Abstract:
In 1962, amateur literary theorist and professional mathematician Andrey Kolmogorov wrote: ‘A story is art only if the characters and situations it describes stand a chance of becoming
Abstract:
A (countable) group G is homogeneous if whenever g,h are tupples of the same type in G, there is an automorphism of G sending g to h.
We give a characterization of freely-indecomposable torsion-free hyperbolic groups which are homogeneous, in terms of a particular decomposition as a graph of groups - their JSJ decomposition. This is joint work with Chloe Perin.
האירוע הזה כולל שיחת וידאו ב-Google Hangouts.
Abstract: In this talk, I will introduce diffeological spaces and some (co)homology theories on these spaces. I will also talk on Thom-Mather spaces and their (co)homology in the diffeological context.
Abstract: While algebraic topology is now well established as an applicable branch of mathematics, its emergence in neuroscience is surprisingly recent. In this talk I will present a summary of an ongoing joint project with mathematician and neuroscientists. I will start with some basic facts on neuroscience and the digital reconstruction of a rat’s neocortex by the Blue Brain Project in EPFL.
Abstract: Let X be a simplicial complex on n vertices without missing faces of dimension larger than d. Let L_k denote the k-Laplacian acting on real k-cochains of X and let μ_k(X) denote its minimal eigenvalue. We study the connection between the spectral gaps μ_k(X) for k ≥ d and μ_{d-1}(X). Applications include:
1) A cohomology vanishing theorem for complexes without large missing faces.
2) A fractional Hall type theorem for general position sets in matroids.
Abstract: Let G be a finitely generated group and let G>G_1>G_2 ... be a sequence of finite index normal subgroups of G with trivial intersection.
We expect that the asymptotic behaviour of various group theoretic invariants of the groups G_i should relate to algebraic, topological or measure theoretic properties of G.
A classic example of this is the Luck approximation theorem which says that the growth of the ordinary Betti numbers of sequence G_i is given by the L^2-Betti number of (the classifying space) of G.
In the first talk we gave a brief outline of the contents of the course. In the rest of the semester we will get deeper into some topics. In the coming lecture ( and the next one) we will discuss Kazhdan property T and its connections with expanders and with first cohomology groups. No prior knowledge will be assumed.
