BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gabor Etesi (Budapest University of Technology and Economics) DTSTART:20201021T190000Z DTEND:20201021T200000Z DTSTAMP:20260420T052915Z UID:NYC-NCG/28 DESCRIPTION:Title: The universal von Neumann algebra of smooth 4-manifolds with an applicati on to gravity\nby Gabor Etesi (Budapest University of Technology and E conomics) as part of Noncommutative geometry in NYC\n\n\nAbstract\nMaking use of its smooth structure only\, out of a connected\noriented smooth $4$ -manifold a von Neumann algebra is constructed. As a\nspecial four dimensi onal phenomenon this von Neumann algebra is\napproximated by algebraic (i. e.\, formal) curvature tensors of the\nunderlying $4$-manifold and the von Neumann algebra itself is a\nhyperfinite factor of ${\\rm II}_1$ type hen ce is unique up to abstract\nisomorphisms of von Neumann algebras. Neverth eless over a fixed\n$4$-manifold this von Neumann algebra admits a represe ntation on a Hilbert\nspace such that its unitary equivalence class is pre served by\norientation-preserving diffeomorphisms. Consequently the Murray --von\nNeumann coupling constant of this representation is well-defined an d gives\nrise to a new and computable real-valued smooth $4$-manifold inva riant: In\nan appropriate sense this invariant along all simply connected closed\n$4$-manifolds is generated by its surely non-trivial value on\n${\ \mathbb C}P^2$ (with its standard smooth structure) alone.\n\nIn the secon d half of the seminar (i.e. if time remains) some consequences\nof this co nstruction for quantum gravity are also discussed. Namely\nreversing the c onstruction by starting not with a particular smooth\n$4$-manifold but wit h the unique hyperfinite ${\\rm II}_1$ factor\, a\nconceptually simple but manifestly four dimensional\, covariant\,\nnon-perturbative and genuinely quantum theory is introduced whose\nclassical limit is general relativity in an appropriate sense. Therefore\nit is reasonable to consider it as a sort of quantum theory of gravity. In\nthis model\, among other interestin g things\, the observed positive but\nsmall value of the cosmological cons tant acquires a natural explanation.\n\nReference\n\n1. G. Etesi: The univ ersal von Neumann algebra of smooth four-manifolds\,\nto appear in Adv. Th eor. Math. Phys.\, arXiv: 1712.01828 [math-ph]\;\n\n2. G. Etesi: Gravity a s a four dimensional algebraic quantum field theory\,\nAdv. Theor. Math. P hys. 20\, 1049-1082 (2016)\, arXiv: 1402.5658 [hep-th].\n LOCATION:https://researchseminars.org/talk/NYC-NCG/28/ END:VEVENT END:VCALENDAR