Spaces of Embeddings: Connections and Applications (19w5232)


(University of Oregon)

(University of Victoria)

(University of Louisiana at Lafayette)

Ismar Volic (Wellesley College)


The Banff International Research Station will host the "Spaces of Embeddings: Connections and Applications" workshop in Banff from October 13, 2019 to October 18, 2019.

Imagine a vibrating string. In mathematics, we would call this a one-dimensional motion (the dimension being the time over which the vibration occurs) of a one-dimensional object (the string) in three dimensions (our spatial universe). Mathematicians are interested in much more general music, where the object, the place in which it is vibrating and even the “time” over which it vibrates can all have many dimensions. Understanding the structure of such objects, which mathematicians call “spaces of embeddings”, is a basic question in the field of topology. Like much rich mathematics, it connects with many other areas in mathematics and beyond. These include the study of all possible ways to combine objects (operads), the study of quantities which can be defined through breaking things apart (topological field theories), and more elementary (but not easy!) subjects including graph theory and knot theory.

In this workshop, we bring together researchers in all of these areas, who constitute a diverse collection of mathematicians (by time in career, gender, and nationality) to contemplate vibrating strings and their impact throughout mathematics and beyond.

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).