Four Lectures on Euler Integrals

TL;DR

This paper provides a comprehensive introduction to Euler integrals, highlighting their applications in physics and the mathematical techniques used to analyze them.

Contribution

It offers a self-contained overview of Euler integrals, connecting applications in physics with mathematical methods like polyhedral geometry and computational algebra.

Findings

Demonstrates the use of polyhedral geometry in Euler integrals

Shows how differential equations relate to Euler integrals

Illustrates computational algebra techniques for analyzing Euler integrals

Abstract

These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate the diverse mathematical techniques involved in the study of Euler integrals, including polyhedral geometry, very affine varieties, differential equations, and computational algebra.