I am working in the intersection of probability theory and mathematical physics.
Spin models from statistical mechanics describe collective macroscopic behaviour of many interacting objects from individual local interactions. Due to the large degree of freedom and some physical properties, those mathematical models can only be described in a probabilistic way, by e.g. Gibbs measures. Those models display a wide range of critical phenomena, such as: existence of multiple infinite volume measures, emergence of separation lines or synchronization.
In particular, I am fascinated by the following questions: