Algebraic Combinatorics in Mathematical Chemistry. Methods and Algorithms. I. Permutation Groups and Coherent (Cellular) Algebras.

This is an extensive review of recent work on the foundations of statistical mechanics. Subject matters discussed include: interpretation of probability, typicality, recurrence, reversibility, ergodic . . . . .

This is a set of easy-to-read lecture notes for a short first-year Ph.D. student course on Applied Dynamical Systems, which was given at the London Taught Course Centre in Spring 2008. The notes cover . . . . .

The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including st . . . . .

Contents: Cauchy-Davenport inequality, Plunnecke's theorem, sum set estimates; Freiman's theorem (both in the torsion and torsion-free cases), Gowers-Walters theorem, Chang's refinement of Freiman's t . . . . .

Some geometric structures with associated Riemannian metrics have been considered in the book.