Feynman integrals are indispensable for precision calculations in quantum field theory. They
occur as soon as one goes beyond the leading order in perturbative quantum field theory …

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 …

In theory there is no difference between theory and practice. In practice there is. Yogi Berra
A SINGULAR Introduction to Commutative Algebra offers a rigorous intro duction to …

A classic problem in mathematics is solving systems of polynomial equations in several
unknowns. Today, polynomial models are ubiquitous and widely used across the sciences …

A bstract We elaborate on the connection between Gel'fand-Kapranov-Zelevinsky systems,
de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman …

Sure to be influential, Watanabe's book lays the foundations for the use of algebraic
geometry in statistical learning theory. Many models/machines are singular: mixture models …

One may say that the history of hypergeometric functions started practically with a paper by
Gauss (cf.[Gau]). There, he presented most of the properties of hypergeometric functions that …

Abstract In the Lee-Pomeransky representation, Feynman integrals can be identified as a
subset of Euler-Mellin integrals, which are known to satisfy Gel'fand-Kapranov-Zelevinsky …

A bstract We provide evidence through two loops, that rational letters of polylogarithmic
Feynman integrals are captured by the Landau equations, when the latter are recast as a …

. These hypergeometric series are the N-dimensional analogue of Kummer's solutions in the
theory of Gauss's classical hypergeometric equation. The use of this function in the theory of …