VI Mexican School on Gravitation and Mathematical Physics

Alejandro Corichi, National Autonomous University of Mexico (UNAM)
The Division of Gravitation and Mathematical Physics of the Mexican Physical Society organized its VI school, November 21-28th, near Playa del Carmen, in the Mexican Riviera. These schools take place every other year and are focused on a special topic. This year the school was named ``Approaches to Quantum Gravity''. The setting was specially welcoming, being an all inclusive resort that allowed the participants to fully enjoy the amenities of the hotel (and the beach), while focusing on the scientific program of the school.

The idea of the organizers was to have top class representatives from at least three approaches to quantum gravity deliver lectures for graduate students and non-experts. The overall opinion is that the goal was achieved and the school was rather successful. There were about 100 participant in total, with about half of them students from both Mexico and abroad.

The speakers were chosen to cover the two main approaches to quantum gravity, namely string theory and loop quantum gravity, as well as other approaches and related subjects. On the stringy side the courses were delivered by R. Kallosh and A. Peet, together with plenary talks by A. Guijosa and E. Caceres. On the loop side, the invited speakers for the courses were A. Ashtekar and C. Rovelli. Ashtekar had to cancel at the last minute so he was replaced by the author, M. Bojowald and L. Smolin. There were also plenary talks by M. Bojowald, A. Perez and L. Smolin, on loop related issues. On the `other approaches category' there was a course on time-space non-commutativity by A.P. Balachandran and a course on selected classical topics by P. Chrusciel. The list of distinguished plenary speakers also included J. Barrow, A. Linde and R. Wald, who spoke on variable fundamental constants, inflationary cosmology and QFT on curved space, respectively.

String Theory was very well represented by R. Kallosh and A. Peet who delivered set of lectures on ``De Sitter vacua and the String Landscape'' (Kallosh) and ``Black Holes in String Theory" (Peet). They gave a very though overview of recent research results and the cutting edge research on the subject. R. Kallosh first motivated the need for a theoretical explanation for the value of the positive cosmological constant observed. She then described a recent model she has been working on that involves choosing certain vacua from the string landscape, that is, from the very large set of possible vacua for the theory. Kallosh also described recent work on black holes and the search for the fundamental degrees of freedom of the theory. The set of lectures delivered by A. Peet were particularly illuminating. She described the basics of string theory, with some clarifications that answer some common misconceptions outsiders sometimes have. She described in detail the D-brane approach to BH entropy, AdS-CFT correspondence and the newly discovered fuzzball solutions. She ended the set of lectures with an inspiring challenge for the participants of the school.

On the loop side of the school, the author introduced the basics of loop quantum geometry, Bojowald applied the formalism to cosmological solutions, arriving at the so called loop quantum cosmology, and Smolin described the challenges and possible resolutions for the dynamics of the theory. C. Rovelli gave a very nice set of lectures on the white-board, motivating and building loop quantum gravity from scratch. The courses were complemented by lectures on black holes, spin foams and phenomenological aspects of loop quantum cosmology.

The day before the school ended, R. Wald moderated a discussion panel where the theme was Strings vs. Loops. The discussion was polite but lively, and questions like ``what are fundamental degrees of freedom in string theory?" and ``how does one make sense of spatially smeared operators in LQG?" were discussed. The general agreement was that the discussion was very civil, but there was not enough time to discuss some more controversial issues.

The school ended by an inspiring lecture by Lee Smolin who discussed various possible experimental indications for the need of a quantum theory of gravity and a new length scale as a fundamental entity. For more information on the program of the School see

Jorge Pullin 2005-03-10