The articles in this volume are based on talks given at the Special Session on
“Noncommutative birational geometry, representations and cluster algebras” dur-
ing the Annual Meeting of the American Mathematical Society held in January of
2012 in Boston. The papers presented here deal with various aspects of noncom-
mutative birational geometry and related topics. The focus of the papers is mostly
on structure and representations of quantum groups and algebras, braided alge-
bras, rational series in free groups, Poisson brackets on free algebras, and related
problems in combinatorics.
The volume is useful for researchers and graduate students in mathematics
and mathematical physics who want to be introduced to different areas of current
research in the new area of noncommutative algebra and geometry.