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.
The expander Chernoff bound states that random walks over expanders are good samplers, at least for a certain range of parameters. In this talk we will be interested in “Parity Samplers” that have the property that for any test set, about half of the sample sets see the test set an *even* number of times, and we will check whether random walks over expanders are good parity samplers. We will see that:
1. Random walks over expanders fare quite well with the challenge, but, 2. A sparse Random complex does much better.
