BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Peter Kronheimer (Harvard) DTSTART:20200505T140000Z DTEND:20200505T151500Z DTSTAMP:20260423T024740Z UID:rlgts/1 DESCRIPTION:Title: Ge nus versus double-points for immersed surfaces\nby Peter Kronheimer (H arvard) as part of Regensburg low-dimensional geometry and topology semina r\n\n\nAbstract\nIf X is a simply-connected closed 4-manifold containing a n oriented embedded surface S of genus g\, is there always an immersed sph ere S' which represents the same homology class and has only g transverse double-points? Colloquially\, can we "trade handles for double points"? Th is is an open question\, though a "relative" version of the question (conc erning surfaces in the 4-ball bounding a given knot in the 3-sphere) is kn own to have a negative answer. For closed surfaces in closed 4-manifolds\, a particularly interesting class of examples comes from algebraic geometr y\, and includes the question of whether two smooth quintic surfaces can i ntersect in a singular rational curve. We will explore whether gauge theor y might be a tool that can be used to explore these questions.\n LOCATION:https://researchseminars.org/talk/rlgts/1/ END:VEVENT END:VCALENDAR