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:20260422T185741Z UID:BIRS_20w5088/1 DESCRIPTION:Title: Relative adjunction inequalities and their applications\nby Matth ew Hedden as part of Interactions of gauge theory with contact and symplec tic topology in dimensions 3 and 4\n\n\nAbstract\nI'll discuss ongoing joi nt work with Katherine Raoux that uses knot Floer homology to establish re lative adjunction inequalities. These inequalities bound the Euler charact eristics of properly embedded smooth cobordisms between links in the bound ary of certain smooth 4-manifolds. The inequalities generalize the slice g enus bound for the "tau" invariant studied by Ozsvath-Szabo and Rasmussen. I will use our inequalities to define concordance invariants of links\, p rove new results about contact structures\, motivate a 4-dimensional inter pretation of tightness\, and to show that knots with simple Floer homology in lens spaces (or L-spaces) minimize rational slice genus amongst all cu rves in their homology class\, upgrading a remarkable result of Ni and Wu pertaining to the rational Seifert genus.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5088/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Lipshitz DTSTART:20200608T160000Z DTEND:20200608T170000Z DTSTAMP:20260422T185741Z 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 topology in d imensions 3 and 4\n\n\nAbstract\nWe will use the Ozsváth-Szabó and Kronh eimer-Mrowka spectral sequences to show that the module structure on Khova nov homology detects split links. This is joint work with Sucharit Sarkar. \n LOCATION:https://researchseminars.org/talk/BIRS_20w5088/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Vera Vertesi DTSTART:20200609T150000Z DTEND:20200609T160000Z DTSTAMP:20260422T185741Z UID:BIRS_20w5088/3 DESCRIPTION:Title: Bordered contact invariants\nby Vera Vertesi as part of Interacti ons of gauge theory with contact and symplectic topology in dimensions 3 a nd 4\n\n\nAbstract\nThe relationship between contact topology and various Floer homologies has been a fundamental tool to settle open question in lo w dimensional topology. The contact invariant in Heegaard Floer homology w as one of the main instrument in these applications. In this talk I will e xtend the definition of the contact invariant for bordered Floer homology. The bordered contact invariant satisfies a gluing formula and recovers th e contact invariant for closed and sutured manifolds. The main tools for t his extension are foliated open books\, and I will spend most of the time explaining these\, and another application concerning the additivity of th e support norm for tight contact structures. Parts of this talk is joint w ork with Alishahi\, Foldvari\, Hendricks\, Licata\, and Petkova.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5088/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Lambert-Cole DTSTART:20200609T160000Z DTEND:20200609T170000Z DTSTAMP:20260422T185741Z 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://researchseminars.org/talk/BIRS_20w5088/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Hanselman DTSTART:20200611T140000Z DTEND:20200611T150000Z DTSTAMP:20260422T185741Z UID:BIRS_20w5088/5 DESCRIPTION:Title: Knot Floer homology as immersed curves\nby Jonathan Hanselman as part of Interactions of gauge theory with contact and symplectic topology in dimensions 3 and 4\n\n\nAbstract\nI will describe how the knot Floer ho mology of a knot K can be represented by a decorated collection of immerse d curves in the marked torus. The surgery formula for knot Floer homology 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 immersed curves with a line of slope p/q. For a simplified “UV = 0” version of knot Floer homology\, the analogous statements follow from earlier work wi th Rasmussen and Watson by passing through the bordered Floer homology of the knot complement\, but a more direct approach allows us to capture the stronger “minus” invariant by adding decorations to the curves. Often recasting algebraic structures in terms of geometric objects in this way l eads to new insights and results\; I will mention some applications of thi s immersed curves framework\, including obstructions to cosmetic surgeries .\n LOCATION:https://researchseminars.org/talk/BIRS_20w5088/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Kristen Hendricks DTSTART:20200612T140000Z DTEND:20200612T150000Z DTSTAMP:20260422T185741Z UID:BIRS_20w5088/6 DESCRIPTION:Title: Rank inequalities for the Heegaard Floer homology of branched covers< /a>\nby Kristen Hendricks as part of Interactions of gauge theory with con tact and symplectic topology in dimensions 3 and 4\n\n\nAbstract\nIn joint work with T. Lidman and R. Lipshitz\, we show that for K a nullhomologous knot in a 3-manifold Y and Sigma(Y\,K) a double cover of Y branched along K\, there exists a spectral sequence related the Heegaard Floer homology of Sigma(Y\,K) and Y\, and a corresponding rank inequality for HFhat. This extends recent work of T. Large and previous work of R. Lipshitz\, and S. Sarkar\, and I.