| Date of Class | Material covered |
|---|---|
| 01/19 | lecture 1: the one about the cut cone decomposition of L1-metrics. Most of the material covered was taken from section 3 in A. Naor's ICM article. |
| 01/21 | lecture 2: the one about integrality gaps of the Sparsest Cut Problem Most of the material covered was taken from sections 4.1 4.2, 4.3 in A. Naor's ICM article. |
| 01/26 | lecture 3: the one about scale maps with deficiency |
| 01/28 | lecture 4: the one about J. Lee's gluing technique Most of the material can be found in M. Ostrovskii's book, section 3.4. |
| 02/02 | lecture 5: the one about Bourgain's embedding method Most of the material can be found in M. Ostrovskii's book, section 3.4. |
| 02/04 | lecture 6: the one about stochastic padded decompositions Most of the material can be found in M. Ostrovskii's book, section 3.4. |
| 02/09 | lecture 7: the one about the combinatorial definition of expander graphs Most of the material can be found in M. Ostrovskii's book, section 4.2. |
| 02/11 | lecture 8: the one about the spectral characterization of expander graphs Most of the material can be found in Nowak and Yu's book, section 5.6. The introductory chapter of Davidoff-Sarnak-Valette book is an excellent introduction to the speactral aspect of expander graphs. |
| 02/16 | lecture 9: the one about Matoušek's extrapolation technique The presentation of Matoušek's extrapolation technique follows closely the original argument of Matoušek. |
| 02/18 | lecture 10: the one about dimension reduction in L2 The presentation of the Johnson-Lindenstrauss dimension reduction was mostly taken from Matoušek's article on this topic. |
| 02/23 | lecture 11: the one about the impossibility of dimension reduction in L1 The proof of the Brinkman-Charikar theorem on the impossibility of dimension reduction in L1 was taken from Krauthgamer-Lee-Naor article and uses the Laakso graphs of Lang and Plaut. Two proofs of the crucial but classical uniform convexity inequality in Lp (see the Ball-Carlen-Lieb article for the original proofs and a historical account of the inequality) can be found on A. Naor's webpage (A. Naor's take and J. Matoušek's take). |
| 02/25 | lecture 12: the one about the Euclidean distortion of the Hamming cubes and the introduction to the Ribe progam A good reference for the Euclidean distortion of the Hamming cubes is Matoušek's lecture notes section 3.4. As far as the Ribe program is concerned I suggest the following excellent readings: K. Ball's Bourbaki Seminar and A. Naor's 10th Takagi Lectures. The class will meet from 1pm to 2:15pm this Thursday in BLOC 220 to avoid a conflict with the Noncommutative Geometry Colloquium of N. Higson. |
| 03/01 | lecture 13: the one about metric characterizations of the superreflexive class in terms of graph preclusions: binary trees (embeddability issue) |
| 03/03 | class canceled; we will make it up by extending a bit a few subsequent lectures |
| 03/08 | lecture 14: the one about metric characterizations of the superreflexive class in terms of graph preclusions: binary trees (non-embeddability issue) |
| 03/10 | lecture 15: the one about metric characterizations of the superreflexive class in terms of graph preclusions: fractal built graphs |
| 03/22 | lecture 16: the one about local-to-global theorems and their applications |
| 03/24 | lecture 17: the one about the barycentric gluing technique |
| 03/29 | lecture 18: the one about Rolewicz property (β) and the distortion of ω-regular trees |
| 03/31 | lecture 19: the one about snowflake exponents and compression exponents |
| 04/05 | lecture 20: the one about Kalton-Randrianarivony inequality |
| 04/07 | lecture 21: the one about the large scale geometry of groups and the Milnor-Svarc lemma The material from this lecture can be found in Nowak-Yu chapter 1. |
| 04/12 | lecture 22: the one about proper affine isometric actions and equivariant embeddings The material from this lecture can be found in Nowak-Yu chapter 6 |
| 04/14 | lecture 23: the one about equivariant embeddability of the Heisenberg group into ergodic spaces The material from this lecture is extracted for the article of a Austin, Tessera and Naor. |
| 04/19 | class canceled; we will make it up by extending a bit the remaining lectures |
| 04/21 | lecture 24: the one about equivariant embeddings of amenable groups The material from this lecture can be found in Bemyamini-Lindenstrauss chapter 8 |
| 04/26 | lecture 25: the one about compression exponents and the speed of random walks: the equivariant setting Class will meet at 5pm in BLOC 506A. The material from this lecture is extracted from the article of Naor and Peres. |
| 04/28 | lecture 26: the one about compression exponents and the speed of random walks: the non-equivariant setting The material from this lecture is extracted from the article of Austin, Naor and Peres. |