The papers in this volume are based on the talks given at the conference on quantum groups dedicated to the memory of Joseph Donin, which was held at the Technion Institute, Haifa, Israel in July 2004. A survey of Donin's distinguished mathematical career is included. Several articles, which were directly influenced by the research of Donin and his colleagues, deal with invariant quantization, dynamical $R$-matrices, Poisson homogeneous spaces, and reflection equation algebras. The topics of other articles include Hecke symmetries, orbifolds, set-theoretic solutions to the pentagon equations, representations of quantum current algebras, unipotent crystals, the Springer resolution, the Fourier transform on Hopf algebras, and, as a change of pace, the combinatorics of smoothly knotted surfaces. The articles all contain important new contributions to their respective areas and will be of great interest to graduate students and research mathematicians interested in Hopf algebras, quantum groups, and applications. Information for our distributors: This book is copublished with Bar-Ilan University (Ramat-Gan, Israel).
Joseph Donin's mathematical research, 1966-2003 by A. Mudrov and S. Shnider Geometric and unipotent crystals II: From unipotent bicrystals to crystal bases by A. Berenstein and D. Kazhdan The small quantum group and the Springer resolution by R. Bezrukavnikov and A. Lachowska Relation between two geometrically defined bases in representations of $GL_n$ by A. Braverman, D. Gaitsgory, and M. Vybornov Fourier transforms for Hopf algebras by M. Cohen and S. Westreich Quantization of some Poisson-Lie dynamical $r$-matrices and Poisson homogeneous spaces by B. Enriquez, P. Etingof, and I. Marshall Basic representations of quantum current algebras in higher genus by B. Enriquez, S. Pakuliak, and V. Rubtsov Poincare-Birkhoff-Witt expansions of the canonical elliptic differential form by G. Felder, R. Rimanyi, and A. Varchenko Geometry of non-commutative orbits related to Hecke symmetries by D. Gurevich and P. Saponov Drinfeld double for orbifolds by V. Hinich Symmetrically factorizable groups and set-theoretical solutions of the pentagon equation by R. M. Kashaev and N. Reshetikhin Dynamical reflection equation by P. P. Kulish and A. I. Mudrov On the combinatorics of Carter-Rieger-Saito movies in the theory of smoothly knotted surfaces in $\mathbb{R}^4$ by G. Lancaster, R. Larson, and J. Towber.
