Postdoctoral Research Award 2019
Jeffrey Meier, a postdoctoral research and teaching associate in the Department of Mathematics, addresses the field of low-dimensional topology. “Low-dimensional” generally refers to dimensions less than five, and topology research often probes the structures of spaces by looking at embedded objects in those spaces. A major low-dimensional topology problem is to understand three-dimensional spaces, four-dimensional spaces and the interactions between them. Meier’s research has focused on the interplay between three- and four-dimensional topology with a special attention to knot theory in those dimensions. Knotting phenomena occur when looking at embedded surfaces in four-dimensional space. Such surfaces may be thought of as surfaces swept out in space-time by a knot that is moving around in space over a period of time. Very little is known about four-dimensional knot theory, but he has made several significant contributions to the subject since beginning his postdoctoral position.