The ICMP 2006 will start in Rio de Janeiro tomorrow. It is a traditional meeting which began in Moscow in 1972 and is held each three years. During the conference the Poincare Medal is awarded and this year I heard it will go to Ludvig Faddeev. There are several other satellite meetings going on or ending now, like the Workshop on Pure Spinors organized by Nathan Berkovits in Sao Paulo.
yesterday and today it is happening the Young Researchers Symposium, a meeting promoted by the ICMP to attract younger people and where a Field medalist gives a talk. This year this seminar will be delivered by E. Witten.
The symposium started yesterday with a very nice talk by Faddeev on quantum groups. As he explained quantum groups are neither quantum nor groups. They are deformations of the phase space and the group structure. He started with spin chains using the XXX Heisenberg model along the lines of his well known review. He went on to the XXZ model and its connection with deformed algebras, Yang-Baxter, braid groups, and so on. During the talk he gave many historical accounts related to the subject and distributed a copy of a new preprint "History and Perspectives of Quantum Groups". Very interesting.
Berkovits gave a talk about string amplitudes and pure spinors. Too technical for an audience of mathematicians and physicists from several areas. Anyway it is too hard to explain his goal without going into the technical details. At the end he said that it is possible to extend his pure spinor formalism to 11 dimensions and maybe get more information on M theory. The talk of David Ruelle went the other way. Almost no equations. Too difficult to understand many of his statements and the line of reasoning. Maybe for people working in the area it was easier. He talked about dynamical systems, chaos, turbulence and nonequilibrium statistical mechanics. He told that the solar system is not stable and some guys in the audience seemed very worried about that! Many historical notes were told mainly about Poincare. Like the butterfly effect that had in fact begin with a seagull and not with a butterfly.
There were other sessions where younger people presented their work. The day ended with a reception and Brazilian music, chorinho and samba. Very good.