Quantum gravity and noncommutative geometry

Fuzzy spaces and noncommutative eigenvalue equations

Metrics, geodesics and gauge theories on fuzzy spaces. Quasicoherent states of fuzzy spaces, solving equations with matrix valued eigenvalues, adiabatic transport in a fuzzy space. Dynamics of fuzzy spaces. Fuzzy surface plots.

Quantum gravity matrix models

BFSS matrix models of quantum gravity in string theory: emergent gravity and torsion at the Planck scale, entanglement and decoherence of a fermionic string, emergent foliated spacetimes, relation between extradimensions and fast evolutions at the Planck scale, geometry of the chiral oscillations. Dark matter models.

Black holes and wormholes

Decoherence of qubits at the neighbourhood of the event horizon of a black hole, models of quantum micro black holes and wormholes. Philosophical questions about quantum gravity (Everett's many world interpretation, quantum multiverses, analogy between quantum spacetimes and quantum computers).
  1. D. Viennot & O. Moro, Adiabatic transport of qubits around a black hole, Class. Quant. Gravity 34, 055005 (2017).
  2. D. Viennot & L. Aubourg, Chaos, decoherence and emergent extradimensions in D-brane dynamics with fluctuations, Class. Quant. Gravity 35, 135007 (2018).
  3. D. Viennot, Emergent gravity and D-brane adiabatic dynamics: emergent Lorentz connection, Class. Quant. Gravity 38, 245004 (2021)
  4. D. Viennot, Fuzzy Schwarzschild (2+1)-spacetime, J. Math. Phys. 63, 082302 (2022)
  5. D. Viennot, Geometric phases, Everett's many-worlds interpretation of quantum mechanics, and wormholes, Quantum Studies: Math. Found. 11, 307 (2024)
  6. D. Viennot, Metrics and geodesics on fuzzy spaces, J. Phys. A: Math. Theor. 57, 425201 (2024)