# Workshop on Symbolic Combinatorics and Computational Differential Algebra

**Location: ** Fields Institute, Room 230

## Overview

This workshop is devoted to algorithmic developments in Combinatorics and Differential Algebra with a particular focus on the interaction of these two areas.

* Symbolic Combinatorics:* Symbolic algorithms and software have recently been developed that allow researchers to discover and prove combinatorial identities as well as understand analytic and algebraic properties of generating functions. These functions seldom have closed form solutions and even when they do, direct evaluation may be intractable. Recent work in Symbolic Combinatorics has focused on representing such functions by annihilating differential or difference operators and then using techniques from differential and difference algebra, as well as analysis, to analyze these equations and their solutions. Besides methods relating to creative telescoping and verication of function identities, other areas of emphasis will include effective methods in difference algebra, the Galois theories of difference equations, and the interaction of differential and difference algebra in combinatorics.

* Computational Differential Algebra* is an approach to nonlinear or linear differential equations and differential structures, focusing not only on finding explicit closed form solution, but also on simplifying such equations to yield preconditioning for subsequent numerical solution, as well clearer understanding of the qualitative behavior of solutions. Highlighted aspects will include differential-elimination completion algorithms; geometric differential algebra, moving frames and differential invariants; differential Galois theory and integrability; complexity and open problems.

## Schedule

09:00 |
George Labahn, University of Waterloo |

10:10 |
Markus Rosenkranz, University of Kent |

11:30 |
Austin Roche, Maplesoft |

14:00 |
Manuel Kauers, Johannes Kepler University |

15:30 |
Peter J. Olver, University of Minnesota |

09:00 |
Alin Bostan, INRIA |

10:10 |
Carlos Arreche, North Carolina State University |

11:30 |
Joachim von zur Gathen |

14:00 |
Rika Yatchak, Johannes Kepler University |

15:10 |
Marni Mishna, Simon Fraser University |

09:00 |
Elizabeth Mansfield, University of Kent |

10:10 |
Alexey Ovchinnikov, CUNY Queens College |

11:30 |
Peter Paule, Johannes Kepler University |

09:00 |
Evelyne Hubert, INRIA Méditerranée |

10:10 |
Doron Zeilberger, Rutgers University |

11:30 |
Ekaterina Shemyakova, State University of New York at New Paltz |

14:00 |
Johannes Middeke, Johannes Kepler University |

15:10 |
Frédéric Chyzak, INRIA Saclay Île-de-France |

09:00 |
Cyril Banderier, Univ Paris 13 |

10:10 |
Moulay A. Barkatou, XLIM, CNRS, University of Limoges |

11:30 |
Greg Reid, Western University |

14:00 |
The generalized inverses of Ore matrices and applications
Yang Zhang, University of Manitoba |

15:10 |
Effective Analytic Combinatorics in Several Variables, With Applications to Lattice Path Enumeration
Stephen Melczer, ENS Lyon and University of Waterloo |

09:00 |
Christian Krattenthaler, Universitaet Wien |

10:10 |
Formal Reduction of Singularly-Perturbed Linear Differential Systems
Sumayya Suzy Maddah |

11:30 |
Georg Regensburger, Austrian Academy of Sciences |