Finite approximate subrings in general rings admit a structure theorem where nilpotent quotients obstruct additive and multiplicative growth, yielding a general sum-product framework and a ring-theoretic analogue of Gromov's polynomial growth theorem.
Integrable geodesic flows on surfaces
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Constructs a Riemannian metric on the 2-torus such that its universal cover does not admit global Riemann normal coordinates.
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.
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On the structure of approximate rings
Finite approximate subrings in general rings admit a structure theorem where nilpotent quotients obstruct additive and multiplicative growth, yielding a general sum-product framework and a ring-theoretic analogue of Gromov's polynomial growth theorem.
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On the existence of geodesic vector fields on closed surfaces
Constructs a Riemannian metric on the 2-torus such that its universal cover does not admit global Riemann normal coordinates.
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Wasserstein Distances on Quantum Structures: an Overview
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.