We report on the computation of the shift of the Bose-Einstein condensation
temperature for a homogenous weakly interacting Bose gas in leading order in
the diluteness parameter a n^(1/3), where `a' is the scattering length and `n'
is the particle density. The perturbative series, which is afflicted by
infrared divergences, is resummed by means of variational perturbation theory.
Using coefficients through seven loops, we arrive at Delta T_c/T_c = 1.27 +/-
0.11 a n^(1/3), which compares favorably with recent Monte-Carlo data.Comment: Talk presented at the 12th International Laser Physics Workshop,
LPHYS'03 (Hamburg, Germany, August 25-29, 2003