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.

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.
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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.
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).