Geometric Methods in Physics XXXVIII Workshop, Bialowieza, Poland, 2019

The book consists of articles based on the XXXVIII Bialowieza Workshop on Geometric Methods in Physics, 2019. The series of Bialowieza 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 The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics.

Part I: Contributions to theXXXVIII 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 tau functions.- 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.

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.