SS18 - Noncommutative Symbolic Computation
Symbolic computation plays an important role in the study of many important functions and their special values. By constructing noncommutative formal series based on words using these symbols, one can often discover key properties of these functions and values in a uniform way. On the other hand, noncommutative formal series can be considered as a generalization of language theory in theoretical computer science. As the algorithms and combinatorics of these series is based on those of words, these two fields naturally reinforce each other. They form an ideal framework for developing software based on computer algebra systems with rigor and efficiency. In particular, they allow the symbolic manipulation of several classes of special functions (such as Eulerian functions, hypergeometric functions, hyperlogarithms, harmonic sums, etc.) and of special values involved in solutions of differential equations. We invite contributions with the following topics:
- Combinatorial Indexing and Calculus
- Ecalle’s Mould Calculus
- Free Lie Algebras
- Hopf Algebras and Their Combinatorics
- Noncommutative Differential Equations
- Multiple Zeta Values (or Zeta Polymorphism) and Polylogarithms
- Representative functions (Sweedler’s duals and their combinatorics)
Session organizers
Talks
| Jianqiang Zhao - Unramified Variants of Motivic Multiple Zeta Values |
| Vincel Hoang Ngoc Minh - Various bialgebras of representative functions on free monoids |
| Steven Charlton - Goncharov's Programme, and Symmetries of Weight 6 Multiple Polylogarithms |
| Olivier Bouillot - Multiple Divided Bernoulli Polynomials and Numbers |
| Jean-Yves Enjalbert - Multiplicative structure of some multivariate functions |
| Gérard H. E. Duchamp - Extension by continuity of the domain of Poly- and Hyper-logarithms |