Contents -- The International Solvay Institutes -- 23rd Solvay Conference on Physics -- Opening Session -- 1 . History -- 1.1 Rapporteur talk: Solvay Redivivus. by Peter Galison -- 1.1.1 Three Miracles -- 1.1.2 SOLVAY -1: Einstein-Lorentz, Einstein-Poincare -- 1.1.3 Ignoramus, Ignorabimus at Solvays-5 and Solvay- -- 1.1.4 Solvay Redivivus -- Bibliography -- 1.2 Discussion -- 2 . Quantum Mechanics -- 2.1 Rapporteur talk: Generalizing Quantum Mechanics, by James B . Hartle -- 2.1.1 Abstract -- 2.1.2 Introduction -- 2.1.3 Quantum Mechanics Today -- 2.1.4 Spacetime and Quantum Theory -- 2.1.5 The Quantum Mechanics of Closed Systems -- 2.1.6 Quantum Theory in 3+- Form -- 2.1.7 Generalized Quantum Theory -- 2.1.8 A Quantum Theory of Spacetime Geometry -- 2.1.9 Beyond Spacetime -- 2.1.10 Emergence/Excess Baggage -- 2.1.11 Emergence of Signature -- 2.1.12 Beyond Quantum Theory -- 2.1.13 Conclusivri -- Acknowledgments -- Bibliography -- 2.2 Discussion -- 3 . Singularities -- 3.1 Rapporteur talk: Singularities. by Gary W . Gibbons -- 3.1.1 Introduction -- 3.1.2 Singularity Theorems -- 3.1.2.1 The Strong Energy Condition -- 3.1.3 Cosmic Censorship -- 3.1.4 Classical Boundary Conditions and Stability -- 3.1.5 Boundary Conditions in Cosmology -- 3.1.5.1 Instability of Flat space -- 3.1.5.2 Hofava- Witten solution from Heterotic M-Theory -- 3.1.5.3 Exact static supersymmetric solution -- 3.1.5.4 Time-dependent solutions -- 3.1.5.5 Local Static Form: Chamblin-Reall picture -- 3.1.6 Higher dimensional resolutions -- 3.1.7 Singularities at the end of Hawking Evaporation -- 3.1.8 Maldacena's Conjecture -- Bibliography -- 3.2 Discussion -- 3.3 Prepared Comments -- 3.3.1 Gary Horowitz: Singularities in String Theory -- Acknowledgment: -- Bibliography -- 3.4 Discussion -- 3.5 Prepared Comments.

3.5.1 Eva Silverstein: Singularities: Closed String Tachyons and Singularities -- 3.5.1.1 Singularities and Winding Modes -- 3.5.1.2 Discussion and Zoology -- Acknowledgements -- Bibliography -- 3.6 Discussion -- 3.7 Prepared Comments -- 3.7.1 Thibault Damour: Cosmological Singularities and E10 -- Conclusion -- Acknowledgments: -- Bibliography -- 3.8 Discussion -- 3.9 Prepared Comments -- 3.9.1 Abhay Ashtekar: Singularities: quantum nature of the big bang in loop quantum gravity -- 3.9.1.1 Introduction -- 3.9.1.2 Novel features of loop quantum cosmology -- 3.9.1.3 A Simple model -- Bibliography -- 3.10 Discussion -- 4 . Mathematical Structures -- 4.1 Rapporteur talk: Mathematical Structures. by Robbert Dijkgraaf -- 4.1.1 Abstract -- 4.1.2 Quantum Theory and Mathematics -- 4.1.2.1 String theory and mathematics -- 4.1.2.2 What is quantum geometry? -- 4.1.3 The quantum geometry of string theory -- 4.1.3.1 Quantum mechanics and point particles -- 4.1.3.2 Conformal field theory and strings -- 4.1.3.3 Functorial description -- 4.1.3.4 Stringy geometry and T-dualaty -- 4.1.3.5 Topological string theory -- 4.1.4 Non-perturbative string theory and branes -- 4.1.4.1 Summing over string topologies -- 4.1.4.2 Topological strings and quantum crystals -- 4.1.4.3 U-dualities -- 4.1.5 D-branes -- 4.1.5.1 Branes and matrices -- 4.1.5.2 D-branes and K-theory -- 4.1.5.3 Example: the index theorem -- 4.1.5.4 Non-perturbative dualities -- 4.1.6 The Role of Mathematics -- Acknowledgement -- Bibliography -- 4.2 Discussion -- 4.3 Prepared Comments -- 4.3.1 Renata Kallosh: Stabilization of moduli in string theory -- Bibliography -- 4.3.2 Dieter Lust: A short remark on flux and D-brane vacua and their statistics -- Bibliogruphy -- 4.3.3 Michael Douglas: Mathematics and String Theory: Understanding the landscape -- 4.3.3.1 Historical analogies -- 4.3.3.2 The chemical analogy.

