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Applications of Abstract Differential Geometry to Quantum Gravity: a Sheaf and Category-Theoretic Approach

Objectif

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.

Champ scientifique (EuroSciVoc)

Mots‑clés

Thème(s)

Appel à propositions

FP6-2002-MOBILITY-11
Voir d’autres projets de cet appel

Régime de financement

EIF - Marie Curie actions-Intra-European Fellowships

Coordinateur

NATIONAL AND KAPODISTRIAN UNIVERSITY OF ATHENS
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6 Christou Lada Street
ATHENS
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