Formal differential geometry and Nambu-Takhtajan algebra [PDF]
Banach Center Publications, 1997 YURI L. DALETSKII, Vitaly Kushnirevitch
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Differential geometry of systems of projections in Banach algebras [PDF]
Pacific Journal of Mathematics, 1990 Gustavo Corach +2 more
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Regularising Transformations for Complex Differential Equations with Movable Algebraic Singularities [PDF]
Mathematical physics, analysis and geometry, 2022 In a 1979 paper, Okamoto introduced the space of initial values for the six Painlevé equations and their associated Hamiltonian systems, showing that these define regular initial value problems at every point of an augmented phase space, a rational ...
T. Kecker, G. Filipuk
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On the Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry [PDF]
, 2021 This paper presents the relationship between differential algebra and tropical differential algebraic geometry, mostly focusing on the existence problem of formal power series solutions for systems of polynomial ODE and PDE. Moreover, it improves an approximation theorem involved in the proof of the fundamental theorem of tropical differential ...
Boulier, François +3 more
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Differential Equations for Approximate Solutions of Painlevé Equations: Application to the Algebraic Solutions of the Painlevé-III $({\rm D}_7)$ Equation [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2023 It is well known that the Painlevé equations can formally degenerate to autonomous differential equations with elliptic function solutions in suitable scaling limits.
R. Buckingham, P. Miller
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Meromorphic modular forms and the three-loop equal-mass banana integral
Journal of High Energy Physics, 2022 We consider a class of differential equations for multi-loop Feynman integrals which can be solved to all orders in dimensional regularisation in terms of iterated integrals of meromorphic modular forms.
Johannes Broedel +2 more
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Tropical fans, scattering equations and amplitudes
Journal of High Energy Physics, 2021 We describe a family of tropical fans related to Grassmannian cluster algebras. These fans are related to the kinematic space of massless scattering processes in a number of ways.
James Drummond +3 more
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Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces
Journal of High Energy Physics, 2022 For spacetimes containing quiescent singularity hypersurfaces we propose a general notion of junction conditions based on a prescribed singularity scattering map, as we call it, and we introduce the notion of a cyclic spacetime (also called a multiverse)
Bruno Le Floch +2 more
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Algebraic singularities of scattering amplitudes from tropical geometry
Journal of High Energy Physics, 2021 We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar N $$ \mathcal{N} $$ = 4 super Yang-Mills theory.
James Drummond +3 more
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Generalising G2 geometry: involutivity, moment maps and moduli
Journal of High Energy Physics, 2021 We analyse the geometry of generic Minkowski N $$ \mathcal{N} $$ = 1, D = 4 flux compactifications in string theory, the default backgrounds for string model building. In M-theory they are the natural string theoretic extensions of G2 holonomy manifolds.
Anthony Ashmore +3 more
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