Results 11 to 20 of about 164,535 (282)

Algebraic geometry and local differential geometry [PDF]

Annales scientifiques de l'École normale supérieure, 1979
Griffiths, Phillip, Harris, Joseph
openaire   +3 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

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   +4 more sources

Schubert problems, positivity and symbol letters

Journal of High Energy Physics, 2022
We propose a geometrical approach to generate symbol letters of amplitudes/integrals in planar N $$ \mathcal{N} $$ = 4 Super Yang-Mills theory, known as Schubert problems. Beginning with one-loop integrals, we find that intersections of lines in momentum
Qinglin Yang
doaj   +1 more source

Duals of Feynman Integrals. Part II. Generalized unitarity

Journal of High Energy Physics, 2022
The first paper of this series introduced objects (elements of twisted relative cohomology) that are Poincaré dual to Feynman integrals. We show how to use the pairing between these spaces — an algebraic invariant called the intersection number — to ...
Simon Caron-Huot, Andrzej Pokraka
doaj   +1 more source

Multidimensional Toda type systems [PDF]

, 1996
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.Comment: 29 pages, LaTeX ...
A. N. Leznov, A. V. Razumov, A. V. Razumov, A. V. Razumov, B. Dubrovin, C.-L. Terng, G. Darboux, J. E. Humphreys, J.-L. Gervais, J.-L. Gervais, K. Tenenblat, L. A. Ferreira, L. Bianchi, L. Fehér, M. J. Ablowitz, M. Sato, M. V. Saveliev, M. V. Saveliev, N. Bourbaki, S. Cecotti, S. Cecotti, V. E. Korepin, Yu. A. Aminov   +22 more
core   +2 more sources

Tangent Categories from the Coalgebras of Differential Categories [PDF]

, 2019
Following the pattern from linear logic, the coKleisli category of a differential category is a Cartesian differential category. What then is the coEilenberg-Moore category of a differential category? The answer is a tangent category!
Cockett, Robin, Lemay, Jean-Simon Pacaud, Lucyshyn-Wright, Rory B. B.   +2 more
core   +2 more sources

New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory [PDF]

, 2011
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational ...
Acvevedo M., Anderson I., C. G. Torre, Heck A., I. M. Anderson, Kobayashi S.   +5 more
core   +4 more sources

Smoothly splitting amplitudes and semi-locality

Journal of High Energy Physics, 2022
In this paper, we study a novel behavior developed by certain tree-level scalar scattering amplitudes, including the biadjoint, NLSM, and special Galileon, when a subset of kinematic invariants vanishes without producing a singularity.
Freddy Cachazo, Nick Early, Bruno Giménez Umbert   +2 more
doaj   +1 more source

Stokes polytopes: the positive geometry for ϕ 4 interactions

Journal of High Energy Physics, 2019
In a remarkable recent work [1], the amplituhedron program was extended to the realm of non-supersymmetric scattering amplitudes. In particular it was shown that for tree-level planar diagrams in massless ϕ 3 theory (and its close cousin, bi-adjoint ϕ 3 ...
Pinaki Banerjee, Alok Laddha, Prashanth Raman   +2 more
doaj   +1 more source