CatsiNCAGe

CatsINCAGe (Categories in Noncommutative Algebraic Geometry) is an NWO Vidi project, led by me. Its goal is to study noncommutative deformations of (singular / stacky) surfaces and higher-dimensional varieties.

More information can also be found on the NWO project page.

Abstract for a general audience

Some phenomena in algebraic geometry can only be explained by enlarging what is understood by a geometric shape. We have to allow noncommutativity, where the multiplication $ab$ is not necessarily equal to $ba$, in order to find the noncommutative (or quantum) shapes that describe certain aspects of reality. Physics is an important source of inspiration for this, where quantum mechanics is inherently noncommutative.

The project proposes to (a) study known noncommutative surfaces from novel viewpoints (b) find new noncommutative shapes in higher dimensions and understand the interactions between ordinary shapes and quantum shapes.

Team members

  • Pieter Belmans (PI)
  • Matthijs Holstege (master student, then PhD student)
  • Yuki Mizuno (postdoc)

Visitors

  • November 2025: Okke van Garderen

Activities

Publications

These publications acknowledge support from the CatsINCAGe grant: