High Dimensional Expanders and Ramanujan Complexes

Expander graphs have played, in the last few decades, an important role in computer science, and  in the last decade, also in pure mathematics.  In recent years a theory of "high-dimensional expanders" is starting to emerge - i.e., simplical complexes which generalize various properties of expander graphs. This has some geometric motivations (led by Gromov) and combinatorial ones (started by Linial and Meshulam).  The talk will survey the various directions of research and their applications, as well as potential applications in math and CS.  Some of these lead to questions about buildings and representation theory of p-adic groups.

We will survey the work of a number of people. The works of the speaker in this direction are with various subsets of  { S. Evra, K. Golubev,  T. Kaufman,  D. Kazhdan , R. Meshulam, S. Mozes }