Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

YouTube

Iterated Beta Integrals - Generalizing Hyperlogarithms and Beta Integrals

Hausdorff Center for Mathematics via YouTube

Overview

Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!
Explore a comprehensive lecture on iterated beta integrals, a type of iterated integrals on branched universal abelian coverings of the projective line. Delve into the recent work conducted by Nobuo Sato and Minoru Hirose at Nagoya University, examining how these integrals generalize hyperlogarithms and beta integrals. Discover the unique property of translation invariance and its implications for equalities between iterated integrals on translation-equivalent coverings. Investigate how this property leads to non-trivial equalities between special values of hyperlogarithms for genus-zero pairs of translation-equivalent coverings. Examine famous formulas such as Zagier's 2-3-2 formula for multiple zeta values, its analog for multiple t-values, and the 2-1 formula for multiple zeta star values. Learn about the classification of all genus-zero pairs and the discovery of new interesting cases, including the resolution of Charlton's conjecture concerning the area of a family of Lawson surfaces.

Syllabus

Nobuo Sato: Iterated Beta Integrals

Taught by

Hausdorff Center for Mathematics

Reviews

Start your review of Iterated Beta Integrals - Generalizing Hyperlogarithms and Beta Integrals

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.