Liao, Chao 

Title: Counting hypergraph colourings in the local lemma regime

Abstract: The local lemma is a powerful tool to show the existence of q-colourings for k-uniform hypergraphs under a simple degree bound. The original lemma is non- constructive, but Moser-Tardos' algorithm allows us to efficiently find such a colouring. However, if we want to uniformly at random generate one, the classic Markov chain approach does not work any longer in the said regime. In this talk, we will present an alternative approach to approximately counting and sampling hypergraph colorings in the local lemma regime. It is based on the recent work of Moitra (STOC, 2017). Our main contribution is to remove certain restrictions in Moitra's approach. Based on joint work with Heng Guo, Pinyan Lu, and Chihao Zhang.