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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.
List of contents
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.
