Group Theoretical Methods in Physics

Introductory talk.- Creating "clouds".- Opening remarks.- Laudatio for Professor Francesco Iachello.- Symmetry.- Dynamical and fundamental symmetries in particles and nuclei.- Spectrum generating groups - idea and application.- The role of dynamic symmetries and supersymmetries in nuclear physics.- SO(3,2) for oscillator and hydrogenlike systems.- Conformal groups in the Kepler problem.- Potential group in optics: The maxwell fish-eye system.- Transition to chaos in hadronic systems.- The dynamical group of Riemann ellipsoids.- An algebraic model of cluster states in odd-mass nuclei.- Compact to noncompact transition and nuclear collective levels.- $$\overline {SL(3,R)} \times T^6$$ as a nuclear collective motion group.- Exceptional groups and the interacting boson approximation.- An overview of quantum groups.- Integrable theories, Yang-Baxter algebras and quantum groups: An overview.- Finite - dimensional irreducible representations of the quantum superalgebra Uq[gl(n/I)].- Projection operator method and Q-analog of angular momentum theory.- Quantum algebras and symmetries of dynamical systems.- Coulomb gas realization of simple quantum groups.- String theory, quantum gravity and quantum groups.- q-Oscillator realizations of the quantum superalgebras sl q (m, n)andosp q (m, 2n).- Relativistic oscillator = q-oscillator.- Some aspects of the angular momentum coefficients in SUq (2).- Contractions and analytic continuations of the irreducible representations of the quantum algebra suq(2).- Universal R-matrix for quantum supergroups.- Recent progress in non-commutative geometry.- Algebraic gauge theory and noncommutative geometry.- Classification of the symmetries of ordinary differential equations.- Conditional symmetries and conditional integrability for nonlinear systems.- Cohomology and symmetry of differential equations.- Derivations of semi-basic forms and symmetries of second-order equations.- Hamilton-Jacobi equations in SU(2, 2) homogeneous spaces.- Linearization of PDEs.- Perturbed nonlinear equations: Application to the Korteweg-Devries equation considered as a perturbed Euler equation.- Algebraic version of the soliton perturbation theory.- Extended chiral conformal models with a quantum group symmetry.- Conformal reduction of WZNW theories and W-algebras.- The resurrection of a forgotten symmetry: De broglie' s symmetry.- Relativistic invariance of a many body system with a Dirac oscillator interaction.- Derivation of the geometrical berry phase.- Gauge translations and the Berry phase.- Geometric quantization: Regular representations and modular algebras.- Geometro-stochastic quantization and quantum geometry.- SO(4,1)-Coherent states and the geometro-stochastic quantization of a gauge theory for extended objects.- Covariant quantum mechanics and the symmetries of its radiation fields.- Double stratonovich - Hubbard trick and novel path integral for a system of interacting fermions.- Nonrelativistic limit of superfield theories.- Remarks on the supersymmetric WKB quantization formula.- Particle in a self-dual monopole field: example of supersymmetric quantum mechanics.- Supersymmetry and electron angular momentum.- Parasupersymmetries and Lie superalgebras.- Quantum chaos: Spectra and states.- Quantum ergodicity and eigenvalue problems for plane polygons.- "Classical" in terms of general statistical models.- Temporal decoherence in Lorentz-squeezed hadrons.- Physical significance of correlated and squeezed states.- On the symmetry and dynamics of squeezed and correlated states.- Correlated States of Quantum Chain.- Interaction of weak coherent light with a system of two - level atoms in a lossless cavity.- Time dependent quantum tunnelling.- Non-spurious harmonic oscillator states with arbitrary permutational symmetry.- Symmetry analysis of the qualitative intramolecular phenomena.- Algebras of the SU(n) vector invariants and some of their applications.- Product formulas for Q-representatives.- Tensor products for affine Kac-Moody algebras.- Atypical modules of the lie superalgebra gl (m/n).- Vector coherent state theory of the non-compact orthosymplectic superalgebras.- The composition factors of kac modules of sl(M/N).- Clifford algebras, spinors and finite geometries.- Reducibility of Euclidean motion groups.- Software packages: Space groups and their representations.- Software packages: Transformation coefficients for space groups.- Icosahedral dissectable tilings from the root lattice D6.- Groups with G-number parameters.- Regge Calculus with torsion.- Quasiperiodicity: Local and global aspects.- Derivative Moufang transformations.- On the explicit form of consistent anomalies.- Berry phases and Wyckoff positions for energy bands in solids.- Crystallography of quasicrystals: The problem of restoration of broken symmetry.