Knot Theory Informed by Random Models and Experimental Data (24w5217)

The Banff International Research Station will host the “Knot Theory Informed by Random Models and Experimental Data” workshop in Banff from March 31 - April 5, 2024.

Over its history, knot theory has yielded many questions and conjectures that drove the development not only of this field of study, but also of several other fields of mathematics. However even taken together, these questions and conjectures do not fully describe the wealth of surprising intrinsic properties of knots and links, of underlying graphs related to link projections, of the 3-manifolds that are link complements, and of the simplicial complexes that correspond to decompositions of such manifolds. One of way to generate new questions is through a probabilistic viewpoint and experimental data. Several new random models of knots and 3-manifolds have appeared recently, and probabilistic, experimental, and computer-aided studies of knots have been increasingly common. Such approaches allow to establish geometric and topological properties of knots beyond well-studied families, and often suggest a perspective encompassing less-known cases. This approach also often points at connections with the fields of probability and combinatorics. Therefore the main topic of the workshop will be probabilistic and experimental study of geometric and topological properties of links, and the interplay of such properties with probability and combinatorics. We will also look at other new directions that this mixing of research fields leads to.

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), and Alberta Technology and Innovation.