BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:Morse Index Stability and the Min-Max Sphere Eversion (Geometry Se
 minar)
DTSTART:20240318T110000
DTEND:20240318T120000
DTSTAMP:20260407T164123Z
UID:01242ecf8d11c930f67277f91682379779bad5ffa31814c407f09d03
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr. Alexis Michelat\nAbstract:\n\nIn 1957\, Stephen Smale show
 ed that the space of immersions of the 2-sphere into Euclidean 3-space is 
 path-connected. In particular\, there exists a path of smooth immersions c
 onnecting the standard embedding of the 2-sphere to the antipodal embeddin
 g\; such a path is called a sphere eversion. In the early 1980s\, drawing 
 inspiration from work of Robert Bryant\, Robert Kusner proposed to use the
  Willmore energy—a conformally invariant energy of immersions into Eucli
 dean space—as a distance function to determine the “optimal” sphere 
 eversion\, or min-max sphere eversion. More generally\, the Willmore energ
 y can be considered as a quasi-Morse function on the space of immersions o
 f any topological surface into a fixed Riemannian manifold\, and the above
  problem can be reformulated as finding the “best” representative of a
  regular homotopy class.\n\nIn geometric analysis\, upper Morse index boun
 ds are known in a variety of settings (minimal surfaces\, Yang-Mills conne
 ctions\, etc)\, but lower bounds are more elusive. About a year ago (arXiv
 :2212.03124)\, Francesca Da Lio\, Matilde Gianocca\, and Tristan Rivière 
 (ETH Zürich) developed a new method to show upper semi-continuity results
  in geometric analysis—that they applied to conformally invariant Lagran
 gians in dimension 2 (which include harmonic maps with values into closed 
 manifolds). More recently\, this method was also used by Mario Gauvrit (Un
 iversité Paris Cité) for Yang-Mills connections. In this talk\, we will 
 explain how to apply this theory to the Willmore energy (work in collabora
 tion with Tristan Rivière). If time allows\, we will say a word about bih
 armonic maps in dimension 4.
LOCATION:Institute de mathématiques\, salle de séminaires (CM 1 517) htt
 ps://plan.epfl.ch/?room==CM%201%20517
STATUS:CANCELLED
END:VEVENT
END:VCALENDAR