What better place for the mountain-climbing summit than on the summit of the mountain. A summit can mean either a meeting between people who are interested in the same subject or the peak of the mountain.
Although originally meant to describe a meeting between the heads of state, summit can be used to describe any gathering of people who care deeply about the same topic. If, for example, you are the captain of your chess club, you might attend the upcoming Chess Club Summit, at which new rules of the tournament will be discussed. Moreover, while summit also means the very top of a mountain, summit can be used metaphorically to mean a variety of heights, such as the summit of a career, an industry, or any kind of major effort.