19. ja 20. mail esineb Eesti matemaatika ja statistika doktorikooli külalisprofessor Alexander Stolin (University of Göteborg ja Chalmers University of Technology) loengutega kvantrühmadest, kvantgeomeetriast ja nende rakendustest. Loengud toimuvad teisipäeval 19. mail kell 14.15-15.15 ja kolmapäeval 20. mail kell 14.15-15.15 J. Liivi 2 aud. 202.
Esimese loengu teemad on:
1. Lie groups and Lie algebras, definitions and examples.
2. Universal enveloping algebras.
3. Hopf algebras, definitions and examples.
4. Quantum groups as deformations of the universal enveloping algebras.
Teise loengu teemad on:
1. Quantum groups and quantum algebras.
2. Kulish-Reshetikhin example U_q(sl(2))
3. Jordan quantum group.
4. New quantum group related to sl(2).
Abstract. Quantum groups are one of the most popular objects in the modern mathematical physics. They also play a significant role in other areas of mathematics. It turned out that quantum groups provided invariants of knots and they could be used in quantization of Poisson brackets on manifolds. Quantum groups gave birth to quantum geometry, quantum calculus, quantum special functions and many other “quantum” areas. However, the most important applications of quantum groups relate to the theory of integrable models in the mathematical physics. The presence of the quantum group symmetries (or the so called hidden symmetries) was the crucial point in explicit solutions of many sophisticated non-linear equations such as Korteweg-de Vries or sine-Gordon. Quantum groups changed and enriched representation theory and algebraic topology. The program of these two lectures is based on the development of the problems considered in a joint paper by F. Montaner, A. Stolin, E. Zelmanov (Fields Medal, 1994) “Classification of Lie bialgebras over current algebras” published in Selecta Mathematica New Series (2010), 16:935-962.