6 papers
The Stieltjes Bootstrap for Feynman Integrals
Hadrien Brochet, Maximilian Haensch, Johannes Henn +4
We prove that scalar Feynman integrals are Stieltjes functions in each kinematic variable , as well as in the particle masses, for arbitrary loop order, arbitrary nu…
Log Canonical Models and Positive Geometries
Benjamin Hollering, Dmitrii Pavlov, Elizabeth Pratt
Constructing log canonical compactifications of open varieties is a central problem in birational geometry. Finding a natural coordinate system and obtaining the equations of these…
Positivity and Cluster Structures in Landau Analysis
Benjamin Hollering, Elia Mazzucchelli, Matteo Parisi +1
Landau analysis in momentum twistor space can be formulated as the study of varieties of lines in three-dimensional projective space, together with their projections and discrimina…
Landau Analysis in the Grassmannian
Benjamin Hollering, Elia Mazzucchelli, Matteo Parisi +1
Momentum twistors for scattering amplitudes in particle physics are lines in three-space. We develop Landau analysis for Feynman integrals in this setting. The resulting discrimina…
Parke-Taylor varieties
Benjamin Hollering, Dmitrii Pavlov
Parke-Taylor functions are certain rational functions on the Grassmannian of lines encoding MHV amplitudes in particle physics. For particles there are Parke-Taylor functi…
Toric Fiber Products in Geometric Modeling
Eliana Duarte, Benjamin Hollering, Maximilian Wiesmann
An important challenge in Geometric Modeling is to classify polytopes with rational linear precision. Equivalently, in Algebraic Statistics one is interested in classifying scaled…