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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Notes of Guolian Yu’s lecture nr 1

Embeddings and higher index theory As notes, I recommend the book I wrote with my former student Piotr Nowak on the subject. 1. Background 1.1. Topological rigidity In the area of recognition and classification of manifolds, rigidity means the following. … Continue reading

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Notes of Nati Linial’s Lille lecture nr 1

Geometry and combinatorics The theory of expander graphs gives us an idea of the impact combinatorics may have on the rest of mathematics in the future. Most existing combinatorics deals with one-dimensional objects. Understanding higher dimensional situations is important. In … Continue reading

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Notes of Itai Benjamini’s lecture nr 1

The Graphs and Groups workshop consists of 3 mini-courses: Benjamini, Linial, Yu. On graph limits and random metric spaces In 1921 Polya observed that a drunken man finds its way back home, but a drunken bird does not. This started … Continue reading

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