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3-7 Jun 2019 Djursholm (Sweden)
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Description
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: 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:
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