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Computer algebra and combinatorial problems at the interplay of number theory and quantum algebra: the example of Multiple Zeta Values

Georges Racinet

Fachbereich Mathematik und Informatik, Universität Münster


Motivation

During the last fifteen years, some links have been established between at first sight quite far fields of mathematics, namely number theory, topology and quantum algebra. One of the common features of these directions lies in the combinatorial flavor of the objects they deal with. It is therefore relevant to ask what computer algebra can bring to the subject. The experience that the presenter would like to share is that it provides not only stronger evidence for conjectures but can also be used in the quest for proofs. A better understanding of the picture gives then in return more efficient computational methods.

This calculus is often highly non-commutative and comes down in the cases that we will consider to non-commutative polynomials manipulations, hence words combinatorics. We will mostly stick to the objects connected to the multiple zeta values (MZV's), a multi-variable generalization of the values of the Riemann zeta function at positive integers. This has to be considered both as an example and a starting point. We will try to give some insight about the applications of the encountered bestiary.


Outline

Each topic will be covered with a view towards computations and examples will be provided.


Prerequisites

Linear algebra including familiarity with tensor products. Elementary calculus.


Target audience

Computer algebra researchers interested by this possible field of developments, mathematicians interested by computational aspects towards the above outlined applications.


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Last modified on Fri Jul 5 11:46:51 MET DST 2002