This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.

The current state of knowledge on the Monster group, including Majorana theory, Vertex Operator Algebras, Moonshine and maximal subgroups.

Crossing the boundary between differential and algebraic geometry in order to study singular spaces, this book introduces 'C∞-schemes with corners'.

Automatic sequences are sequences over a finite alphabet generated by a finite-state machine. This book presents a novel viewpoint on automatic sequences, and m

Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, a