xviii The Quantum Structure of Space and Time
3. Singularities
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3.3.
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3.3.
3.3.Rapporteur talk: Singularities. by Gary W. Gibbons ........
3.1.1 Introduction ..........................
3.1.2 Singularity Theorems .....................
3.1.3 Cosmic Censorship ......................3.1.5 Boundary Conditions in Cosmology .............
3.1.6 Higher dimensional resolutions ................3.1.8 Maldacena’s Conjecture ....................3.1.4 Classical Boundary Conditions and Stability ........3.1.7 Singularities at the end of Hawking Evaporation ......
Discussion ................................
Prepared Comments ..........................3.3.1 Gary Horowitz: Singularities in String Theory .......
Discussion ................................3.5.1 Eva Silverstein: Singularities: Closed String Tachyons andDiscussion ................................
Prepared Comments ..........................
3.7.1 Thibault Damour: Cosmological Singularities and El ...
Discussion ................................
Prepared Comments ..........................
3.9.1 Abhay Ashtekar: Singularities: quantum nature of the bigbang in loop quantum gravity ................
Discussion ................................
Prepared Comments ..........................Singular it ies ..........................
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874. Mathematical Structures 91
4.1 Rapporteur talk: Mathematical Structures. by Robbert Dijkgraaf. 91
4.1.1 Abstract ............................ 914.1.2 Quantum Theory and Mathematics ............. 91
4.1.3 The quantum geometry of string theory ........... 97
4.1.4 Non-perturbative string theory and branes ......... 107
4.1.5 D-branes ............................ 112
4.1.6 The Role of Mathematics ................... 1164.2 Discussion ................................ 119
4.3 Prepared Comments .......................... 1234.3.1 Renata Kallosh: Stabilization of moduli in string theory. 123
4.3.
and their statistics ....................... 127
4.3.
standing the landscape .................... 132
4.4 Discussion ................................ 140Dieter Lust: A short remark on flux and D-brane vacuaMichael Douglas: Mathematics and String Theory: Under-