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Content archived on 2024-05-29

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

Objective

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.

Fields of science (EuroSciVoc)

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Keywords

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Topic(s)

Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.

Call for proposal

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FP6-2002-MOBILITY-11
See other projects for this call

Funding Scheme

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EIF - Marie Curie actions-Intra-European Fellowships

Coordinator

NATIONAL AND KAPODISTRIAN UNIVERSITY OF ATHENS
EU contribution
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Address
6 Christou Lada Street
ATHENS
Greece

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Total cost

The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.

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