Representation Theory Mathematical Physics and Integrable Systems : In Honor of Nicolai Reshetikhin Over the course of his distinguished career Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields including representation theory integrable systems and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra differential and algebraic geometry and perspectives arising from physics this volume explores topics such as the development of new and powerful knot invariants new perspectives on enumerative geometry and string theory and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory exactly solvable models in statistical mechanics and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory Mathematical Physics and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them ranging from graduate students to junior mid career and senior researchers. Andruskiewitsch Angiono Heckenberger Examples of Finite Dimensional Pointed Hopf Algebras in Positive Characteristic Bakalov de Sole Kac Vignoli Poisson Vertex Algebra Cohomology and Differential Harrison Cohomology Cattaneo Mnev Wernli Theta Invariants of Lens Spaces via the BV BFV Formalism Chari Davis Moruzzi Jr. Generalized Demazure Models and Prime Representations of in Type $D_n$ Corteel Mandelshtam Williams Cylindric Rhombic Tableaux and the Two Species ASEP on a Ring Di Francesco Kedem Macdonald Operators and Quantum Q Systems for Classical Types Gautam Toledano Laredo Wendlandt The Meromorphic R Matrix of the Yangian Gerasimov Shatashvili On Spectral Cover Equations in Simpson Integrable Systems Giaquinto Gilman Tingley Peter Weyl Bases Preferred Deformations and Schur Weyl Duality Hernandez Quantum Periodicity and Kirillov Reshetikhin Modules Hsiao Szenes A Note on the E Polynomials of a Stratification of the Hilbert Scheme of Points Johnson Freyd Galois Action on VOA Gauge Anomalies Johnson Freyd Heisenberg Picture Quantum Field Theory Jones Irreducibility of the WYSIWYG Representations of Thompson’s Group Kirillov Rigged Configurations and Unimodality Mkrtchyan Turning Point Processes in Plane Partitions with Periodic Weights of Arbitrary Period Al Qasimi The Skein Category of the Annulus Serganova Tensor Product of the Fock Representation with its Dual and the Deligne Category Smirnov Exact Density Matrix for Quantum Group Invariant Sector of XXZ Model Turaev Loops in Surfaces and Star Fillings.