Summation Theory of Difference Rings and Applications - Lecture 2

This lecture is the second part of a three-part mini-course by Carsten Schneider on summation theory of difference rings and applications, recorded at the Centre International de Rencontres Mathématiques during the thematic meeting "Enumerative combinatorics and effective aspects of differential equations" on February 25, 2025. Explore the core concepts of difference ring theory with detailed insights into the algorithmic framework, focusing on the representation of indefinite nested sums and products within the difference ring setting. Learn about a toolbox that enables the construction of summation objects whose sequences are algebraically independent of one another. The complete mini-course covers tools in the summation package Sigma, parameterized telescoping, recurrence solving for indefinite nested sums over nested products, and applications to complex problems in enumerative combinatorics, number theory, and elementary particle physics. The video includes chapter markers and keywords for selective viewing, and is part of CIRM's Audiovisual Mathematics Library which offers enriched content with abstracts, bibliographies, and Mathematics Subject Classification.