Inverse Expander Mixing for Hypergraphs
  We formulate and prove inverse mixing lemmas in the settings of simplicial complexes and k-uniform hypergraphs. In the hypergraph setting, we extend results of Bilu and Linial for graphs. In the simplicial complex setting, our results answer a question of Parzanchevski et al. 
Emma Cohen, Dhruv Mubayi, Peter Ralli, Prasad Tetali
math.CO