4.3.3.3 Two-dimensional CFT -- 4.3.3.4 Topological open strings and derived categories -- 4.3.3.5 Computational complexity theory -- 4.3.3.6 Conclusions -- Acknowledgments -- Bibliography -- 4.4 Discussion -- 4.5 Prepared Comments -- 4.5.1 Nikita Nekrasov: On string theory applications in condensed matter physics -- 4.5.1.1 Electrons o n a lattice, with noisy electric field -- 4.5.1.2 Dimers and three dimensional partitions -- 4.5.1.3 Topological strings and S-duality -- 4.5.1.4 Discussion -- Bibliography -- 4.5.2 Shing-Tung Yau: Mathematical Structures: Geometry of Six-Dimensional String -- Bibliography -- 4.6 Discussion -- 4.7 Prepared Comments -- 4.7.1 Hermann Nicolai: E10 and K(E10): prospects and challenges -- Acknowledgments: -- Bibliography -- 4.7.2 Michael Atiyah: Beyond string theory? -- Bibliography -- 4.8 Discussion -- 5 . Emergent Spacetime -- 5.1 Rapporteur talk: Emergent Spacetime. by Nathan Seiberg -- 5.1.1 Introduction -- 5.1.2 Ambiguous space -- 5.1.2.1 Ambiguous space in classical string theory -- 5.1.2.2 Ambiguous space an quantum string theory -- 5.1.2.3 Comments about locality -- 5.1.3 Non-standard theories without gravity -- 5.1.4 Derived general covariance -- 5.1.5 Examples of emergent space -- 5.1.5.1 Emergent space without gravity -- 5.1.5.2 Emergent space with gravity: matrix model of 2d gravity -- 5.1.5.3 Emergent space with gravity: Gauge/Gravity duality -- 5.1.5.4 Emergent space with gravity: linear dilaton backgrounds -- 5.1.5.5 Emergent space an the BFSS matrix model -- 5.1.6 Emergent time -- 5.1.7 Conclusions and speculations -- Bibliography -- 5.2 Discussion -- 5.3 Prepared Comments -- 5.3.1 Tom Banks: The Holographic Approach to Quantum Gravity -- 5.3.1.1 The variables of quantum gravity -- 5.3.1.2 Holographic cosmology -- 5.3.1.3 de Sitter space -- Bibliography.

5.3.2 Igor Klebanov: Confinement, Chiral Symmetry Breaking and String Theory -- Acknolwedgements: -- Bibliography -- 5.3.3 Juan Maldacena: Comments on emergent space-time -- Bibliography -- 5.3.4 Alexander Polyakov: Beyond space-time -- 5.3.4.1 Gauge /String correspondence -- 5.3.4.2 de Sitter Space and Dyson's instability -- 5.3.4.3 Descent to four dimensions -- 5.3.4.4 Screening of the cosmological constant -- Bibliography -- 5.4 Discussion -- 6 . Cosmology -- 6.1 Rapporteur talk: The cosmological constant and the string land- scape, by Joseph Polchinski -- 6.1.1 The cosmological constant -- 6.1.1.1 Faxed-A theories -- 6.1.1.2 Adjustable-A theories -- 6.1.2 The string landscape -- 6.1.2.1 Constructions -- 6.1.2.2 Phenomenological issues -- 6.1.2.3 What is string theory? -- 6.1.3 Conclusions -- Acknowledgments: -- Bibliography -- 6.2 Discussion -- 6.3 Prepared Comments -- 6.3.1 Steven Weinberg -- 6.3.2 Renata Kallosh: Inflationary models as a test of string theory -- Bibliography -- 6.3.3 Andrei Linde: Eternal inflation in stringy landscape and the anthropic principle -- Bibliographg -- 6.4 Discussion -- 6.4.1 Paul J . Steinhardt: A modest proposal for solving the cos- mological constant problem -- Bibliography -- 6.5 Discussion -- 7 . Closing remarks. by David Gross -- Answer by Marc Henneaux.