Geometric Methods in Physics XXXVII: Workshop and Summer School, Białowieża, Poland, 2018 (Trends in Mathematics Book 37)

The book consists of articles based on the XXXVII Białowieża Workshop on Geometric Methods in Physics, 2018. 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. This edition of the workshop featured a special session dedicated to Professor Daniel Sternheimer on the occasion of his 80 th birthday. The previously unpublished papers present cutting-edge current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past seven 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 book also includes abstracts of the five lecture series that were given at the seventh school. Front Matter ....Pages i-xviii Front Matter ....Pages 1-1 On canonical parametrization of phase spaces of Isomonodromic Deformation Equations (Mikhail V Babich)....Pages 3-12 On some deformations of the Poisson structure associated with the algebroid bracket of differential forms (Alina Dobrogowska, Grzegorz Jakimowicz, Karolina Wojciechowicz)....Pages 13-23 Generation of Painlevé V transcendents (David Bermudez, David J. Fernández, Javier Negro)....Pages 24-33 Hamiltonian Dynamics for the Kepler Problem in a Deformed Phase Space (Mahouton Norbert Hounkonnou, Mahougnon Justin Landalidji)....Pages 34-48 Notes on integrable motion of two interacting curves and two-layer generalized Heisenberg ferromagnet equations (Gulgassyl Nugmanova, Zhaidary Myrzakulova, Ratbay Myrzakulov)....Pages 49-56 About the solutions to the Witten—Dijkgraaf— Verlinde—Verlinde associativity equations and their Lie-algebraic and geometric properties (Anatolij K. Prykarpatski)....Pages 57-67 2+2-Moulton Configuration – rigid and flexible (Naoko Yoshimi)....Pages 68-74 Melnikov functions in the rigid body dynamics (Paweł Lubowiecki, Henryk Żołądek)....Pages 75-82 Front Matter ....Pages 83-83 E(2)-covariant integral quantization of the motion on the circle and its classical limit (Rodrigo Fresneda, Jean Pierre Gazeau, Diego Noguera)....Pages 85-91 On Deformation Quantization using Super Twistorial Double Fibration (Yuji Hirota, Naoya Miyazaki, Tadashi Taniguchi)....Pages 92-99 Deformation Quantization of Commutative Families and Vector Fields (Georgiy I. Sharygin)....Pages 100-120 Co-Toeplitz Quantization: A Simple Case (Stephen Bruce Sontz)....Pages 121-126 Front Matter ....Pages 127-127 On the quantum flag manifold \({{SU}_{q}} (3)/{\mathbb{T}^2}\) (Tomasz Brzeziński, Wojciech Szymański)....Pages 129-139 A Hopf algebra without a modular pair in involution (Sebastian Halbig, Ulrich Krähmer)....Pages 140-142 Front Matter ....Pages 143-143 Hopf–Rinow theorem in Grassmann manifolds of C∗-algebras (Eduardo Chiumiento)....Pages 145-152 Short geodesics for Ad invariant metrics in locally exponential Lie groups (Piotr Kielanowski, Anatol Odzijewicz, Emma Previato)....Pages 153-160 Front Matter ....Pages 161-161 On Conjugacy of Subalgebras of Graph C∗-Algebras (Piotr Kielanowski, Anatol Odzijewicz, Emma Previato)....Pages 163-173 A Direct Proof for an Eigenvalue Problem by Counting Lagrangian Submanifolds (Piotr Kielanowski, Anatol Odzijewicz, Emma Previato)....Pages 174-180 Applications of the Fundamental Theorems of Projective and Affine Geometry in Physics (Piotr Kielanowski, Anatol Odzijewicz, Emma Previato)....Pages 181-187 Modeling the dynamics of a charged drop of a viscous liquid (Piotr Kielanowski, Anatol Odzijewicz, Emma Previato)....Pages 188-194 The orthogonal systems of functions on lattices of SU(n + 1), n < ∞ (Piotr Kielanowski, Anatol Odzijewicz, Emma Previato)....Pages 195-203 The Super Orbit Challenge (Piotr Kielanowski, Anatol Odzijewicz, Emma Previato)....Pages 204-211 Weighted generalization of the Szegö kernel and how it can be used to prove general theorems of complex analysis (Piotr Kielanowski, Anatol Odzijewicz, Emma Previato)....Pages 212-218 Front Matter ....Pages 219-219 Amenability, flatness and measure algebras (Piotr Kielanowski, Anatol Odzijewicz, Emma Previato)....Pages 221-233 Functional Analysis techniques in Optimization and Metrization problems (Piotr Kielanowski, Anatol Odzijewicz, Emma Previato)....Pages 234-239 Twistor Geometry and Gauge Fields (Piotr Kielanowski, Anatol Odzijewicz, Emma Previato)....Pages 240-245 Quantum Dirichlet forms and their recent applications (Piotr Kielanowski, Anatol Odzijewicz, Emma Previato)....Pages 246-254 Lagrangian approach to Geometric Quantization (Piotr Kielanowski, Anatol Odzijewicz, Emma Previato)....Pages 255-258 Preface -- In Memoriam Bogdan Mielnik -- Some aspects of the work of Daniel Sternheimer -- On canonical parametrization of phase spaces of Isomonodromic Deformation Equations -- On some deformations of the Poisson structure associated with the algebroid bracket of differential forms -- Generation of Painlevé V transcendents -- Hamiltonian Dynamics for the Kepler Problem in a Deformed Phase Space -- Notes on integrable motion of two interacting curves and two-layer generalized Heisenberg ferromagnet equations -- About the solutions to the Witten-Dijkgraaf-Verlinde-Verlinde associativity equations and their Lie-algebraic and geometric properties -- 2+2-Moulton Configuration - rigid and flexible -- Melnikov functions in the rigid body dynamics -- E(2)-covariant integral quantization of the motion on the circle and its classical limit -- On Deformation Quantization using Super Twistorial Double Fibration -- Deformation Quantization of Commutative Families and Vector Fields -- Co-Toeplitz Quantization: A Simple Case -- On the quantum flag manifold SUq(3)/T2 -- A Hopf algebra without a modular pair in involution -- Hopf-Rinow theorem in Grassmann manifolds of C∗-algebras -- Short geodesics for Ad invariant metrics in locally exponential Lie groups -- On Conjugacy of Subalgebras of Graph C∗-Algebras -- A Direct Proof for an Eigenvalue Problem by Counting Lagrangian Submanifolds -- Applications of the Fundamental Theorems of Projective and Affine Geometry in Physics -- Modeling the dynamics of a charged drop of a viscous liquid -- The orthogonal systems of functions on lattices of SU(n + 1), n < ∞ -- The Super Orbit Challenge -- Weighted generalization of the Szegö kernel and how it can be used to prove general theorems of complex analysis -- Amenability, flatness and measure algebras -- Functional Analysis techniques in Optimization and Metrization problems -- Twistor Geometry and Gauge Fields -- Quantum Dirichlet forms and their recent applications -- Lagrangian approach to Geometric Quantization