Differential Geometric Methods in Theoretical Physics

to the 18th Conference on ‘Differential Geometrical Methods in Theoretical Physics’.- Baxterization.- Geometric Classification of Commutative Algebras of Ordinary Differential Operators.- Geometrical Aspects of Solvable Two Dimensional Models.- Explicit Soliton-Generating Bäcklund Transformations.- Integrability Conditions: Recent results in the theory of integrable models.- Nonlinear Differential Equations in Physics and Their Geometrical Integrability Properties.- Integrability Off Criticality and Quantum Integrable Systems.- Quantization of the Chiral Solitonic Bag Model.- Structure of Superselection Sectors in Low-Dimensional Quantum Field Theory.- Cyclic Cohomology, Supersymmetry and KMS States the KMS States as Generalized Elliptic Operators.- Symmetrics of Quantum Space, Braid Representation, and Classification of Subfactors.- New Kinematics (Statistics and Symmetry) in Low-Dimensional QFT with Applications to Conformal QFT2.- Infinite Index Embeddings.- Non-Compact Current Algebras and Heterotic Superstring Vacua.- Aspects of Perturbed Conformal Field Theory, Affine Toda Field Theory and Exact S-Matrices.- Codes, Lattices and Conformal Field Theory.- Topics on Conformal Field Theory.- Feigin-Fuchs Representation of Conformal Field Theory.- Coulomb-Gas Construction on Higher-Genus Riemann Surfaces.- Conformal Algebras and Non-linear Differential Equations.- S Matrices of the Tricritical Ising Model and Toda Systems.- Quantum Groups, Braiding Matrices and Coset Models.- Gauged WZW Models and the Coset Construction of Conformal Field Theories.- Flat Connection, Conformal Field Theory and Quantum Group.- Classical and Quantum Calabi-Yau Manifolds.- Conformal Field Theories and Category Theory.- Quantum Bäcklund Transformations and Conformal Algebras.- ACoset-Construction for Integrable Hierarchies.- Away From Criticality: Some Results From the S Matrix Approach.- Normal Ordered Products and Parafields in Conformal Field Theory.- Chiral Gauge Field Theory in Two Dimensions.- Monodromy Properties of Conformal Field Theories and Quantum Groups.- Matrix elements of unitary representations of the quantum group SUq(1, 1) and the basic hypergeometric functions.- A q-Analogue of the Lie Superalgebra OSp(2,1) and its Metaplectic Representation.- q-Deformation of SU(1, 1) Conformal Ward Identities and q-Strings.- Q-Deformation of sl(2, c) × ZN and Link Invariants.- Quantum Group Duality in Vertex Models and Other Results in the Theory of Quasitriangular Hopf Algebras.- Physics at the Planck Length and p-Adic Field Theories.- Non-Archimedean Geometry and Applications to Particle Theory.- Beyond Conformal Field Theory.- Hidden Symmetries of Strings and Their Relevance for String Quantization.- Hamiltonian Flows, SU(?), SO(?), USp (?), and Strings.- A Geometric Approach to the String BRS Cohomology.- Progress in Multi-Genus Calculations for the Spinning String.- The Minimal Set of the Generators of Dehn Twists on a High Genus Riemann Surface.- Strings and Teichmueller Space.- Holomorphic Differentials on Punctured Riemann Surfaces.- Anomalies, BRS Symmetry and Superconnections.- General Covariance and Strings.- Spontaneous Symmetry Breaking in 4-Dimensional Heterotic String.- Superghost Fields in N = 2 Superconformal Algebra.- Topological Quantum Field Theories: Relations Between Knot Theory and Four Manifold Theory.- Topological Quantum Theories and Representation Theory.- Topological Chern-Simons Gauge Theories and “New” Knot/Link Polynomials.- Observables in Topological Yang-Mills Theory and the Gribov Problem.-Linking the Gauss-Bonnet-Chern Theorem, Essential Hopf Maps and Membrane Solitons with Exotic Spin and Statistics.- Moduli Spaces and Topological Quantum Field Theories.- Knots in Physics.- Supermanifold, Symplectic Structure and Geometric Quantization of BRST Systems.- Ambitwistors and Conformal Gravity.- Toward Classification of Classical Lie Superalgebras.- Status of the Algebraic Approach to Super Riemann Surfaces.- Projective Embeddings of Complex Supermanifolds.- Some Results on Line Bundles over SUSY-Curves.- Instantons From Supersymmetric Conformal Chiral Scalar Superfield Theories.- Einstein-Hermitian Bundles over Complex Surfaces.- Symplectic Reduction of the Minimally Coupled Massless Superparticle in D=10.- Quantum Gravity and the Berry Phase.- Gravity and Lorentz Breakdown in Higher-Dimensional Theories and Strings.- Current Algebra and Extended 2D Gravity with Higher Spin Gauge Field.- The Parametric Manifold Picture of Space-Time.- Gravity as an SO(3, 2) Gauge Theory.- Heuristics of Solitary Waves in Non-Integrable Field Theories.- Lattice Approach of the Antiferromagentic Heisenberg Model in 2+1 Dimensions and the Hopf Chern-Simons Terms.- Is It Possible To Do Canonical Quantum Field Theory Rigorously?.- A Global Theory of Parametrized Quantum Mechanics.- Principal Bundles Versus Lie Groupoids in Gauge Theory.- Static and Axially Symmetric Soliton Solutions to the Self-Dual SU(3) and SU(2) Gauge Fields in a Euclidean Space.- Superalgebra and Superspace of Vector Spinor Generators.- Participants.- Author Index.