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Unifying Foundations for Physics and Mathematics

Unifying Foundations for Physics and MathematicsPeter WoitColumbia UniversityMathematics DepartmentParis, Oct. 30, 2021 Peter Woit (Columbia University Mathematics Department) Unifying Foundations for Physics and MathematicsOctober 20211 / 13 Outline1 Unification in Physics2 Unification in Mathematics3 Unifying Math and Physics4 Last ThoughtsNote: These slides ~ Woit (Columbia University Mathematics Department) Unifying Foundations for Physics and MathematicsOctober 20212 / 13 Unification in PhysicsGeneral RelativityThe gravitational force is described by theGeneral theory of Relativity (1915)Dynamical variables: geometry of space-timeClassical dynamical equations: Einstein equations for metricThe Mathematics used is(Pseudo)-Riemannian geometryRiemann (1854).

representation theory, relating Galois groups of number elds and their ... The theorem can then be understood in terms of the ... Methodological implications for mathematics: fundamental physics will remain an ongoing inspiration for new deep mathematical ideas.

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