Alex Lubotzky and I are running together a year long course at HU on High Dimensional Expanders. High dimensional expanders are simplical (and more general) cell complexes which generalize expander graphs. The course will take place in Room 110 of the mathematics building on Tuesdays 10-12.
Topics will include:
- Some background on expander graphs and on simplicial complexes and homology
- The geometric definition of high dimensional expanders in the recent paper: Overlap properties of geometric expanders. by J. Fox, M. Gromov, V. Lafforgue, A. Naor, and J. Pach;
- A cohomological definition arising in Linial-Meshulam’s work about homology of random complexes; possible definitions based on high Laplacians,
- Ramanujan complexes;
- Potential applications to error correcting codes and quantum error correcting codes.
(I will add further relevant links, and a more detailed description later.)