As before, the purpose of the workshop was to gather a group of experts in the recent developments of the different formulations of the Einstein equations and their applications to numerical relativity. In particular, these workshops have as their main focus both the sharing of ideas as well as the direct comparison of the results of actual numerical simulations, in the hope of learning what makes one formulation better suited for numerical work than others. The workshops have a very open and relaxed format, extended over a two week period, to allow time for informal discussions and work sessions (and I mean really work sitting in front of the laptop). Of course, eating mexican food and drinking tequila are also a part of it, as our boat trip in the canals of Xochimilco can show.
There where over 25 talks this time, and it would take too much space to mention them all here (but have a look at the web page http://www.appleswithapples.org, where most of the talks can be found as PS or PDF files). In my own personal opinion, the highlights included Jeff Winicour's introductory talk describing the aims of the Apples with Apples meetings, Denis Pollney's talk on test-suites for numerical relativity, Carsten Gundlach's talk on well posed BSSN, Scott Hawleys' talk on constrained evolution, Hisaaki Shinkai and Gen Yoneda's talk on constraint propagation analysis, and Manuel Tiglio's talk on dynamical control of constraint violation. Of special interest where a series of talks on well posed boundary condition, from Jeff Winicour and Bela Szilagyi's work with the Abigel code, to Mihaela Chirvasa's talk on absorbing boundary conditions, and of course Olivier Sarbach's talk on constraint preserving boundary conditions. Results from the conformal field equation approach were also presented by Sascha Husa and Christiane Lechner. A particular highlight was the participation of Nina Jansen and her passionate discussion of tests performed on different systems following the paper coming out of the first Apples with Apples meeting ( gr-qc/0305023). Nina's participation helped us focus on which of those tests are really useful, and what direction should be taken to suggest new tests. At the end of the meeting, an agreement was reached for the several groups represented to test their codes following the test-suite suggested in gr-qc/0305023.
If anything, the meeting helped us realize that the numerical community is finally addressing the issues of well posedness of evolution systems, gauge conditions, and boundary conditions head on. Mysteries remain as to why some well posed formulations perform well numerically and other do not, but significant progress has certainly been made.
And now, to the future. Oscar Reula has graciously offered to host
``Apples with Apples III'' in Cordoba, Argentina. Final dates are
still not clear, but the meeting will probably take place in late 2004
or early 2005. Winter in the U.S. and Europe, but summer down below
the equator. See you in Argentina!