This book is the first volume of proceedings from the joint conference X International Symposium "Quantum Theory and Symmetries" (QTS-X) and XII International Workshop "Lie Theory and Its Applications in Physics" (LT-XII), held on 19-25 June 2017 in Varna, Bulgaria. The QTS series was founded on the core principle that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium at the forefront of theoretical and mathematical physics. The LT series covers the whole field of Lie theory in its widest sense, together with its applications in many areas of physics. As an interface between mathematics and physics, the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In dividing the material between the two volumes, the Editor has sought to select papers that are more oriented toward mathematics for the first volume, and thosefocusing more on physics for the second. However, this division is relative, since many papers are equally suitable for either volume. The topics addressed in this volume represent the latest trends in the fields covered by the joint conferences: representation theory, integrability, entanglement, quantum groups, number theory, conformal geometry, quantum affine superalgebras, noncommutative geometry. Further, they present various mathematical results: on minuscule modules, symmetry breaking operators, Kashiwara crystals, meta-conformal invariance, the superintegrable Zernike system.

Inhalt

PART 1: Plenary Talks, Toshiyuki Kobayashi and Alex Leontiev, Image of Conformally Covariant, Symmetry Breaking Operators for Rp;q.- Anthony Joseph, Trails for Minuscule Modules and Dual Kashiwara Functions for the B(¥) Crystal.- Ivan Todorov, From Euler's Play with Infinite Series to the Anomalous Magnetic Moment.- Tamar Friedmann, On the Derivation of the Wallis Formula for p in the 17th and 21st Centuries.- Ivan Dimitrijevic, Branko Dragovich, Zoran Rakic, Jelena Stankovic, Variations of Infinite Derivative Modified Gravity.- Malte Henkel and Stoimen Stoimenov, Infinite-Dimensional Metaconformal Symmetries: 1D Diffusion-Limited Erosion and Ballistic Transport in (1+2) Dimensions.- A.P. Isaev, M.A. Podoinitsyn, Behrends-Fronsdal Spin Projection Operator in Space-Time with Arbitrary Dimension.- Takeo  Kojima, Wakimoto Realization of the Quantum Affine Superalgebra Uq(bsl(MjN)).- N.I. Stoilova, J. Thierry-Mieg, J. Van der Jeugt, On Superdimensions of Some Infinite-Dimensional Irreducible Representations of osp(mjn).- G. Manolakos, G. Zoupanos, Non-commutativity in Unified Theories and Gravity.- PART 2: Representation Theory,  Jean-Emile Bourgine, Webs of Quantum Algebra Representations in 5d N = 1 Super Yang-Mills.- Patrick Moylan, Parallelizations for Induced Representations of SO0(2,q).- Takuya Matsumoto, Screening Operators for the Lattice Vertex Operator Algebras of Type A1 at Positive Rational Level.- Hendrik De Bie, Roy Oste, Joris Van der Jeugt, Symmetries of the S3 Dirac-Dunkl Operator.- PART 3: Integrability, Natig M. Atakishiyev, George S. Pogosyan, Cristina Salto-Alegre, Kurt Bernardo Wolf, Alexander Yakhno, The Superintegrable Zernike System.- Iana I. Anguelova, The Two Bosonizations of the CKP Hierarchy: Bicharacter Construction and Vacuum Expectation Values.- A.R. Aguirre, J.F. Gomes, A.L. Retore, N.I. Spano, A.H. Zimerman, Recursion Operator and B¨acklund Transformation for Super mKdV Hierarchy.- Kyriakos Charalambous and Christodoulos Sophocleous, Lie Symmetry Analysis of a Third-Order Equation Arising from a General Class of Lotka-Volterra Chains.- PART 4: Entanglement, Hichem Eleuch, Michael Hilke, Richard MacKenzie, Probing Anderson Localization Using the Dynamics of a Qubit.- Mike Hewitt, Pure Spinors, Impure Spinors and Quantum Mechanics.- H. Dimov, S. Mladenov, R. Rashkov, T. Vetsov, Higher-Derivative Oscillators in AdS5£S5 T-dual Penrose Limits.- PART 5: Quantum Groups and Related Structures, A´ ngel Ballesteros, Rutwig Campoamor-Stursberg, Eduardo Ferna´ndez-Saiz, Francisco J. Herranz, Javier de Lucas, A Unified Approach to Poisson-Hopf  Deformations of Lie-Hamilton Systems Based on sl(2).- Huafeng Zhang, Two-Parameter Quantum General Linear Supergroups.- Doman Takata, Noncommutative Geometry and an  Index Theory Of Infinite-Dimensional Manifolds.- PART 6: Various Mathematical Results, Cristian Anghel, A Stable Version of Terao Conjecture.- J.F. Colombeau, J. Aragona, P. Catuogno, S.O. Juriaans, Ch. Olivera, Multiplication of Distributions and Nonperturbative Calculations of Transition Probabilities.- Alexander Ganchev, About Markov, Gibbs, ... Gauge Theory ... Finance.- Rosa M. Navarro and Jos´e M. S´anchez, A Method for Classifying Filiform Lie Superalgebras.- Maryna Nesterenko and Severin Posta, Equivalence of Vector Field Realizations of Lie Algebras from the Lie Group Point of View.- List of Participants.