From Multiple Polylogarithms to the Universal Vector Extension of an Elliptic Curve

Explore a Fields Number Theory Seminar lecture that delves into the connection between multiple polylogarithms and the universal vector extension of elliptic curves. Join Dr. Tiago J. Fonseca from IMECC - Unicamp as he guides you through a comprehensive exploration of this fascinating topic. Begin with an introduction and outline before diving into the motivation behind the research and examining relevant examples. Discover the intricate connections between various mathematical concepts, including unipotent vector bundles, canonical extensions, and their analogs. Learn about Brown and Lading's contributions, vector unipotent vector bundles, and the universal vector extension. Gain insights into the Lemon theorem and classification theorem, and conclude with an examination of the KSB equation and construction. This in-depth presentation offers a valuable opportunity to expand your understanding of advanced number theory concepts and their applications in elliptic curve theory.

Introduction
Outline
Motivation
Example
Connections
Unipotent vector bundles
Canonical extension
Analogs
Brown and Lading
Vector unipotent vector bundles
Universal vector extension
Lemon theorem
Classification theorem
KSB equation
KSB construction