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:20221026T190000Z DTEND:20221026T200000Z DTSTAMP:20260420T053337Z UID:NYC-NCG/107 DESCRIPTION:Title: The universal von Neumann algebra of smooth four-manifolds revisited \nby Gabor Etesi (Budapest University of Technology and Economics) 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 N eumann algebra is constructed. As a\nspecial four dimensional phenomenon t his von Neumann algebra contains\nalgebraic (i.e.\, formal or coming from a metric) curvature tensors of the\nunderlying $4$-manifold and the von Ne umann algebra itself is a\nhyperfinite factor of ${\\rm II}_1$-type hence is unique up to abstract\nisomorphisms of von Neumann algebras. Over a fix ed $4$-manifold this\nuniversal von Neumann algebra admits a particular re presentation on a\nHilbert space such that its unitary equivalence class i s preserved by\norientation-preserving diffeomorphisms consequently the Mu rray--von\nNeumann coupling constant of this representation is well-define d and gives\nrise to a new and computable real-valued smooth $4$-manifold invariant.\nIts link with Jones' subfactor theory is noticed as well as co mputations\nin the simply connected closed case are carried out.\n\nApplic ation to the cosmological constant problem is also discussed.\nNamely\, th e aforementioned mathematical construction allows to reformulate\nthe clas sical vacuum Einstein equation with cosmological constant over a\n$4$-mani fold as an operator equation over its tracial universal von\nNeumann algeb ra such that the trace of a solution is naturally identified\nwith the cos mological constant. This framework permits to use the observed\nmagnitude of the cosmological constant to estimate by topological means\nthe number of primordial black holes about the Planck era. This number\nturns out to be negligable which is in agreement with known density\nestimates based on the Press--Schechter mechanism.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/107/ END:VEVENT END:VCALENDAR