Objetivo The propesed mathematical physics research project is in the context of quantum gravity (QG). In view of the grave failure of classical differential geometric methods in attempts to quantize general relativity (GR) by retaining a smooth background geometr ical spacetime manifold, we shall take an alternative combinatory- algebraic route. The sought after QG has also been expected to shed more light on the problem of singularities and associated unphysical infinities assailing the pointed macroscopic spacet ime continuum of GR. Thus, to both ends, Mallios' Calculus and in extenso, base manifold-free, sheaf-theoretic Abstract Differential Geometry (ADG) will be applied to a finitistic-algebrainc scenario for quantum spacetime struture and dynamics that has be en recently proposed by this applicant in connection with sorkin's discrete causal set approach to Lorentzian QG. Also, again due to the inadequacy of the differential manifold model for spacetime at Planck scales, ma noncommutative topology, its sheaf the ory, and the concomitant organization of the resulting noncommutative sheaves' into a pointless quantum category or quantum topos suitable for addressing deep logico-geometrical issues in QG, will be developed. Ámbito científico natural sciencesphysical sciencesrelativistic mechanicsnatural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesmathematicspure mathematicstopologyalgebraic topologynatural sciencesmathematicspure mathematicsgeometrynatural sciencesphysical sciencestheoretical physics Palabras clave (discrete Lorentzian) quantum gravity General relativity abstract differential geometry category theory causal sets noncommutative spaces sheaf theory singularities Programa(s) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Tema(s) MOBILITY-4.1 - Marie Curie European Reintegration Grants (ERG) Convocatoria de propuestas FP6-2002-MOBILITY-11 Consulte otros proyectos de esta convocatoria Régimen de financiación EIF - Marie Curie actions-Intra-European Fellowships Coordinador NATIONAL AND KAPODISTRIAN UNIVERSITY OF ATHENS Aportación de la UE Sin datos Dirección 6 Christou Lada Street ATHENS Grecia Ver en el mapa Coste total Sin datos
