BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Automorphic Spectra and the Conformal Bootstrap
DTSTART;VALUE=DATE-TIME:20211213T140000Z
DTEND;VALUE=DATE-TIME:20211213T153000Z
DTSTAMP;VALUE=DATE-TIME:20220518T204600Z
UID:indico-event-1100106@indico.cern.ch
DESCRIPTION:Speakers: Sridip Pal (IAS)\n\nWe point out that the spectral g
eometry of hyperbolic manifolds provides a remarkably precise model of the
modern conformal bootstrap. As an application\, we use conformal bootstra
p techniques to derive rigorous computer-assisted upper bounds on the lowe
st positive eigenvalue $\\lambda_1(X)$ of theLaplace-Beltrami operator on
closed hyperbolic surfaces and 2-orbifolds $X$. In a number of notable cas
es\, our bounds are nearly saturated by known surfaces and orbifolds. For
instance\, our bound on all genus-2 surfaces $X$ is $\\lambda_1(X)\\leq 3.
8388976481$\, while the Bolza surface has $\\lambda_1(X)\\approx 3.8388872
58$. \n\nI will explain that hyperbolic surface are of the form H\\G/K wi
th G=PSL(2\,R)\, K=SO(2) and H being Fuchsian group. For a given hyperboli
c surface\, one can define a Hilbert space of local operators\, transformi
ng under a unitary irrep of a conformal group (PSL(2\,R)) and introduce a
notion of operator product expanion (OPE). The associativity of this OPE r
eflects the associativity of function multiplication on the space H\\G and
leads to the bootstrap equations. Now the functions on H\\G can be though
t of automorphic forms on the surface H\\G/K and I will show that the scal
ing dimensions of these operators are in fact related to the automorphic s
pectra in particular the Laplacian eigenvalues on the manifold. Hence the
bootstrap equations lead to the bound on the Laplacian eigenvalues.\n\nhtt
ps://indico.cern.ch/event/1100106/
LOCATION:zoom only (CERN)
URL:https://indico.cern.ch/event/1100106/
END:VEVENT
END:VCALENDAR