This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.

This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The exposition starts from the basic of the subject, introducing ergodicity, mixing and entropy. The ergodic theory of smooth dynamical systems is treated. Numerous examples are presented carefully along with the ideas underlying the most important results. Moreover, the book deals with the dynamical systems of statistical mechanics, and with various kinetic equations. For this second enlarged and revised edition, published as Mathematical Physics I, EMS 100, two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations were added. This book is compulsory reading for all mathematicians working in this field, or wanting to learn about it.

This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.

This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.

The volume contains selected articles presented in the ZOOM conference on History of Mathematics in Jain Literature, December 2020, and also contains articles invited by the editors on specific topics.The main objective for the conference was to bring to the attention of historians in mathematics that there is a plenty of literature written by monks and scholars in Jaina literature that contains elements of arithmetic, algebra and geometry, independent of discoveries by other cultures in the past. The talks and the discussions at the conference highlighted a need for a volume that can be recommended as a reference book for a course on History of Mathematics in the Departments of Mathematics and Education in colleges and universities. This is our hope that the present volume would fill up the gap on the lack of knowledge of past Jaina contributions.

Algebraic Groups and Arithmetic is an area in which major advances have been made in recent decades. The School of Mathematics of the Tata Institute of Fundamental Research has been one of the significant contributors to the progress, under the leadership of Professor M.S. Raghunathan. The Tata Institute organised a conference on the theme during 17-22 December 2001, on the occasion of Professor Raghunathan turning sixty. The conference received enthusiastic response, and there were lectures by several experts on forefront topics in the theme, including group-theoretic aspects, diophantine approximation, modular forms, representation theory, interactions with topology and geometry, dynamics on homogeneous spaces. This volume is a collection of papers emerging from the Conference. In addition to original papers by several leading mathematicians in the area, it also includes two expository papers on the work of Professor M.S. Raghunathan, by the late Professor Armand Borel and Professor Gopal Prasad, which had also been presented at the Conference.