## Geometry Seminar - Abstracts

### Talk

Tuesday 18 October 2022, 16:00 - 17:00 in HG02.032

**Mikhail Isachenkov** (UvA)

*Double-scaled SYK and quantum homogeneous spaces*

### Abstract

In this talk I will discuss an application of quantum homogeneous spaces to the quest of understanding quantum gravity. Sachdev-Ye-Kitaev (SYK) model, a simple toy model remarkably capturing many features of quantum gravity in two-dimensional AdS space, got a lot of attention in the physics literature of the last several years. I will review some basics of quantum homogeneous spaces and of the SYK model and then explain how a certain (double-scaled) limit of the SYK model is exactly solvable and governed by quantum group symmetry. This provides an explicit insight into the bulk algebra of observables for quantum gravity in this low-dimensional setup. If time permits, I will discuss physical implications of this result and interesting future mathematical research directions.

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