This Research Trimester encompasses all aspects of the theory of multiple zeta values and their generalizations known as multiple polylogarithms, including applications in modern quantum field theory. This event is a follow-up activity of the European Science Foundation - Exploratory Workshop "New Approaches To Multiple Zeta Values", which took place at ICMAT from September 30 - October 2, 2013.

The theory of multiple zeta values is a rather recent research topic in mathematics. A systematic study only started in the early 1990s with the seminal works of M. Hoffman (U.S. Naval Academy, Annapolis, USA) and D. Zagier (MPIM Bonn, Germany & Collège de France, Paris, France) - although the prehistory can be traced back to Euler in the 18th century. The whole set of MZVs first appeared under the name "Moule Zeta" in the work of the French mathematician J. Ecalle (CNRS, Paris Sud, Orsay, France), in vol. 1 and 2 of his 1981 preprints on "Les fonctions résurgentes". Since then multiple zeta values and their generalizations known as multiple polylogarithms, have turned into a vibrant research field, which touches upon several areas of modern mathematics, including number theory, combinatorial algebra (regularized double shuffle relations), algebraic geometry (motives), and Lie group theory (Kashiwara-Vergne conjecture). This rich mathematical spectrum is complemented through deep connections with high-energy physics.

The Research Trimester aims at exploring all aspects of multiple zeta values and multiple polylogarithms through workshops and lecture courses. The main emphasis during the trimester will lie on the research-in-teams activity (Oct.+Nov., 2014). We will invite teams of (3-5) researchers to ICMAT to pursue promising research projects. A research seminar will run in parallel during this period. The research-in-teams activity is complemented by short introductory lectures outlining the background and goal of each project.

Opening Workshop

ICMAT, September 2014

Research-in-Teams

ICMAT, October+November 2014

Final Conference

ICMAT, December 2014

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