The topic of the summer school is motivated by recent applications of group actions to various questions in algebra, geometry, number theory and computer science which have given rise to the development of new theoretical results as well as algorithms for computer algebra software. The theme is approachable for young researchers via the theory of permutation groups and there are many open questions, both on the theoretical side and with regards to applications.
Mini-courses:
Colva RONEY-DOUGAL(University of St Andrews)
Introduction: permutation groups, group actions, and “base and strong generating set”
The O’Nan Scott theorem and methods for the classification of primitive permutation groups
Aschbacher’s Theorem and computational methods for matrix groups
Random generation of groups
Cheryl E PRAEGER (University of Western Australia)
Primitive and quasiprimitive - lessons from algebraic graph theory (distance transitive graphs and normal graph quotients)
Theory of Quasiprimitive permutation groups - and normal quotients of edge-transitive graphs
Overview of simple groups factorisations and their applications, especially to classify the maximal subgroups of symmetric groups
Growth of groups (Pyber, Tao et al) and conjectures of Sims and Weiss for arc-transitive graphs
Alice C NIEMEYER (RWTH University, Aachen)
Deterministic and randomised algorithms in group theory
Proportions of elements in permutation groups and matrix groups, estimation methods
Computational methods for permutation groups
Growth of subgroups: Sylow subgroups of primitive permutation groups
Spotlight lectures:
Joanna FAWCETT (Imperial College, London)
Donna M TESTERMAN (EPFL, Lausanne)
Rebecca WALDECKER (MLU Halle-Wittenberg)
Organisers:
Donna M TESTERMAN
Cheryl E PRAEGER
Rebecca WALDECKER
Collaborating Institutions and Sponsors:
This summer school is being organised at the Institut Mittag-Leffler under the auspices of the European Women in Mathematics and the European Mathematical Society.