The book consists of articles based on the XXXVII Bialowieza Workshop on Geometric Methods in Physics, 2018. 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. This edition of the workshop featured a special session dedicated to Professor Daniel Sternheimer on the occasion of his 80th 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The previously unpublished papers present cutting-edge current research, typically grounded in geometry and analysis, with applications to classical and quantum physics.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 Bialowieza 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.
Inhaltsverzeichnis
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 formsand their recent applications. - Lagrangian approach to Geometric Quantization.
