Topic: The theory of large deviations is concerned with understanding probabilities of rare events (and their applications in efficient numerical simulations of rare events and connections with PDEs such as HJB equations). It is also closely related to optimizations and calculus of variations. We will probably cover some general results and some concrete examples. We may use these notes https://math.berkeley.edu/~rezakhan/LD.pdf or some other classic books, recent research papers, etc.