CONTENTS -- Preface -- Organizers and Committees -- List of Participants -- Conference Photo -- I. Invited Lectures -- Integrable Structures in the Gauge/String Corespondence G. Arutyunov -- 1. Gauge/String Duality -- 2. Integrable Structure of Gauge Theory -- 3. Integrable Structure of String Theory -- 4. Matching the Spectra of Gauge and String Theories -- 5. Discussion -- Acknowledgments -- References -- Fluxes in M-theory on 7-manifolds: G2-, SW(3)- and SU( 2)-structures K. Behrndt, C. Jeschek -- 1. Introduction -- 2. Warp Compactification in the Presence of Fluxes -- 3. G-Structures -- 3.1. G2 Structures -- 3.2. SU(3) Structures -- 3.3. SU(2) Structures -- 4. BPS Constraints -- 4.1. G2 Structure -- 4.2. SU(3) Structure -- 4.3. SU(2) Structure -- Acknowledgments -- References -- Noncommutative Quantum Field Theory: Review and Its Latest Achievements M. Chaichian -- 1. Introduction -- 2. Noncommutative Gauge Groups. A No-go Theorem -- 2.1. Charge Quantization Problem in NC QED -- 2.2. A No-go Theorem -- 2.3. NC Standard Model. A Solution to the Charge Quantization Problem -- 3. Lamb Shift in NC QED. Bounds on -- 4. Noncommutative Quantum Field Theory and Spin-statistics Theorem -- 5. CPT Theorem in NC Field Theories -- 5.1. The CPT hnsformation of Local Elementary Fields -- 5.2. CPT Theorem for Local Fields -- 5.3. CPT Theorem for Noncommutative Fields -- 6. Conclusions -- Acknowledgments -- References -- Shadows of Quantum Black Holes N. Kaloper -- 1. Black Holes in AdS/CFT with a Cutoff: the Role of Tunneling -- 1.1. Resolving the Mystery of the Missing 3 + 1 Black Hole -- 2. Conclusions -- Acknowledgements -- References -- Yukawa Quasi-Unification and Inflation G. Lazarides, C. Pallis -- 1. Introduction -- 2. The SUSY GUT Model -- 3. The Yukawa Quasi-Unification Condition -- 4. The resulting CMSSM.

5. Cosmological and Phenomenological Constraints -- 6. The Allowed Parameter Space -- 7. The Inflationary Scenario -- 7.1. The Shifted Inflationary Path -- 7.2. Inflationary Observables -- 7.3. Supergravity Corrections -- 8. Conclusions -- Acknowledgments -- References -- Supersymmetric Grand Unification: The Quest for the Theory A . Melfo, G. Senjanovic -- 1. Introduction -- 2. Why grand unification and why supersymmetry ? -- 3. Supersymmetric SU(5) -- 4. Towards unification: Pati-Salam symmetry -- 5. SO(10) grand unified theory -- 5.1. The pure renormalixable supersymmetric SO(10) -- 5.2. Unification constraints -- 5.3. Proton decay -- 5.4. Leptogenesis -- 6. Summary and Outlook -- 7. Acknowledgements -- References -- Spin Foam Models of Quantum Gravity A . Mikovic -- 1. Introduction -- 2. The Barret-Crane Model -- 3. New Directions -- Acknowledgments -- References -- Riemann-Cartan Space-time in Stringy Geometry B. Sazdovic -- 1. Introduction -- 2. Affine Space-time -- 3. Induced and Extrinsic Geometry -- 3.1. Induced Metric Tensor and Induced Connection -- 3.2. Second Fundamental Form -- 3.3. Mean Extrinsic Curvature -- 4. C-duality -- 5. String Equations of Motion -- 6. Classification of the Space-times -- 6.1. Riemann and Riemann- Cartan Space-time -- 6.2. Stringy Space-time -- 7. String Propagation on the Group Manifold -- 8. The Geometry Induced from the Group Manifold -- 9. Conclusions -- Acknowledgements -- References -- Can Black Hole Relax Unitarily? S. N. Solodukhin -- 1. Introduction -- 2. Relaxation in Black Hole: Quasi-normal Modes -- 3. Relaxation in CFT2 -- 3.1. Universality -- 3.2. Intermediate Regime: Free Fermions -- 3.3. Strongly Coupled CFT2 Dual to AdS3 -- 3.4. The Puzzle and Resolution -- 4. Black Hole Unitarity: Finite k -- 4.1. Fractal Brick Wall -- 4.2. Worm-hole Modification: BTZk -- Acknowledgments -- References.

