This grant will support workshops, a research school and a conference on Trisections and their Generalizations, to be held at the Centre International de Recontres Mathematiques (CIRM) in Marseille, France, during the weeks July 7-11, October 6-10, Oct 13-17 and November 17-21, 2025. CIRM is a well-known international mathematics conference center, and the Principal Investigator of this grant, Professor David T. Gay of the University of Georgia, has been selected as CIRM's "Jean Morlet Chair" for the period July-December 2025 for the purpose of organizing a semester's worth of international activities at CIRM related to his research program in topology. This grant will support the travel and accommodation expenses of US-based mathematicians to participate in some of these events. The research topic, in topology, concerns new methods to study the intrinsic large-scale shapes of a wide range of spaces called manifolds: Manifolds are spaces which at the small scale, look just like the ordinary space around us, perhaps with more dimensions, but which can be tangled up with themselves in strange ways on the large scale. Interesting manifolds arise, for example, when thinking about all the possible configurations of a mechanical system, such as a robot or a human limb, when thinking about all the possible states of a large language model under training in an artificial intelligence system, or when understanding how a protein folds. Trisections, and generalizations of these, give