Lie Group Statistics and Lie Group Machine Learning Based on Souriau Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as Generalized Casimir Invariant Function in Coadjoint Representation [PDF]
Entropy, 2020 In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their “space of evolution” associated to
Frédéric Barbaresco
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Higher Order Geometric Theory of Information and Heat Based on Poly-Symplectic Geometry of Souriau Lie Groups Thermodynamics and Their Contextures: The Bedrock for Lie Group Machine Learning [PDF]
Entropy, 2018 We introduce poly-symplectic extension of Souriau Lie groups thermodynamics based on higher-order model of statistical physics introduced by Ingarden. This extended model could be used for small data analytics and machine learning on Lie groups.
Frédéric Barbaresco
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Integral cohomology of quotients via toric geometry [PDF]
Épijournal de Géométrie Algébrique, 2022 We describe the integral cohomology of $X/G$ where $X$ is a compact complex manifold and $G$ a cyclic group of prime order with only isolated fixed points.
Grégoire Menet
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3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve
SciPost Physics, 2022 This paper studies $3d$ $\mathcal{N}=4$ supersymmetric gauge theories on an elliptic curve, with the aim to provide a physical realisation of recent constructions in equivariant elliptic cohomology of symplectic resolutions.
Mathew Bullimore, Daniel Zhang
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Superconformal quantum mechanics and growth of sheaf cohomology
Journal of High Energy Physics, 2023 We give a geometric interpretation for superconformal quantum mechanics defined on a hyper-Kähler cone which has an equivariant symplectic resolution. BPS states are identified with certain twisted Dolbeault cohomology classes on the resolved space and ...
Nick Dorey, Boan Zhao
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Pieri rule for the affine flag variety [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We prove the affine Pieri rule for the cohomology of the affine flag variety conjectured by Lam, Lapointe, Morse and Shimozono. We study the cap operator on the affine nilHecke ring that is motivated by Kostant and Kumar’s work on the equivariant ...
Seung Jin Lee
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Chern characters in equivariant basic cohomology
Comptes Rendus. Mathématique, 2021 The purpose of this Note is to establish a geometric realization of the cohomological isomorphism in the case of a transversely oriented Killing foliation on a compact smooth manifold through equivariant basic Chern characters.
Liu, Wenran
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On Schubert calculus in elliptic cohomology [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 An important combinatorial result in equivariant cohomology and $K$-theory Schubert calculus is represented by the formulas of Billey and Graham-Willems for the localization of Schubert classes at torus fixed points.
Cristian Lenart, Kirill Zainoulline
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Double Schubert polynomials for the classical Lie groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 For each infinite series of the classical Lie groups of type $B$, $C$ or $D$, we introduce a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank.
Takeshi Ikeda +2 more
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Schwinger-Keldysh formalism. Part II: thermal equivariant cohomology
Journal of High Energy Physics, 2017 Causally ordered correlation functions of local operators in near-thermal quantum systems computed using the Schwinger-Keldysh formalism obey a set of Ward identities.
Felix M. Haehl +2 more
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