The work of Cédric Villani

Yau, Horng‐Tzer

doi:10.1142/9789814324359_0004

Cited by 4 publications

(5 citation statements)

References 48 publications

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“…A related problem is connected with Cedric Villani's Fields Medal work [16]. Convergence to equilibrium for solutions of the Boltzmann equation can be thought of as a case of a (yet to be formulated) principle of linearized stability.…”

Section: Theorem 2 (Hille-yosida Generation Theorem) An Operator a Imentioning

confidence: 99%

“…The work of Villani and his collaborators gave us a new and better understanding of entropy, thus satisfactorily explaining a nineteenth century mystery. See [16] and the references therein for a nice introduction to these ideas. Questions of instabilities are also involved in Villani's calculations.…”

Section: Theorem 2 (Hille-yosida Generation Theorem) An Operator a Imentioning

confidence: 99%

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Book Review: Semi-bounded differential operators, contractive semigroups, and beyond

Goldstein¹

2017

Bull. Amer. Math. Soc.

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Section: Theorem 2 (Hille-yosida Generation Theorem) An Operator a Imentioning

confidence: 99%

Section: Theorem 2 (Hille-yosida Generation Theorem) An Operator a Imentioning

confidence: 99%

Book Review: Semi-bounded differential operators, contractive semigroups, and beyond

Goldstein¹

2017

Bull. Amer. Math. Soc.

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“…This example is especially topical in view of Villani's 2010 Fields medal (cf. Ambrosio (2011), Yau (2011).…”

Section: Meshing Of Dynamics: Examples and Counterexamples In Physics...mentioning

confidence: 99%

Laws, causation and dynamics at different levels

Butterfield

2011

Interface Focus.

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I have two main aims. The first is general, and more philosophical (§2). The second is specific, and more closely related to physics (§§3 and 4). The first aim is to state my general views about laws and causation at different ‘levels’. The main task is to understand how the higher levels sustain notions of law and causation that ‘ride free’ of reductions to the lower level or levels. I endeavour to relate my views to those of other symposiasts. The second aim is to give a framework for describing dynamics at different levels, emphasizing how the various levels' dynamics can mesh or fail to mesh. This framework is essentially that of elementary dynamical systems theory. The main idea will be, for simplicity, to work with just two levels, dubbed ‘micro’ and ‘macro’, which are related by coarse-graining. I use this framework to describe, in part, the first four of Ellis' five types of top-down causation.

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“…Much had already been achieved by Newton, d'Alembert, Lagrange, Poisson, Hamilton, Stokes, Gibbs and many others. One specific mathematical problem Hilbert had in mind was the approach to equilibrium of Boltzmann's equation [84], to which C. Villani recently made significant contributions [88].…”

Section: Introductionmentioning

confidence: 99%

On Hilbert's sixth problem

Jefferies¹

2022

Preprint

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Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path integrals. The subject is complicated by the fact that their application in flat space-time is quite different from how path integrals are used in, say, topological quantum field theory, where there is no natural notion of time translation. An historical background is given in this paper and a few mathematical approaches to Feynman path integrals in the context of nonrelativistic quantum mechanics and scalar quantum fields with polynomial self-interactions are outlined.

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The work of Cédric Villani

Cited by 4 publications

References 48 publications

Book Review: Semi-bounded differential operators, contractive semigroups, and beyond

Book Review: Semi-bounded differential operators, contractive semigroups, and beyond

Laws, causation and dynamics at different levels

On Hilbert's sixth problem

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