45 citations · 110 across the 14 of their papers we have counts for
14 papers
Tropical KP Theory on Banana Curves
Simonetta Abenda, Türkü Özlüm Çelik, Claudia Fevola +1
The Kadomtsev-Petviashvili (KP) equation is the cornerstone of integrable systems, whose solutions reflect deep connections in algebraic geometry. Banana curves are reducible ratio…
Algebraic and Positive Geometry of the Universe: from Particles to Galaxies
Claudia Fevola, Anna-Laura Sattelberger
In recent years, the intersection of algebra, geometry, and combinatorics with particle physics and cosmology has led to significant advances. Central to this progress is the twofo…
Euler Discriminant of Complements of Hyperplanes
Claudia Fevola, Saiei-Jaeyeong Matsubara-Heo
The Euler discriminant of a family of very affine varieties is defined as the locus where the Euler characteristic drops. In this work, we study the Euler discriminant of families…
Algebraic Approaches to Cosmological Integrals
Claudia Fevola, Guilherme L. Pimentel, Anna-Laura Sattelberger +1
Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rationa…
Principal Landau Determinants
Claudia Fevola, Sebastian Mizera, Simon Telen
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 com…
Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals
Claudia Fevola, Sebastian Mizera, Simon Telen
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 regular…
Vector Spaces of Generalized Euler Integrals
Daniele Agostini, Claudia Fevola, Anna-Laura Sattelberger +1
We study vector spaces associated to a family of generalized Euler integrals. Their dimension is given by the Euler characteristic of a very affine variety. Motivated by Feynman in…
Hirota Varieties and Rational Nodal Curves
Claudia Fevola, Yelena Mandelshtam
The Hirota variety parameterizes solutions to the KP equation arising from a degenerate Riemann theta function. In this work, we study in detail the Hirota variety arising from a r…
The mathematical research-data repository MathRepo
Claudia Fevola, Christiane Görgen
MathRepo, located at https://mathrepo.mis.mpg.de, is an online repository for mathematical research data. In mathematics, research data comes in many different flavours. For instan…
The enumerative geometry of cubic hypersurfaces: point and line conditions
Mara Belotti, Alessandro Danelon, Claudia Fevola +1
In order to count the number of smooth cubic hypersurfaces tangent to a prescribed number of lines and passing through a given number of points, we construct a compactification of…
Likelihood Degenerations
Daniele Agostini, Taylor Brysiewicz, Claudia Fevola +3
Computing all critical points of a monomial on a very affine variety is a fundamental task in algebraic statistics, particle physics and other fields. The number of critical points…
KP Solitons from Tropical Limits
Daniele Agostini, Claudia Fevola, Yelena Mandelshtam +1
We study solutions to the Kadomtsev-Petviashvili equation whose underlying algebraic curves undergo tropical degenerations. Riemann's theta function becomes a finite exponential su…
Tangent Quadrics in Real 3-Space
Taylor Brysiewicz, Claudia Fevola, Bernd Sturmfels
We examine quadratic surfaces in 3-space that are tangent to nine given figures. These figures can be points, lines, planes or quadrics. The numbers of tangent quadrics were determ…
Pencils of Quadrics: Old and New
Claudia Fevola, Yelena Mandelshtam, Bernd Sturmfels
Two-dimensional linear spaces of symmetric matrices are classified by Segre symbols. After reviewing known facts from linear algebra and projective geometry, we address new questio…