BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dalimil Mazac (IAS) DTSTART:20220208T193000Z DTEND:20220208T203000Z DTSTAMP:20260423T024510Z UID:nhetc/41 DESCRIPTION:Title: A utomorphic Spectra and the Conformal Bootstrap\nby Dalimil Mazac (IAS) as part of NHETC Seminar\n\n\nAbstract\nI will explain that the spectral geometry of hyperbolic manifolds provides a remarkably faithful model of t he modern conformal bootstrap. In particular\, to each hyperbolic D-manifo ld\, one can associate a Hilbert space of local operators\, which is a uni tary representation of a conformal group. The local operators live in an e mergent (D-1)-dimensional spacetime. The scaling dimensions of the operato rs are related to the eigenvalues of the Laplacian on the manifold. The op erators satisfy an operator product expansion. Finally\, one can define th eir correlation functions and derive bootstrap equations constraining the spectrum. As an application\, I will use conformal bootstrap techniques to derive upper bounds on the lowest positive eigenvalue of the Laplacian on closed hyperbolic surfaces and 2-orbifolds. In a number of notable cases\ , the bounds are nearly saturated by known surfaces and orbifolds. For ins tance\, the bound on all genus-2 surfaces is λ1≤3.8388976481\, while th e Bolza surface has λ1≈3.838887258. The talk will be based on https://a rxiv.org/abs/2111.12716\, which is joint work with P. Kravchuk and S. Pal. \n LOCATION:https://researchseminars.org/talk/nhetc/41/ END:VEVENT END:VCALENDAR