Monthly Archives: September 2012

End of Lille 2012 workshop, problem session

1. Itai Benjamini Take Gromov’s density model for random groups. Fix generators. Pick independently and uniformly at random relators of length . Gromov shows that, when is large, the quotient is infinite if . Zuk shows that the quotient has … Continue reading

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Notes of Guolian Yu’s lecture nr 4

1. Proof of stable rigidity The rigidity problems reduces to some algebra: First from homotopy to simple homotopy (collapsing cells) involves algebraic K-theory. Then from simple homotopy to homeomorphisms involves different algebra. Both steps are achievable by splitting space in … Continue reading

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Notes of Itai Benjamini’s lecture nr 3

1. Local limits, continued 1.1. Random triangulations of higher genus surfaces Guth, Parlier and Young 2010: Glue triangles along sides in order to get surfaces. Use uniform distribution on such data. They give bounds on the size (max length of … Continue reading

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Notes of Nati Linial’s Lille lecture nr 3

1. Sparsity Perfect sparsity characterizes infinite trees. 1.1. Girth For a finite graph, sparsity is closely related to girth. Girth equals the minimum for which the graph contains a -configuration, i.e. a subgraph with vertices et edges. Question. How large … Continue reading

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Notes of Itai Benjamini’s lecture nr 2

Today we study a series of examples of random perturbations of homogeneous spaces. Typically, the perturbation depends one one real parameter. When the parameter reaches a critical value, the spaces obtained are more exotic. 1. Variants of percolation 1.1. First … Continue reading

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Notes of Nati Linial’s Lille lecture nr 2

1. Proof of Bregman’s theorem, continued A proof of Bregman’s theorem can be found in Alon and Spencer’s book. Although I taught it several times, for a long time, I felt I did not understand that proof. Once, Zur Luria … Continue reading

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Notes of Eric Goubault’s lecture

This talk belongs in the CEMPI inaugural conference, Lille, september 24-29th, 2012. It starts the Graphs and groups workshop inside that conference. Geometry of trace spaces This is a connection between theoretical computer science and algebraic topology. Application to static … Continue reading

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