Creative Research Medal 2021

David T. Gay, professor of mathematics, has made breakthroughs in topology through the development of “trisections of 4-manifolds,” a novel way of representing and studying the topology and geometry of 4-dimensional spaces. In dimensions 3 and 4, manifolds are the models for our universe (considering space as 3-dimensional, and space-time as 4-dimensional). In recent decades, the study of manifolds has been one of the most active fields of research in mathematics, building historical interactions between mathematics and physics. In 2016 Gay, in collaboration with Robion Kirby, introduced the notion of a trisection of a 4-manifold and proved the foundational existence and uniqueness results, an effective way of constructing and studying all smooth 4-manifolds. This transformative finding led to a series of papers by Gay and others, introducing new concepts and approaching longstanding problems in new ways.