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:20220118T095212Z
UID:indico-event-1100106@indico.cern.ch
DESCRIPTION:We point out that the spectral geometry of hyperbolic manifold
s provides a remarkably precise model of the modern conformal bootstrap. A
s an application\, we use conformal bootstrap techniques to derive rigorou
s computer-assisted upper bounds on the lowest positive eigenvalue $\\lamb
da_1(X)$ of theLaplace-Beltrami operator on closed hyperbolic surfaces and
2-orbifolds $X$. In a number of notable cases\, our bounds are nearly sat
urated by known surfaces and orbifolds. For instance\, our bound on all ge
nus-2 surfaces $X$ is $\\lambda_1(X)\\leq 3.8388976481$\, while the Bolza
surface has $\\lambda_1(X)\\approx 3.838887258$. \n\nI will explain that
hyperbolic surface are of the form H\\G/K with G=PSL(2\,R)\, K=SO(2) and H
being Fuchsian group. For a given hyperbolic surface\, one can define a H
ilbert space of local operators\, transforming under a unitary irrep of a
conformal group (PSL(2\,R)) and introduce a notion of operator product exp
anion (OPE). The associativity of this OPE reflects the associativity of f
unction multiplication on the space H\\G and leads to the bootstrap equati
ons. Now the functions on H\\G can be thought of automorphic forms on the
surface H\\G/K and I will show that the scaling dimensions of these operat
ors are in fact related to the automorphic spectra in particular the Lapla
cian eigenvalues on the manifold. Hence the bootstrap equations lead to th
e bound on the Laplacian eigenvalues.\n\nhttps://indico.cern.ch/event/1100
106/
LOCATION:CERN zoom only
URL:https://indico.cern.ch/event/1100106/
END:VEVENT
END:VCALENDAR