Singularities, D-modules, and Connections to Physics (25w5338)


Uli Walther (Purdue University)

Christine Berkesch (University of Minnesota)

Linquan Ma (Purdue University / IAS)

Claudia Miller (Syracuse University)

Sebastian Olano (University of Toronto)


The Banff International Research Station will host the “Singularities, D-modules, and Connections to Physics” workshop in Banff from September 14 - 19, 2025.

Many phenomena in science, geometry and engineering can be formulated in terms of polynomial equations; for example, $x^2+y^2=1$ describes a circle. Algebraic geometry studies the nature of the solutions to such polynomial equations: one wants to predict locally erratic behavior at ``singularities'', as well as understand global phenomena such as ``cohomology''. Commutative algebra has developed over time as the language in which algebraic geometry is carried out best. However, over the last four decades, it has become clear that it is advantageous to incorporate "D-modules'' into the toolset, a sophisticated version of the principles of calculus.

The purpose of the workshop is to bring together specialists in commutative algebra and singularity theory on one side and physicists on the other, and to foster new research on both sides using the framework of D-modules common to both sides. During the workshop, several existing conjectures will be tested and investigated, but also new ideas will be created and exchanged, spurring new advances in our understanding.

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.