Abstracts of lectures for Banff meeting, Groups and Geometries, May 4-8, 2015

s of lectures for Banff meeting, Groups and Geometries, May 4-8, 2015 Michael Aschbacher: Quaternion fusion packets Abstract I’ll discuss work on a fusion theoretic version of the so-called Classical Involution Theorem for groups. The project is part of a program to simplify part of the proof of the theorem classifying the finite simple groups.I’ll discuss work on a fusion theoretic version of the so-called Classical Involution Theorem for groups. The project is part of a program to simplify part of the proof of the theorem classifying the finite simple groups. Pierre-Emmanuel Caprace, Nicola Radu: A compact space of isomorphism classes of simple locally compact automorphism groups of trees, I and II Abstract Several important families of examples of non-discrete simple locally compact groups arise as automorphism groups of trees: simple algebraic groups of rank one over local fields, Kac-Moody groups of rank two over finite fields, as well as a large number of groups initially studied by Burger and Mozes and defined by prescribing their local action in terms of a given finite permutation group. The goal of the first part of this talk is to explain that a large set of isomorphism classes of simple locally compact groups acting on a given tree can be given a compact Hausdorff topology. Several questions arise then naturally, and will be addressed in the second part of the talk: Can we describe limits of known isomorphism classes? Which isomorphism classes form isolated points?Several important families of examples of non-discrete simple locally compact groups arise as automorphism groups of trees: simple algebraic groups of rank one over local fields, Kac-Moody groups of rank two over finite fields, as well as a large number of groups initially studied by Burger and Mozes and defined by prescribing their local action in terms of a given finite permutation group. The goal of the first part of this talk is to explain that a large set of isomorphism classes of simple locally compact groups acting on a given tree can be given a compact Hausdorff topology. Several questions arise then naturally, and will be addressed in the second part of the talk: Can we describe limits of known isomorphism classes? Which isomorphism classes form isolated points? Andrew Chermak: Locally grouped spaces Abstract That the finite simple groups and the simple algebraic groups have various structural properties in common need come as no great surprise since as we now know all but a small number of the finite simple groups are derivable from algebraic groups. But some degree of mystery remains, as is indicated by the proliferation of exotic fusion systems which, as it seems, share many of the same sorts of structural properties after the fact, but for which general organizing principles are largely absent. Why not start at the other end of the thread ? The talk will propose a scheme (pun intended) for unifying these various classes of groups and sort-of groups.That the finite simple groups and the simple algebraic groups have various structural properties in common need come as no great surprise since as we now know all but a small number of the finite simple groups are derivable from algebraic groups. But some degree of mystery remains, as is indicated by the proliferation of exotic fusion systems which, as it seems, share many of the same sorts of structural properties after the fact, but for which general organizing principles are largely absent. Why not start at the other end of the thread ? The talk will propose a scheme (pun intended) for unifying these various classes of groups and sort-of groups.