Japanese Journal of Mathematics

, Volume 9, Issue 2, pp 137–169

Ramanujan complexes and high dimensional expanders

Special Feature: The Takagi Lectures

DOI: 10.1007/s11537-014-1265-z

Cite this article as:
Lubotzky, A. Jpn. J. Math. (2014) 9: 137. doi:10.1007/s11537-014-1265-z


Expander graphs in general, and Ramanujan graphs in particular, have been of great interest in the last four decades with many applications in computer science, combinatorics and even pure mathematics. In these notes we describe various efforts made in recent years to generalize these notions from graphs to higher dimensional simplicial complexes.

Keywords and phrases

expanding graphs high dimensional expanders Ramanujan graphs Ramanujan complexes overlapping property 

Mathematics Subject Classification (2010)

05C99 22E35 05C65 

Copyright information

© The Mathematical Society of Japan and Springer Japan 2014

Authors and Affiliations

  1. 1.Einstein Institute of MathematicsHebrew UniversityJerusalemIsrael