Statistical mechanics describes the typical behaviour of macroscopic systems based on knowledge of how their microscopic constituents interact. Many powerful methods and techniques have been developed in order to understand statistical mechanical systems. However, many of these lack a firm mathematical basis and providing a rigorous mathematical framework constitutes a major challenge to mathematicians.
The Statistical Mechanics project addresses questions which lie at the interface of probability theory, combinatorics, analysis, and both theoretical and mathematical physics and which contribute to providing a firm mathematical basis for well-established physics methods.
Specific projects include questions concerning:
- Study aspects of 2D universality including conformal invariance and going beyond nearest neighbour integral models.
- Extend 2D models to higher dimensions.
- Move beyond the CFT realm.