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Geometry and the Quantum: Basics
Ali H. Chamseddine, Alain Connes, Viatcheslav Mukhanov
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Fe…
Quanta of Geometry: Noncommutative Aspects
Ali H. Chamseddine, Alain Connes, Viatcheslav Mukhanov
In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real sca…
The Cyclic and Epicyclic Sites
Alain Connes, Caterina Consani
We determine the points of the epicyclic topos which plays a key role in the geometric encoding of cyclic homology and the lambda operations. We show that the category of points of…
The Arithmetic Site
Alain Connes, Caterina Consani
We show that the non-commutative geometric approach to the Riemann zeta function has an algebraic geometric incarnation: the "Arithmetic Site". This site involves the tropical semi…