Instructor: Florent Baudier
Office: Blocker 623B
Office hours: online and by appointment
Lectures: TR 11:30 a.m.-12:45 p.m. ONLINE via ZOOM
Course description:
Textbooks-Lecture notes:
J. Matousek,
Lecture notes on metric embeddings (freely available online).
Assignments:
Homework #1: TBA
Final presentations: TBA
Lecture notes
Tentative Schedule
| Date of Class |
Material covered |
| Thursday 08/20 |
Organizational laius; introduction, Sparsest Cut problem |
| Tuesday 08/25 |
Cut cone decomposition, linear programming relaxation |
| Thursday 08/27 |
Geometric embeddings, LP-integrality gap |
| Tuesday 09/01 |
L1-distortion, stochastic embeddings into tree-metrics |
| Thursday 09/03 |
Stochastic decompositions and hierachichal tree decompositions |
| Tuesday 09/08 |
Embeddings of outerplanar graphs, lower bound for stochastic embeddings of series-parallel graphs into tree-metrics |
| Thursday 09/10 |
Fourier analysis on the hypercube and Enflo type 2 |
| Tuesday 09/15 |
Linear codes and quotient metrics |
| Thursday 09/17 |
Khot-Naor construction |
| Tuesday 09/22 |
Expander graphs |
| Thursday 09/24 |
Rademacher type and Enflo type |
| Tuesday 09/29 |
p-uniformly smooth spaces have Enflo type p |
| Thursday 10/01 |
Duality uniform smoothness/uniform convexity |
| Tuesday 10/06 |
Solution of Enflo's problem by Ivanishvili-van Handel-Volberg |
| Thursday 10/08 |
Ribe program, embeddability of diamond graphs |
| Tuesday 10/13 |
Diamond-convexity |
| Thursday 10/15 |
diamond convexity implies Walsh-Paley martingale cotype |
| Tuesday 10/20 |
Pisier's renorming theorem |
| Thursday 10/22 |
nonpositive curvature |
| Tuesday 10/27 |
q-barycentric metric spaces |
| Thursday 10/29 |
Mendel-Naor metric cotype |
| Tuesday 11/03 |
Nonlinear martingales |
| Thursday 11/05 |
Solution to Gromov's problem by Eskenazis-Mendel-Naor |
| Tuesday 11/10 |
Rademacher cotype implies sharp metric cotype under K-convexity |
| Thursday 11/12 |
Markov convexity |
| Tuesday 11/17 |
Markov convexity of the Heisenberg group (guest lecture by C. Gartland) |
| Thursday 11/19 |
|
| Thursday 11/24 |
Closing lecture |
| Tuesday 12/01-Wednesday 12/09 |
Final examinations week |