The two big events for US high school students with a project in science have now ended: the winners of the 2011 Siemens Competition in Math, Science & Technology have been announced a few days ago, while last march the 2011 Intel Science Talent Search delivered its winners.
As usual, there are some very high quality projects. Math projects are as popular as ever, which is nice to see: 1st and 6th at Intel, and 2nd and 3rd at Siemens individual category, and 5th and 6th at Siemens team category.
As for competitions open to worldwide high school students, the 2011 Intel ISEF prizes were announced last may (page 30 for Math). Voici le site où les élèves français peuvent s’inscrire : en 2011 deux équipes française on gagné un prix, l’une en math, l’autre en astrophysique, bravo à eux!
Finally, not prizes, but still math at high school level: last summer took place the first International Mathematical Summer School for Students (i.e. high-school to 2nd year of university) in Bremen, Germany. The many hour-long videos of the lectures are now available: go here and click on lectures, they are spread over several days.