xxWorkshop on computational invariant theory of permutation groups and applications

Workshop on computational invariant theory of permutation groups and applications

Wednesday 13th - Friday 15th June 2001 Station Biologique de l’ENS, 1, rue Chxteau Foljuif (south-east of Paris), FRANCE

Organizer: Nicolas M. Thixry - LAPCS, Universitx Claude Bernard Lyonx1, France

With support from the: Laboratoire de Probabilitx, Combinatoire et Statistiques

Contact: nthiery@users.sf.net

   Web page: http://www.lapcs.univ-lyon1.fr/~nthiery/workshop.html

Scope 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. Thixry: 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 polynxmes multisymxtriques xlxmentaires, et applications / Computation of the ideal of the relations between the elementary multisymmetric polynomials, and applications. Bibliography about multisymmetric polynomials Jean-Charles Faugxre: 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, Universitx de Rennes 1, FRANCE Antoine Coste, chargx de recherche, CNRS, Universitx Paris-Sud, France Ruth Enoch, graduate student in Purdue University, USA Jean-Charles Faugxre, chargx de recherche, CNRS, LIP6, Universitx Paris VI, France Adriano Garsia, Professor, University of California at San-Diego, USA Florent Hivert, maxtre de confxrence, Universitx Marne-la-Vallxe, France Ugur Madran, graduate student, Department of Mathematics, Bilkent University, Turkey Ioannis Michos, Post-Doc au LIAFA, Universite Paris 7 M.Angeles Gxmez Molleda, Doctorant, Universidad de Cantabria, Spain Mufit Sezer, graduate student in Purdue University, USA Jim Shank, University of Kent at Canterbury, UK Nicolas M. Thixry, maxtre de confxrences, Universitx 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