Algebraic Graph Theory and Applications (25w5432)

The Banff International Research Station will host the “Algebraic Graph Theory and Applications” workshop in Banff from October 12 - 17, 2025.

When two objects interact, mathematicians model this interaction by simply putting two dots on a piece of paper and connecting them. This suspiciously simple procedure can generate a complex network of dots and lines, and the bigger the network, the more its connections only are sufficient to answer several deep question about the real world scenario it models. Be it for social networks, biological systems or quantum particles, beautiful mathematics can arise by simply examining the way the dots combine.

In this workshop we focus on two types of problems. The first is finding optimal structures in networks (such as big clusters or special partitions), which is usually a hard task even for powerful computers. These problems are quite ubiquitous and appear naturally in various fields of applied math --- from industry to biology. An adequate mathematical modelling of the problem can lead to efficient methods to analyse and solve the problems, and we intend to focus our workshop to understand the interaction between two old and well studied methods. The second problem regards the interaction of quantum particles in the very contemporary application of quantum computing and quantum communication. Here, quantum particles replace the transistors in a circuit, and the way they are combined determines how the algorithms and protocols will work in this new setting.

Common to both problems are the connections between the combinatorics of the dots and traditional areas of mathematics such as algebra, geometry and optimization.

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’s Advanced Education and Technology.