This book collects papers based on the XXXVI Białowieża Workshop on Geometric Methods in Physics, 2017. The Workshop, which attracts a community of experts active at the crossroads of mathematics and physics, represents a major annual event in the field. Based on presentations given at the Workshop, the papers gathered here are previously unpublished, at the cutting edge of current research, and primarily grounded in geometry and analysis, with applications to classical and quantum physics. In addition, a Special Session was dedicated to S. Twareque Ali, a distinguished mathematical physicist at Concordia University, Montreal, who passed away in January 2016.
For the past six years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising a series of advanced lectures for graduate students and early-career researchers. The extended abstracts of this year’s lecture series are also included here. The unique character of the Workshop-and-School series is due in part to the venue: a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in eastern Poland. Lectures are given in the Nature and Forest Museum, and local traditions are interwoven with the scientific activities.
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FM.- Part I:Quantum Mechanics and Mathematics – Twareque Ali in Memoriam.-In Memory of S. Twareque Ali.- Two-dimensional non commutative Swanson model and its bicoherent states.- Universal Markov kernels for quantum observables.- Coherent states associated to the Jacobi group and Berezin quantization of the Siegel-Jacobi ball.- 1D & 2D Covariant affine integral quantizations.- Diffeomorphism group representations in relativistic quantum field theory.- Part II: Noncommutative Geometry.- Skew derivations on down-up algebras.- On noncommutative geometry of the Standard Model: fermion multiplet as internal forms.- Recursion operator in a noncommutative Minkowski phase space.- Decompactifying spectral triples.- Dirac operator on a noncommutative Toeplitz torus.- Part III: Quantization.- Field quantization in the presence of external fields.- Quantization of Mathematical Theory of Non-Smooth Strings.- The reasonable effctiveness of mathematical deformation theory in physics.- Axiomatic attempt at states in deformation quantisation.- Exact Lagrangian submanifolds and the moduli space of special Bohr-Sommerfeld Lagrangian cycles.- Star Exponentials in Star Product Algebra.- Part IV: Integrable Systems.- Beyond recursion operators.- Kepler Problem and Jordan Algebras.- On Rank Two Algebro-Geometric Solutions of an Integrable Chain.- Part V: Differential Geometry and Physics.- The Dressing Field Method of Gauge Symmetry Reduction: Presentation and Examples.- A differential model for B-type Landau-Ginzburg theories.- On the Dirac type operators on symmetric tensors.- Surfaces which behave like vortex lines.- On the spin geometry of supergravity and string theory.- Conic sub-Hilbert-Finsler structure on a Banach manifold.- On Spherically Symmetric Finsler metrics.-Part VI: Topics in Spectral Theory.- Homogeneous rank one perturbations and inverse square potentials.- Generalized Unitarity Relation for Linear Scattering Systems in One Dimension.- Differential equations on polytopes: Laplacians and Lagrangianmanifolds, corresponding to semiclassical motion.-Part VII: Representation Theory.- Coadjoint orbits in representation theory of pro-Lie groups.- Conformal symmetry breaking on differential forms and some applications.- Representations of the anyon commutation relations.-Part VIII: Special Topics .- Remarks to the Resonance-Decay Problemin Quantum Mechanics from a Mathematical Point of View.- Dynamical generation of grapheme.- Eight kinds of orthogonal polynomials of Weyl group C2 and tau method.- Links between quantum chaos and counting problems.- Part IX: Extended Abstracts of the Lectures at “School on Geometry and Physics”.- Integral invariants (Poincaré-Cartan) and hydrodynamics.- Invitation to Hilbert C∗ -modules and Morita-Rieffel equivalence.- After Plancherel formula.- A glimpse of noncommutative geometry.- An Example of Banach and Hilbert manifold: the universal Teichmüller space.- Extensions of Symmetric Operators and Evolution Equations on Singular Spaces.
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