Deformed Coordinate Spaces Derivatives J. Wess -- 1. Introduction -- 2. Deformed Coordinate Spaces -- 3. Derivatives -- 4. Deformed Symmetry Algebra -- 5. Fields -- References -- II. Short Lectures -- Deformed Coherent State Solution to Multiparticle Stochastic Processes B. Aneva -- 1. Introduction -- 2. Coherent States of a q-Deformed Heisenberg Algebra -- 3. Squeezed States of a Deformed Oscillator Algebra -- 4. Deformed Squeezed and Coherent State Solution to the n-Species Diffusion Process -- Acknowledgements -- References -- Non-Commutative GUTs, Standard Model and C, P, T Properties from Seiberg-Witten Map P. Aschieri -- 1. Introduction -- 2. Seiberg-Witten Map and NC Particle Models -- 2.1. Noncommutative SO(10) -- 2.2. Noncommutative SU(5) -- 2.3. (GUT Inspired) Noncommutative Standard Model -- 2.4. Higgs Sectors -- 3. Hermiticity and Reality Properties of SW Map -- 3.1. Noncommutativity and Chirality -- 4. C, P, T Properties of SW Map and of NCYM Actions -- Acknowledgments -- References -- Seesaw, Susy and SO(10) B. Bajc -- 1. Introduction -- 2. Seesaw -- 3. SO(10) -- 4. Type I Versus Type II Seesaw -- 5. SUSY -- 6. Further Developments -- Acknowledgments -- References -- On the Dynamics of BMN Operators of Finite Size and the Model of String Bits S. Bellucci, C. Sochichiu -- 1. Introduction -- 2. Fermionic Doubling -- 3. Almost supersymmetry -- 4. Fermion Doubling/Nondoubling in the BMN Correspondence -- 5. Doubling and Supersymmetry -- 6. Discussion -- Acknowledgements -- References -- Divergencies in expanded Noncommutative SU( 2) Yang-Mills Theory M. Buric and V. Radovanovic -- 1. Introduction -- 2. The Model -- 3. One-loop Effective Action -- 4. Divergencies -- 5. Discussion -- Acknowledgment -- References -- Heterotic String Compactifications with Fluxes G. L. Cardoso, G. Curio, G. Dall'Agata and D. Lust -- 1. Introduction.

2. Fluxes and Torsion -- References -- Symmetries and Supersymmetries of the Dirac-type operators on Euclidean Taub-NUT space I. I. Cotaescu, M. Visinescu -- 1. Introduction -- 2. Dirac Equation on a Curved Background -- 3. Dirac Operators of the Taub-NUT Space -- 4. Equivalent Representations -- 5. Discrete Transformations -- 6. Hidden Symmetries and the Fifth Dirac Operator -- 7. Concluding Remarks -- Acknowledgments -- References -- Real and p-Adic Aspects of Quantization of Tachyons G. S. Djordjevic, Lj. Nesic -- 1. Introduction -- 2. p-Adic Numbers and Related Analysis -- 3. Path Integral in Ordinary and p-Adic Quantum Mechanics -- 4. p-Adic Strings and Tachyons -- 5. Quantum Mechanical Analogue of Tachyon Matter -- 6. Conclusion -- Acknowledgments -- References -- Skew-Symmetric Lax Polynomial Matrices and Integrable Rigid Body Systems V. Dragovic, B. Gajic -- 1. Introduction -- 2. Lagrange bitop -- 3. Properties of spectral curve -- 4. Geometry of the Prym variety II and Mumford's relation -- 5 . Conclusion -- Acknowledgement -- References -- Supersymmetric Quantum Field Theories D. R. Grigore -- 1. Introduction -- 2. Quantum Supersymmetric Theory -- 3. The Vector Multiplet -- 4. The New Vector Multiplet -- References -- Parastatistics Algebras and Combinatorics T. Popov -- 1. Introduction -- 2. Homogeneous Algebras -- 3. The Symmetric and the Linear Group -- 4. The Algebras + and + as GL(D)-modules -- 5 . The Plactic Algebra -- 6. Hecke Algebra and the Quantum Linear Group -- 7. Deformation of + and + and -- Acknowledgments -- References -- Noncommutative D-branes on Group Manifolds J . Pawelczyk, H. Steinacker -- 1. Introduction -- 2. CFT and the Classical Description of Untwisted D- branes -- 3. Quantum Algebras and Symmetries for Branes -- 4. Representations of M and Quantum D-branes -- 4.1. Position of D.

4.2. The Space of Harmonics on D -- References -- High-Energy Bounds on the Scattering Amplitude in Noncommutative Quantum Field Theory A . Tureanu -- 1. Introduction -- 2. Jost-Lehmann-Dyson Representation -- 3. Analyticity of the Scattering Amplitude in cos Lehmann's Ellipse -- 3.1. Causality in NC QFT -- 4. Enlargement of the Domain of Analyticity in cos and Use of Unitarity. Martin's Ellipse -- 5. Conclusion and Discussions -- Acknowledgments -- References -- Many Faces of D-branes: from Flat Space, via AdS to pp-waves M. Zamaklar -- 1. Introduction -- 2. The Probe Brane Approach -- 2.1. From Flat Space to AdS -- 2.2. From AdS to pp-waves -- 3. The Supergravity Approach -- 4. The Algebraic Approach -- References -- Abstracts and Titles of Reports not Included in the Volume -- Perturbation of Spectra of Operator Matrices -- Boundary Liouville Theory and 2D Quantum Gravity -- Manifestation of TeV Gravity -- The Rational Topology of Gauge Groups and of Spaces of Connections -- String Theory and Matrix Models -- Strong Interactions and Stability in Quasi Localized Gravity -- Strings and Branes in Non-compact Backgrounds -- Two Dimensional Gravity and Liouville Field Theory -- Acknowledgements -- Sponsors -- Statement of intention -- Epilogue.