Probability, Geometry, and Groups
From TorontoMathWiki
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
- Mendel, Naor, "Towards a Calculus for Non-Linear Spectral Gaps"
- Mendel, Naor, "Nonlinear spectral calculus and super-expanders"
- Mendel, Naor, "Expanders with respect to Hadamard spaces and random graphs"
- Assaf Naor's lecture on superexpanders at BIRS, August 2013
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 22nd, 2013
- Michał Kotowski: Random groups and property (T)
- following Addendum to: Random walk in random groups by Lior Silberman
- Michał Kotowski: Random groups and property (T)
- 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)
- based on Girth and Euclidean distortion by N. Linial, A. Naor, A. Magen
- Andrew Stewart: Random walks and Hilbert compression
- Michał Kotowski: Lower bounds on embeddings via girth (notes)
Notes
Some notes by Michał (might be useful to someone else)
- October 5th, 2012 - Lower bounds on embeddings via girth / Random walks and Hilbert compression
- March 1st, 2013 - Gromov's monster group
List of future topics
Some topics we are planning to cover, along with useful references:
- Superexpanders
- Assaf Naor's talk on superexpanders from the Metric Geometry, Geometric Topology and Groups workshop in Banff, 2013
- M. Mendel, A. Naor Expanders with respect to Hadamard spaces and random graphs
- Embedding doubling metric spaces, Assouad’s theorem
- A. Naor, O. Nieman, Assouad's theorem with dimension independent of the snowflaking
- Diamond graphs and the Laakso graphs
- J. Lee, A. Naor, Embedding the Diamond Graph in L_p and Dimension Reduction in L_1
- J. Lee, M. Mendel, A. Naor, Metric Structure in L_1: Dimension, snowflakes, and average distortion
- infinite lamplighter groups
- G.N. Arzhantseva, V.S. Guba, M.V. Sapir Metrics on diagram groups and uniform embeddings in a Hilbert space
- T. Austin, A. Naor, Y. Peres The wreath product of Z with Z has Hilbert compression exponent 2/3
- finite lamplighter groups
- (upper bound) T. Austin, A. Naor, A. Valette, The Euclidean distortion of the lamplighter group
- (lower bound) J. R. Lee, A. Naor, and Y. Peres, Trees and Markov convexity
- Random walks and Hilbert space
- T. Austin, A. Naor, Y. Peres The wreath product of Z with Z has Hilbert compression exponent 2/3
- Embedding Heisenberg group in L^1
- J. Cheeger, B. Kleiner, A. Naor, A (\log n)^{\Omega(1)} integrality gap for the Sparsest Cut SDP
- J. Cheeger, B. Kleiner. Metric differentiation, monotonicity and maps to L1
- J. Cheeger, B. Kleiner, A. Naor, Compression bounds for Lipschitz maps from the Heisenberg group to L1
- A. Naor, L_1 embeddings of the Heisenberg group and fast estimation of graph isoperimetry
- Baum-Connes conjecture, Novikov conjecture
- E. Guentner, J. Kaminker, Geometric and Analytic Properties of Groups
- A. Valette, I. Chatterji, G. Mislin, Introduction to the Baum-Connes Conjecture
- Gromov's construction of random groups
- M. Gromov, Random walk in random groups
- L. Silberman Addendum to: Random walk in random groups
- G. Arzhantseva, T. Delzant Examples of random groups
- Y. Ollivier Cayley graphs containing expanders, after Gromov
- Hilbert space compression - applications
- Automaton groups