e Yang-Mills equation (known as instantons). The Heegaard Floer chain comp
lex is generated by the intersection points of curves in a Heegaard diagra
m for Y and its differential counts solutions to the Cauchy-Riemann equati
on (known as pseudoholomorphic Whitney discs). In the talk I will show tha
t these invariants are the same when the 3-manifold is surgery on S^3 alon
g a torus knot. This is joint work with Tye Lidman and Christopher Scaduto
.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5088/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Kotelskiy
DTSTART:20200612T160000Z
DTEND:20200612T170000Z
DTSTAMP:20260404T060944Z
UID:BIRS_20w5088/10
DESCRIPTION:Title: The earring correspondence on the pillowcase\nby Artem Ko
telskiy as part of Interactions of gauge theory with contact and symplecti
c topology in dimensions 3 and 4\n\n\nAbstract\nGiven a decomposition of a
knot K into two four-ended tangles T and T'\, the (holonomy perturbed) tr
aceless-SU(2)-character-variety functor produces Lagrangians R(T) and R(T'
) in the pillowcase P. Hedden\, Herald and Kirk used this to define Pillow
case homology\, conjecturally the symplectic counter-part of the singular
instanton homology I(K). Important in their construction is how R(T) and i
ts restriction to P are affected by “adding an earring”\, a process us
ed by Kronheimer and Mrowka to avoid reducibles. The object that governs t
his process turns out to be an immersed Lagrangian correspondence from pil
lowcase to itself. We will describe this correspondence in detail\, and st
udy its action on Lagrangians. In the case of the (4\,5) torus knot\, we w
ill see that a correction term from the bounding cochains must be added. W
e will indicate a particular figure eight bubble which recovers the desire
d bounding cochain\, as predicted by Bottman and Wehrheim. This is ioint w
ork with G. Cazassus\, C. Herald and P. Kirk.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5088/10/
END:VEVENT
END:VCALENDAR