The Summer Institutes, three weeks in duration, have been held every decade since the 50s and have been the most influential conferences algebraic geometry has seen.
The forty-fifth Summer Institute will be held at the University of Utah in Salt Lake City, Utah, July 13–July 31, 2015. It will focus on the salient developments in algebraic geometry in the past decade with an added emphasis on expected future directions. See details at summerinst-2015.
The forty-fourth Summer Institute was held at the University of Washington, Seattle, Washington, July 25–August 12, 2005. The goal of this three-week institute was to review major achievements in and around algebraic geometry in the past decade and bring the attendants to the forefront of the relevant subjects.