Probability, Geometry, and Groups

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Time: 3-4 Fridays

Place: BA6183

In this seminar/study group we are going to discuss various topics at the intersection of geometric group theory, probability and geometry. This semester, we'll be reading about expanders and superexpanders, particularly Mendel and Naor's paper "Expanders with respect to Hadamard spaces and random graphs"

Here are:

  • "working notes" about the paper.
  • A "map" of the proof of 1st part the main theorem
  • A "map" of the proof of 2nd part the main theorem (expanders wrt. random graphs)

Our mailing list is at https://groups.google.com/forum/#!forum/toronto-pgg-learning-seminar . You can join by sending an email to toronto-pgg-learning-seminar+subscribe@googlegroups.com .

Contents

Upcoming talks

Past talks

  • November 15th, 2013
    • Marcin: various notions of type for metric spaces
  • November 8th, 2013
    • Marcin: Overview of non-linear spectral calculus
  • November 1st, 2013
    • Michał: outline of the main proof
  • October 25th, 2013
    • Marcin: L^1 Local versus global properties of metric spaces
  • October 18th, 2013
    • Andrew: Zigzag products and graph-theory constructions
  • October 11th, 2013
    • Curt: CAT(0) spaces and Hadamard spaces
  • October 4th, 2013
    • everyone: doing a map of the paper and discussing what we want to cover
  • September 27th, 2013
    • Parker: Introduction to expanders


Resources


Previous talks - 2012/2013

  • April 22nd, 2013
    • Marcin Kotowski: Amenable groups with zero compression exponent - continued
  • April 19th, 2013
    • Michał Kotowski: Random groups and property (T) - continued
    • Marcin Kotowski: Amenable groups with zero compression exponent
  • March 8th, 2013
    • Michał Kotowski: Gromov's monster group - continued
  • March 1st, 2013
    • Michał Kotowski: Gromov's monster group (notes)
  • February 8th, 2013
    • Andrew Stewart: On the stability of the behaviour of random walks under quasi-isometries
  • January 25th, 2013
    • Parker Glynn-Adey: Goemans-Linial approximation to the sparsest cut problem - continued
  • November 30th, 2012
    • Mustazee Rahman: An Introduction to the Heisenberg group - continued
    • Parker Glynn-Adey: Goemans-Linial approximation to the sparsest cut problem
  • November 16th, 2012
    • Marcin Kotowski: L^1 embeddings and the sparsest cut problem
    • Mustazee Rahman: An Introduction to the Heisenberg group
  • November 2nd, 2012
    • Robert Young: Probabilistic constructions of embeddings
  • October 19th, 2012
    • Bálint Virág: Embeddings of lamplighter groups
    • Robert Young: Assouad's theorem
  • October 5th, 2012
    • Michał Kotowski: Lower bounds on embeddings via girth (notes)
    • Andrew Stewart: Random walks and Hilbert compression

Notes

Some notes by Michał (might be useful to someone else)

List of future topics

Some topics we are planning to cover, along with useful references:

  • Superexpanders
  • Hilbert space compression - applications
  • Automaton groups
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