# Noncommutative Shapes: A conference in honor of Michel Van den Bergh's 60th birthday

University of Antwerp

September 14–18, 2020

## Halfway event

On **20 September 2021** we organised an online halfway event.

- 10:00–10:45
- Quantisation in monoidal categories and quantum operads
- Yuri Manin, Max Planck Institute for Mathematics
- The most standard description of symmetries of a mathematical structure produces a group. However, when the definition of this structure is motivated by physics, or information theory, etc., the respective symmetry objects might become more sophisticated: quasigroups, loops, quantum groups, ... In this talk I introduce and study quantum symmetries of very general categorical structures:
*operads*. Its initial motivation were spaces of probability distributions on finite sets. - 10:45–...
- meeting in Gather.town

- 15:00–15:45
- Simultaneous categorical resolutions (video)
- Alexander Kuznetsov, Steklov Mathematical Institute
- It is a classical fact, that for a family of surfaces over a smooth curve with smooth general fiber, if the special fiber has only rational double points as singularities, then after a possible finite base change, one can resolve the singularities of the total space and the special fiber by a common blowup. I will talk about a categorical version of this construction that surprisingly also works in higher dimensions and, if time permits, about its applications.
- 16:00–16:45
- From geometric quantization to noncommutative algebraic geometry (video, notes)
- Marco Gualtieri, University of Toronto
- The usual homogeneous coordinate rings studied in algebraic geometry may be obtained from quantization of the integer multiples of a symplectic structure, via the choice of a complex polarization. I will explain how this framework may be deformed, making contact with noncommutative algebraic geometry. The main tool will be the deformation of the complex polarization to a generalized complex polarization. This is joint work with Francis Bischoff (arXiv:2108.01658).