This project concerns statistical models coming from the fields of mathematics known as statistical mechanics, number theory, and combinatorics. A unifying theme in these models is that objects of central interest can be described as random fields which have a very special correlation structure in their randomness - they are called log-correlated fields. The goal of this project is to understand the geometry of these random fields and apply this understanding to deduce new facts about (and connections between) the various models. An example being to understand how large values can such a log-correlated field take. This type of results will give us new knowledge about models of fundamental importance in statistical mechanics, number theory, and combinatorics. Also these log-correlated fields are expected to be universal objects in that they appear in many models, and the methods proposed here should be general enough to apply in many situations.

2023

2027