Results 11 to 20 of about 2,055,605 (307)

Poisson algebras via model theory and differential-algebraic geometry [PDF]

Journal of the European Mathematical Society, 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. In this article a complete answer is given to this question using techniques from differential-algebraic geometry
Bell, Jason, Launois, Stephane, Sanchez, Omar; id_orcid 0000-0002-8345-0589, Moosa, Rahim   +3 more
openaire   +6 more sources

The fundamental theorem of tropical partial differential algebraic geometry [PDF]

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, 2020
20 pages, 2 figures.
Sebastian Falkensteiner, Cristhian Garay-López, Mercedes Haiech, Marc Paul Noordman, Zeinab Toghani, François Boulier   +5 more
openaire   +6 more sources

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]

Adv Intell Discov
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
europepmc   +2 more sources

Constraints on sequential discontinuities from the geometry of on-shell spaces

Journal of High Energy Physics, 2023
We present several classes of constraints on the discontinuities of Feynman integrals that go beyond the Steinmann relations. These constraints follow from a geometric formulation of the Landau equations that was advocated by Pham, in which the ...
Holmfridur S. Hannesdottir, Andrew J. McLeod, Matthew D. Schwartz, Cristian Vergu   +3 more
doaj   +1 more source

Current Algebra and Differential Geometry

Journal of High Energy Physics, 2005
14 pages. Dedicated to Ludwig Faddeev on the occasion of his 70th birthday.
Alekseev, Anton, Strobl, Thomas
openaire   +3 more sources

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, Jack Foster, Ömer Gürdoğan, Chrysostomos Kalousios   +3 more
doaj   +1 more source

Anyons in geometric models of matter

Journal of High Energy Physics, 2017
We show that the “geometric models of matter” approach proposed by the first author can be used to construct models of anyon quasiparticles with fractional quantum numbers, using 4-dimensional edge-cone orbifold geometries with orbifold singularities ...
Michael Atiyah, Matilde Marcolli
doaj   +1 more source

Singular solutions in soft limits

Journal of High Energy Physics, 2020
A generalization of the scattering equations on X (2, n), the configuration space of n points on ℂℙ1, to higher dimensional projective spaces was recently introduced by Early, Guevara, Mizera, and one of the authors.
Freddy Cachazo, Bruno Umbert, Yong Zhang
doaj   +1 more source

Towards analytic structure of Feynman parameter integrals with rational curves

Journal of High Energy Physics, 2022
We propose a strategy to study the analytic structure of Feynman parameter integrals where singularities of the integrand consist of rational irreducible components.
Jianyu Gong, Ellis Ye Yuan
doaj   +1 more source

Generalized planar Feynman diagrams: collections

Journal of High Energy Physics, 2020
Tree-level Feynman diagrams in a cubic scalar theory can be given a metric such that each edge has a length. The space of metric trees is made out of orthants joined where a tree degenerates.
Francisco Borges, Freddy Cachazo
doaj   +1 more source