Mathematics provides a language in which to formulate the laws that govern nature. It is a language proven to be both powerful and effective. In the quest for a deeper understanding of the fundamental laws of physics, one is led to theories that are increasingly difficult to put to the test. In recent years, many novel questions have emerged in mathematical physics, particularly in quantum field theory. Indeed, several areas of mathematics have lately become increasingly influential in physics and, in turn, have become influenced by developments in physics. Over the last two decades, interactions between mathematicians and physicists have increased enormously and have resulted in a fruitful cross-fertilization of the two communities.This volume contains the plenary talks from the international symposium on Noncommutative Geometry and Representation Theory in Mathematical Physics held at Karlstad University (Sweden) as a satellite conference to the Fourth European Congress of Mathematics. The scope of the volume is large and its content is relevant to various scientific communities interested in noncommutative geometry and representation theory. It offers a comprehensive view of the state of affairs for these two branches of mathematical physics. The book is suitable for graduate students and researchers interested in mathematical physics.

Table of Contents:
Construction of graded differential algebra with ternary differential by N. Bazunova Calculation of the universal Drinfeld twist for quantum su(2) by C. Blohmann Thoughts on membranes, matrices and non-commutativity by M. Cederwall Stable quantum relativistic kinematics by C. Chryssomalakos and E. Okon Cohomology of crossed algebras by A. Davydov Kac-Moody algebras and the cde-triangle by T. Ekedahl Discretized Virasoro algebra by L. D. Faddeev Multiplication formulae for the elliptic gamma function by G. Felder and A. Varchenko New approach to Hermitian $q$-differential operators on $\mathbb{R}^N_q$ by G. Fiore Picard groups in rational conformal field theory by J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert On a class of representations of quantum groups by A. Gerasimov, S. Kharchev, D. Lebedev, and S. Oblezin Shapovalov forms for Poisson Lie superalgebras by M. Gorelik and V. Serganova Triangular Poisson structures on Lie groups and symplectic reduction by T. J. Hodges and M. Yakimov Vertex operator algebras, fusion rules and modular transformations by Y.-Z. Huang Depth two and the Galois coring by L. Kadison Examples of Peirce decomposition of generalized Jordan triple system of second order--Balanced cases by N. Kamiya Graded representations of graded Lie algebras and generalized representations of Jordan algebras by I. Kantor and G. Shpiz Dynamical Yang-Baxter equation and quantization of certain Poisson brackets by E. Karolinsky, A. Stolin, and V. Tarasov Braiding for quantum $g1_2$ at roots of unity by R. Kashaev and N. Reshetikhin Solving Baxter's TQ-equation via representation theory by C. Korff Noncommutative geometry and quantum field theory by P. P. Kulish Conformal field theory and the solution of the (quantum) elliptic Calogero-Sutherland system by E. Langmann Quasi-Lie algebras by D. Larsson and S. D. Silvestrov Time-space and space-times by O. A. Laudal Two-parameter extension of the $\kappa$-Poincare quantum deformation by J. Lukierski and V. D. Lyakhovsky The index problem on manifolds with edges by V. E. Nazaikinskii, A. Y. Savin, B.-W. Schulze, and B. Y. Sternin On $C^*$-algebras generated by some deformations of CAR relations by D. Proskurin, Y. Savchuk, and L. Turowska Krichever-Novikov algebras and their representations by O. K. Sheinman Quantum groups and bounded symmetric domains by S. D. Sinel'shchikov and L. Vaksman Quantization is deformation by D. Sternheimer Monoidal Morita equivalence by K. Szlachanyi Fortieth anniversary of extremal projector method for Lie symmetries by V. N. Tolstoy.