Certain Feynman integrals are associated to Calabi-Yau geometries. We demonstrate how
these integrals can be computed with the method of differential equations. The four-loop …

Using the recent advances in our understanding of non-perturbative aspects of type 11
strings we show how non-trivial exact results for N= 2 quantum field theories can be reduced …

A bstract We describe a systematic approach to cast the differential equation for the l-loop
equal mass banana integral into an ε-factorised form. With the known boundary value at a …

During the last years we have generated a large number of data related to Calabi-Yau
hypersurfaces in toric varieties which can be described by reflexive polyhedra. We classified …

Among the major mathematical approaches to mirror symmetry are those of Batyrev-Borisov
and Strominger-Yau-Zaslow (SYZ). The first is explicit and amenable to computation but is …

Geometry on Arc Spaces of Algebraic Varieties Page 1 Geometry on Arc Spaces of Algebraic
Varieties Jan Denef and Fran<;ois Loeser Abstract. This paper is a survey on arc spaces, a …

A bstract It has recently been demonstrated that Feynman integrals relevant to a wide range
of perturbative quantum field theories involve periods of Calabi-Yau manifolds of arbitrarily …

We review, for a general audience, a variety of recent experiments on extracting structure
from machine-learning mathematical data that have been compiled over the years. Focusing …

We introduce the notion of stringy E-function for an arbitrary normal irreducible algebraic
variety X with at worst log-terminal singularities. We prove some basic properties of stringy E …

We describe our package PALP of C programs for calculations with lattice polytopes and
applications to toric geometry, which is freely available on the internet. It contains routines …