Topology in Dimension 4.5 (22w5065)


(Princeton University)

David Gay (University of Georgia)

(Rice University)

(Stanford University)


The Banff International Research Station will host the "Topology in Dimension 4.5" workshop in Banff from October 30 to November 4, 2022.

Mathematicians often study knotted circles in three-dimensional space as a tool to model physical phenomena such as DNA, molecules, or strings in physics. We are naturally drawn to three-dimensional problems because they seemingly resemble our three-dimensional world -- however, most real-word problems have an implicit fourth dimension: time. This motivates the analogous study of knotted surfaces in four-dimensional spaces. Just as four-dimensional techniques have been critical in our understanding of three-dimensional behaviors, we can make use of five-dimensional techniques to understand knotted surfaces. Two surfaces in a four-dimensional space can be compared by connecting them by a family of surfaces, or more generally, a three-dimensional object embedded in a five-dimensional space. Thus, this area can be thought of as 4.5-dimensional topology: studying four-dimensional mathematics through five-dimensional techniques.

In this workshop, we bring mathematicians at various stages in their careers together to better understand recent work in 4.5 dimensions. In particular, we hope to bridge the gap between a large swath of older results, which are important but completely understood only by a small segment of the community, and current very recent work that has the advantage of modern technology. By combining the perspectives of many mathematicians in this area, we hope to promote new collaborations, raise awareness of cutting-edge research, and open up a literature-dense subfield to young mathematicians.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).