Around Singularities in Poisson Geometry (25w5442)

The Institute for Advanced Study in Mathematics will host the "Around Singularities in Poisson Geometry" workshop in Hangzhou, China from July 6 to July 11, 2025.

Poisson manifolds are an essential tool for the geometric understanding of mechanical systems. One of their core features, is that they permit to model physical constraints, i.e. restrictions on how particles in the system may move in the course of time. This constraint data is geometrically described by foliations, i.e. the decomposition of the space into layers (or leaves), which are not reachable from each other. In this workshop, we will bring together experts from various fields in order to improve our understanding of Poisson (and related) manifolds near singular points, i.e. points where the dimension of nearby leaves is not constant. These points are of uttermost importance, since they are the source of the most complicated and intricate behaviour modeled by Poisson manifolds.

Our focuses will be understanding what types of systems can occur (normal forms), how different similarly looking systems can be (deformation theory) and how we can treat the situations where constraints are more strict in certain points than in others (desingularization). These three questions are intimately intertwined and crucial to understand the behaviour of Poisson manifolds near singular points. Moreover, the same questions naturally occur in several settings (formal, algebraic or smooth) and for many geometric structures (Poisson, Dirac, generalized complex etc.).

In each of the settings and cases, different methods have been successful in treating the singularities. The goal of this workshop is to bring together experts from these various areas in order to share and exchange approaches, techniques and better understand the commonalities and differences between the above settings and structures.

The Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide 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 in Banff 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).