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.)

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*Related*

Is there any chance that material related to this course (notes etc) could be posted online to accommodate remote auditors?

I dont know yet.