My collaborators and I have initiated studies of confinement and deconfinement in Yang-Mills theory with the exceptional center-less gauge group G(2) as well as of Sp(N) gauge theories. Michele Pepe and I have observed cascadic decays of strings connecting external charges in higher-dimensional representations. Together with Ferdinando Gliozzi, we have also performed the first precise numerical calculation of the width of Yang-Mills strings, in quantitative agreement with a systematic low-energy effective string theory.
The sign problem hinders progress in understanding many strongly coupled quantum systems. Mattias Troyer and I have shown that some sign problems are NP-hard, and thus practically impossible to solve. This means that no generally applicable method to solve all sign problems can exist. Still, the meron-cluster algorithm, and the more recently developed nested cluster algorithm can be used to either completely solve or at least substantially alleviate very severe sign problems.