2023-09-15 Lina Li - Graph Homomorphisms of Boolean Lattices скачать в хорошем качестве

2023-09-15 Lina Li - Graph Homomorphisms of Boolean Lattices

Speaker: Lina Li Title: Graph Homomorphisms of Boolean Lattices Abstract: One of the central problems in combinatorics is to determine the number and the typical structure of finite objects with prescribed local constraints. This problem naturally appears in many different contexts, including extremal graph theory, graph colorings, set systems, additive combinatorics, and discrete geometry. In this talk, I will go through some recent results on this topic concerning graph homomorphisms of Boolean lattices. In particular, I will show that for some graph homomorphisms of Boolean lattices, almost all homomorphisms are closely clustered around some ground states. The approach is based on cutting edge tools from different areas, including the container method, the entropy method, and the cluster expansion.