Zobrazeno 1 - 10
of 99
pro vyhledávání: '"Telen, Simon"'
A recurring task in particle physics and statistics is to compute the complex critical points of a product of powers of affine-linear functions. The logarithmic discriminant characterizes exponents for which such a function has a degenerate critical
Externí odkaz:
http://arxiv.org/abs/2410.11675
We study scattering equations of hyperplane arrangements from the perspective of combinatorial commutative algebra and numerical algebraic geometry. We formulate the problem as linear equations on a reciprocal linear space and develop a degeneration-
Externí odkaz:
http://arxiv.org/abs/2410.03614
Autor:
Telen, Simon, Wiesmann, Maximilian
We stratify families of projective and very affine hypersurfaces according to their topological Euler characteristic. Our new algorithms compute all strata using algebro-geometric techniques. For very affine hypersurfaces, we investigate and exploit
Externí odkaz:
http://arxiv.org/abs/2407.18176
Autor:
Pavlov, Dmitrii, Telen, Simon
The Santal\'o point of a convex polytope is the interior point which leads to a polar dual of minimal volume. This minimization problem is relevant in interior point methods for convex optimization, where the logarithm of the dual volume is known as
Externí odkaz:
http://arxiv.org/abs/2402.18955
We consider semi-algebraic subsets of the Grassmannian of lines in three-space called tree amplituhedra. These arise in the study of scattering amplitudes from particle physics. Our main result states that tree amplituhedra in ${\rm Gr}(2,4)$ are pos
Externí odkaz:
http://arxiv.org/abs/2402.06527
Chebyshev varieties are algebraic varieties parametrized by Chebyshev polynomials or their multivariate generalizations. We determine the dimension, degree, singular locus and defining equations of these varieties. We explain how they play the role o
Externí odkaz:
http://arxiv.org/abs/2401.12140
Publikováno v:
Comput. Phys. Commun. 303 (2024) 109278
We reformulate the Landau analysis of Feynman integrals with the aim of advancing the state of the art in modern particle-physics computations. We contribute new algorithms for computing Landau singularities, using tools from polyhedral geometry and
Externí odkaz:
http://arxiv.org/abs/2311.16219
Publikováno v:
Phys. Rev. Lett. 132, 101601 (2024)
We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the Standard Model in dimensional regularization. After highlighting issues in the textbook treatment of Landau
Externí odkaz:
http://arxiv.org/abs/2311.14669
A chopped ideal is obtained from a homogeneous ideal by considering only the generators of a fixed degree. We investigate cases in which the chopped ideal defines the same finite set of points as the original one-dimensional ideal. The complexity of
Externí odkaz:
http://arxiv.org/abs/2307.02560
We develop a new eigenvalue method for solving structured polynomial equations over any field. The equations are defined on a projective algebraic variety which admits a rational parameterization by a Khovanskii basis, e.g., a Grassmannian in its Pl\
Externí odkaz:
http://arxiv.org/abs/2306.14871