BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Dario Prandi (CentraleSupelec)
DTSTART:20210108T150000Z
DTEND:20210108T160000Z
DTSTAMP:20260404T143359Z
UID:SRS/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/SRS/8
 /">Point interactions for 3D sub-Laplacians</a>\nby Dario Prandi (Centrale
 Supelec) as part of Sub-Riemannian Seminars\n\n\nAbstract\nThe aim of this
  seminar is to present some recent results on the essential self-adjointne
 ss of pointed sub-Laplacians in three dimensions. These are the natural (n
 on-negative) hypoelliptic operators $H$ associated with a sub-Riemannian s
 tructure on a 3D manifold $M$\, with domain $\\operatorname{Dom}(H)=C^\\in
 fty_c(M\\setminus \\{p\\})$\, for $p\\in M$.\n\nIf $M=\\mathbb{R}^n$ and t
 he geometry is Euclidean\, $H$ is the standard Laplacian. It is then well-
 known that $H$ is essentially self-adjoint with $\\operatorname{Dom}(H) =C
 ^\\infty_c(\\mathbb{R}^n\\setminus\\{p\\})$ if and only if $n\\ge 4$. This
  follows\, for instance\, by the Euclidean Hardy inequality.\n\nIn this se
 minar we show that\, unlike the Euclidean case\, pointed sub-Laplacians (a
 s-sociated with smooth measures) are essentially self-adjoint already for 
 contact sub-Riemannian manifolds of\n(topological) dimension $3$. Although
  this is not surprising\, since the Hausdorff dimension of these structure
 s is $4$\, we will sow that this result cannot be deduced via Hardy inequa
 lities as in the Euclidean case but requires a much finer machinery. Indee
 d\, our strategy of proof is based on a localicazion argument which allows
  to reduce to the study of the 3D Heisenberg pointed sub-Laplacian. The es
 sential self-adjoitness of the latter is then obtained by exploiting non-c
 ommutative Fourier transform techniques.\n\nThis is a joint work with R. A
 dami (Politecnico di Torino\, Italy)\,  U. Boscain (CNRS &UPMC\, Sorbonne 
 Université\, France)\, and V. Franceschi (Università di Padova\, Italy).
 \n
LOCATION:https://stable.researchseminars.org/talk/SRS/8/
END:VEVENT
END:VCALENDAR