The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics.
For the past eight years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included.
The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities.
The chapter “Toeplitz Extensions in Noncommutative Topology and Mathematical Physics” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Spis treści
Part I: Contributions to the XXXVIII Workshop.- Toeplitz extensions in noncommutative topology and mathematical physics.- Standard groupoids of von Neumann algebras.- Quantum differential equations and helices.- Periodic one-point rank one commuting difference operators.- On the bi-Hamiltonian structure of the trigonometric spin Ruijsenaars-Sutherland hierarchy.- Hermitian-Einstein metrics from non commutative U(1) solutions.- 2-hom-associative bialgebras and hom-left symmetric dialgebras.- Laguerre-Gaussian wave propagation in parabolic media.- Maximal Surfaces on Two-Step Sub-Lorentzian Structures.- Following the Trail of the Operator Geometric Mean.- On Hom-Lie-Rinehart algebras.- One Step Degeneration of Trigonal Curves and Mixing of Solitons and Quasi-Periodic Solutions of the KP Equation.- Fock Quantization of Canonical Transformations and Semiclassical Asymptotics for Degenerate Problems.- Some recent results on contact or point supported potentials.- 2D Yang-Mills theory and taufunctions.- Many-particle Schröodinger type finitely factorized quantum Hamiltonian systems and their integrability.- Quantum master equation for the time-periodic density operator of a single qubit coupled to a harmonic oscillator.- On the construction of non-Hermitian Hamiltonians with all-real spectra through supersymmetric algorithms.- Toeplitz Quantization of an Analogue of the Manin Plane.- The Weyl-Wigner-Moyal formalism on a discrete phase space.- Algebraic geometric properties of spectral surfaces of quantum integrable systems and their isospectral deformations.- Part II: Abstracts of the Lectures at “School on Geometry and Physics.- Soliton equations and their holomorphic solutions.- Diffeomorphism Groups in Quantum Theory and Statistical Physics.- Position-dependent mass systems: Classical and quantum pictures.- Introduction to the algebraic Bethe ansatz.- Noncommutative Fiber Bundles.
O autorze
Piotr Kielanowski is a Professor at the Center for Research and Advanced Studies at the National Polytechnic Institute in Mexico City. He received his Ph.D. from the University Warsaw, specializing in elementary particle theory. His research focuses on exact results in theoretical physics, particularly the phenomenology of the Standard Model and the rigged Hilbert space extension of quantum mechanics. He has co-authored a book on quantum mechanics, and published extensively in scientific journals. He climbed Popocatépetl when it was inactive, and when time permits, he visits his treasured Tatra Mountains in Poland.
Anatol Odzijewicz holds a Ph.D. in Mathematical Physics from the University of Warsaw. He then joined the University of Białystok in Poland, where he is now a Professor at the Department of Mathematics. His research focuses on geometric methods of quantization and the theory of integrable systems with applications to classical and quantum optics, and he has published in leading mathematics and physics journals. In 1982, he began the series of Workshops on Geometric Methods in Physics, held annually each summer in Białowieża, Poland, which have become an important international gathering point for physicists and mathematicians. He was also a founder of the Open-Air Museum of Wooden Architecture in Białowieża, which illustrates the historical daily lives of Russian people in the Podlaskie region.
Emma Previato is a Fellow of the American Mathematical Society (inaugural class 2012) and a Professor of Mathematics at Boston University, USA. Previato earned her Ph.D. in Mathematics from Harvard University, with a dissertation on integrable PDEs based on classical algebraic geometry and special functions. Her research has been published in over 80 journal articles, and includes methods of algebraic geometry, differential algebra, Hamiltonian mechanics, PDEs, and information theory. She is the(co-)editor of five books.
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