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5088/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Josh Greene DTSTART:20200611T150000Z DTEND:20200611T160000Z DTSTAMP:20260422T185741Z UID:BIRS_20w5088/7 DESCRIPTION:Title: The rectangular peg problem\nby Josh Greene as part of Interactio ns of gauge theory with contact and symplectic topology in dimensions 3 an d 4\n\n\nAbstract\nI will discuss the context and solution of the rectangu lar peg problem: for every smooth Jordan curve and rectangle in the Euclid ean plane\, one can place four points on the curve at the vertices of a re ctangle similar to the one given. The solution involves symplectic geometr y in a surprising way. ‘Joint work with Andrew Lobb.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5088/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Aliakbar Daemi DTSTART:20200611T160000Z DTEND:20200611T170000Z DTSTAMP:20260422T185741Z UID:BIRS_20w5088/8 DESCRIPTION:Title: Lagrangians\, SO(3)-instantons and the Atiyah-Floer Conjecture\nb y Aliakbar Daemi as part of Interactions of gauge theory with contact and symplectic topology in dimensions 3 and 4\n\n\nAbstract\nA useful tool to study a 3-manifold is the space of representations of its fundamental grou p into a Lie group. Any 3-manifold can be decomposed as the union of two h andlebodies. Thus representations of the 3-manifold group into a Lie group can be obtained by intersecting representation varieties of the two handl ebodies. Casson utilized this observation to define his celebrated invaria nt. Later Taubes introduced an alternative approach to define Casson invar iant using more geometric objects. By building on Taubes' work\, Floer ref ined Casson invariant into a 3-manifold invariant which is known as instan ton Floer homology. The Atiyah-Floer conjecture states that Casson's origi nal approach can be also used to define a graded vector space and the resu lting invariant of 3-manifolds is isomorphic to instanton Floer homology. In this talk\, I will discuss a variation of the Atiyah-Floer conjecture\, which states that framed Floer homology (defined by Kronheimer and Mrowka ) is isomorphic to symplectic framed Floer homology (defined by Wehrheim a nd Woodward). I will also discuss how techniques from symplectic topology could be useful to study framed Floer homology. This talk is based on a jo int work with Kenji Fukaya and Maksim Lipyanskyi.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5088/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Juanita Pinzon-Caicedo DTSTART:20200612T150000Z DTEND:20200612T160000Z DTSTAMP:20260422T185741Z 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 theory with contact and symplectic topology in dimensions 3 and 4\n\n\nAbstract\nThe Instanton Floer chain complex is generated by flat connections on a princi pal SU(2)-bundle over\, and the differential counts solutions to the Yang- Mills equation (known as instantons). The Heegaard Floer chain complex is generated by the intersection points of curves in a Heegaard diagram for Y and its differential counts solutions to the Cauchy-Riemann equation (kno wn as pseudoholomorphic Whitney discs). In the talk I will show that these invariants are the same when the 3-manifold is surgery on S^3 along a tor us knot. This is joint work with Tye Lidman and Christopher Scaduto.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5088/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Artem Kotelskiy DTSTART:20200612T160000Z DTEND:20200612T170000Z DTSTAMP:20260422T185741Z UID:BIRS_20w5088/10 DESCRIPTION:Title: The earring correspondence on the pillowcase\nby Artem Kotelskiy as part of Interactions of gauge theory with contact and symplectic topol ogy 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) traceless -SU(2)-character-variety functor produces Lagrangians R(T) and R(T') in th e pillowcase P. Hedden\, Herald and Kirk used this to define Pillowcase ho mology\, conjecturally the symplectic counter-part of the singular instant on homology I(K). Important in their construction is how R(T) and its rest riction to P are affected by “adding an earring”\, a process used by K ronheimer and Mrowka to avoid reducibles. The object that governs this pro cess turns out to be an immersed Lagrangian correspondence from pillowcase to itself. We will describe this correspondence 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 bounding cochains must be added. We will indicate a particular figure eight bubble which recovers the desired bound ing cochain\, as predicted by Bottman and Wehrheim. This is ioint work wit h G. Cazassus\, C. Herald and P. Kirk.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5088/10/ END:VEVENT END:VCALENDAR