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Trends in Differential Geometry and Algebraic Topology

Axioms
With this Editorial, we present a Special Issue of Axioms entitled “Trends in Differential Geometry and Algebraic Topology [...]
Byungdo Park
doaj   +2 more sources

On The Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry [PDF]

, 2021
International audienceThis 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 ...
Boulier, François, Falkensteiner, Sebastian, Sanchez, Omar Leon, Noordman, Marc Paul   +3 more
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Poisson algebras via model theory and differential-algebraic geometry [PDF]

, 2017
Brown and Gordon asked whether the Poisson Dixmier–Moeglin equivalence holds for any complex affine Poisson algebra, that is, whether the sets of Poisson rational ideals, Poisson primitive ideals, and Poisson locally closed ideals coincide.
Moosa, Rahim, Omar León Sánchez, Stéphane Launois, Jason Bell, Leon Sanchez, Omar, Sanchez, Omar; id_orcid, Rahim Moosa, Launois, Stephane, Bell, Jason   +8 more
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Model Theory and Differential Algebraic Geometry [PDF]

, 2012
This thesis studies problems in differential algebraic geometry and model ...
James E. Freitag (7963802)
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Tropical Grassmannians, cluster algebras and scattering amplitudes

Journal of High Energy Physics, 2020
We provide a cluster-algebraic approach to the computation of the recently introduced generalised biadjoint scalar amplitudes related to Grassmannians Gr(k, n). A finite cluster algebra provides a natural triangulation for the tropical Grassmannian whose
James Drummond, Jack Foster, Ömer Gürdoğan, Chrysostomos Kalousios   +3 more
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Yano F structures and extended supersymmetry

Journal of High Energy Physics, 2022
It is shown how extended supersymmetry realised directly on the (2, 2) semichiral superfields of a symplectic sigma model gives rise to a geometry on the doubled tangent bundle consisting of two Yano F structures on an almost para-hermitian manifold ...
Ulf Lindström
doaj   +1 more source

Multi linear formulation of differential geometry and matrix regularizations

, 2012
We prove that many aspects of the differential geometry of em-bedded Riemannian manifolds can be formulated in terms of multilinear algebraic structures on the space of smooth functions.
Hoppe, Jens,, Arnlind, Joakim,, Huisken, Gerhard,   +2 more
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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, Claude Duhr, Nils Matthes   +2 more
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The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry [PDF]

, 2020
International audienceTropical Differential Algebraic Geometry considers difficult or even intractable problems in Differential Equations and tries to extract information on their solutions from a restricted structure of the input.
Garay-Lopez, Cristhian Emmanuel, Haiech, Mercedes, Boulier, François, Falkensteiner, Sebastian, Toghani, Zeinab, Garay-López, Cristhian, Noordman, Marc Paul   +6 more
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Cutting the traintracks: Cauchy, Schubert and Calabi-Yau

Journal of High Energy Physics, 2023
In this note we revisit the maximal-codimension residues, or leading singularities, of four-dimensional L-loop traintrack integrals with massive legs, both in Feynman parameter space and in momentum (twistor) space.
Qu Cao, Song He, Yichao Tang
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