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Monthly Archives: March 2017
Notes of Marc Burger’s first Oxford lecture 21-03-2017
Geometric structures, compactifications of representation varieties, and non archimedean geometry 1. From geometric structures to representation Let be a finitely presented group, and be defined by polynomials. Then is a real algebraic set. The representation variety is (not quite Hausdorff, … Continue reading
Notes of Emmanuel Breuillard’s second Oxford lecture 21-03-2017
Approximate groups, II 1. Expansion in Cayley graphs Solvable groups cannot lead to expanders. On the other hand, simple groups do. Theorem 1 (Kassabov-Lubotsky-Nikolov) There is a and a such that every finite simple group has a generating set of … Continue reading
Notes of Henry Wilton’s Oxford lecture 21-03-2017
Surface subgrops of graphs of free groups with cyclic edge groups 1. Gromov’s questions Tits’ Ping-pong Lemma. Let be a non-elementary hyperbolic group. If do not commute, then some high powers of and generate a free subgroup. Hence there exist … Continue reading
Notes of Tullia Dymarz’ Oxford lecture 21-03-2017
Bi-Lipschitz versus quasi-isometry equivalence Advertisement for quasi-isometric rigidity shool, Toulouse, june 26th-july 14th, 2017. 1. Examples Different choices of finite generating systems leads to bi-Lipschitz (write bL) equivalences of a group. However, is qi to but not bL to . … Continue reading
Notes of Goulnara Arzhantseva’s second Oxford lecture 21-03-2017
Constructions of non -exact groups, II 1. Embedding graphs in groups 1.1. Almost quasi-isometric embeddings Say a sequence of maps constitute an almost quasi-isometric embedding if where girth. We shall see that such embeddings from graphs to groups are rather … Continue reading
Notes of Alan Reid’s first Oxford lecture 21-03-2017
Profinite rigidity in low dimensions The third lecture will report on joint work with Martin Bridson and Henry Wilton. This deals with profinite rigidity in the context of 3-manifolds. I will give a crash coarse on profinite completion, and then … Continue reading
Notes of Goulnara Arzhantseva’s first Oxford lecture 20-03-2017
Constructions of non -exact groups Motivation. Coarse properties: graphs and groups. Graphical presentations: from graphs to groups. -exact groups containing expanders. -exact groups having Haagerup property. 1. -algebras These are complete normed algebra with a conjugation . Basic examples are … Continue reading
Notes of Montserrat Casals-Ruiz Oxford lecture 20-03-2017
Commensurability in RAAGs Joint work with Kazachkov and Zakharov. Question. When does quasi-isometry imply commensurability? 1. RAAGs defined by trees I focus of RAAGs which are simultaneously (irreducible) 3-manifold groups. These coincide with RAAGs defined by trees. 1.1. Small diameter … Continue reading
Notes of Marc Burger’s first Leverhulme lecture 15-03-2017
Towards higher Teichmuller theory Study homomorphisms of surface groups to real algebraic groups . A surface group is the fundamental group of a closed surface of genus (boundaries will show up only later). Since has a -generators 1-relator presentation, is … Continue reading
Notes of Marc Troyanov’s Cambridge lecture 14-03-2017
The Binet-Legendre metric in Finsler geometry 1. Minkowski geometry I mean, geometry of a finite dimensional vectorspace equipped with a smooth, non-necessarily symmetric norm . Smooth means smooth away from the origin. Say is strictly convex if at each point … Continue reading
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