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

University of Antwerp

September 12–16, 2022

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).