The invariant theory of permutation groups has potential applications in many
different areas (discrete mathematics, Galois theory, differential equations, algebra,
quantum mechanics, ...). However, the computations involved are very hard,
and the applicability of this theory will be greatly conditioned in the future
by the existence of efficient software. Theory and practice are particularly
intermixed here, since the computation of non trivial examples can help in the
understanding of the structure of those invariant rings, which in turn can yield better
algorithms.
The goal was to gather researchers in connected areas to help define the needs
and the problems and bring up exciting collaborations, especially around software
development.
Topics
Specific topics included but were not limited to:
Applications
Algorithms and implementations
Theoretical aspects
Related problems of isomorphism of permutation groups
Program
The workshop consisted of lectures, short communications by the participants on
their recent research, software demonstrations, and problem sessions. Plenty of time
was reserved for informal discussions, and the workshop continued informally over the
week-end.
Tuesday
Dinner (a cold dinner will be available for those arriving late in the
evening).
Wednesday
Welcome
David Wehlau: The Image of the Transfer for Permutation
Representations Related documents
Nicolas M. Thiéry: Computations in invariant rings of permutation
groups Related article
Lunch
Antoine Coste: Groups in modern physics,
Florent Hivert: Schubert polynomials: a tool for computing in the
natural representation of the symmetric group on polynomials.
Problem session / informal discussion
Dinner
Thursday
Jim Shank: On the invariants of the regular representation of the
cyclic group of order p in characteristic p. Related documents
Mufit Sezer: A sharpening of Noether-Fleischmann Bound Related article
Lunch
Ugur Madran: Lower Degree Bounds of Modular Vector Invariants of
Finite Groups.
Problem session / informal discussion
Dinner
Friday
Emmanuel Briand: Calcul de l’ideal des relations entre les polynômes
multisymétriques élémentaires, et applications / Computation of
the ideal of the relations between the elementary multisymmetric
polynomials, and applications. Bibliography about multisymmetric polynomials
Jean-Charles Faugère: Solving polynomial systems with symmetries;
applications and algorithms.
Lunch
Adriano Garsia: Enumeration of reduced factorizations of
permutations (video)
List of participants
Emmanuel Briand, doctorant, IRMAR, Université de Rennes 1, FRANCE
Antoine Coste, chargé de recherche, CNRS, Université Paris-Sud, France
Ruth Enoch, graduate student in Purdue University, USA
Jean-Charles Faugère, chargé de recherche, CNRS, LIP6, Université Paris
VI, France
Adriano Garsia, Professor, University of California at San-Diego, USA
Florent Hivert, maître de conférence, Université Marne-la-Vallée, France
Ugur Madran, graduate student, Department of Mathematics, Bilkent
University, Turkey
Ioannis Michos, Post-Doc au LIAFA, Universite Paris 7
M.Angeles Gómez Molleda, Doctorant, Universidad de Cantabria, Spain
Mufit Sezer, graduate student in Purdue University, USA
Jim Shank, University of Kent at Canterbury, UK
Nicolas M. Thiéry, maître de conférences, Université Lyon I, France
David Wehlau, Professor, Department of Mathematics and Computer
Science, Royal Military College and Department of Mathematics and
Statistics, Queen’s University, Canada
Welcome to Nicolas' home