Notions of Singularity in Different Characteristics (25w5409)

The Banff International Research Station will host the “Notions of Singularity in Different Characteristics” workshop in Banff from October 5 - 10, 2025.

The geometry of any given variety is shaped by the choice of a coefficient ring for its defining polynomial equations. This ring can be a field of either characteristic zero or positive characteristic. However, it can also merge these two worlds, giving rise to what are known as rings of mixed characteristic. These distinct choices set the stage for fundamentally diverse geometries and subsequent different singularity theories. In recent decades, these seemingly distinct worlds have unveiled deep connections, inspiring collaborative research that promises to drive the main developments in singularity theory.

This workshop is precisely about the connections between the three major singularity theories: MMP-singularities, F-singularities, and BCM-singularities. We aim to bring together experts from these three different yet inherently interconnected fields with the goal of establishing further bridges and collaborations, catching interactions that could build new research lines, and fostering the development of this exciting, nascent field.

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.