BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yangyang Li (Princeton University) DTSTART:20211028T200000Z DTEND:20211028T210000Z DTSTAMP:20260818T134326Z UID:CUNY_GeometricAnalysis/44 DESCRIPTION:Title: Minimal hypersurfaces in a generic 8-dimensional closed ma nifold\nby Yangyang Li (Princeton University) as part of CUNY Geometri c Analysis Seminar\n\n\nAbstract\nIn the recent decade\, the Almgren-Pitts min-max theory has advanced the existence theory of minimal surfaces in a closed Riemannian manifold $(M^{n+1}\, g)$. When $2 \\leq n+1 \\leq 7$\, many properties of these minimal hypersurfaces (geodesics)\, such as areas \, Morse indices\, multiplicities\, and spatial distributions\, have been well studied. However\, in higher dimensions\, singularities may occur in the constructed minimal hypersurfaces. This phenomenon invalidates many te chniques helpful in the low dimensions to investigate these geometric obje cts. In this talk\, I will discuss how to overcome the difficulty in a gen eric 8-dimensional closed manifold\, utilizing various deformation argumen ts. En route to obtaining generic results\, we prove the generic regularit y of minimal hypersurfaces in dimension 8. This talk is partially based on joint works with Zhihan Wang.\n LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/44/ END:VEVENT END:VCALENDAR