Integrability and Universality in Probability

Integrability and universality are key concepts that underlie many developments in modern probability. Integrable probabilistic systems are very special — they possess additional structures that make them amenable to a detailed analysis. The universality principle states that probabilistic systems from the same ‘universality class’ share many features. Thus, generic systems must be similar to the integrable ones in the class. In this lecture, Alexei Borodin will illustrate how these two concepts work together in examples from random matrices to random interface growth.