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.



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)







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.


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