Some 20 years ago, matrix models such as the Ishibashi-Kawai-Kitazawa-Tsuchiya (IKKT) model and the Banks-Fischler-Shenker-Susskind (BFSS) model were proposed as constructive definitions of string- and M- theory, respectively. These are maximally supersymmetric multi-matrix models of Yang-Mills type, which generalize the more conventional random matrix models which played an important role in many contexts such as two-dimensional gravity, combinatorics and quantum chaos. These models share many of the rich aspects of string theory, and provide a non-perturbative and constructive framework. However these and similar models are also of interest from a broader perspective.

The aim of this 1-week workshop is to assess the status of these and related models, to strengthen the scientific contacts of the groups working in this context, and to initiate new ideas and collaborations.Topics that will be addressed include:

- numerical results from simulations of IKKT, BFSS and related models, and mathematical models for their description and interpretation,
- The relation with gravity and string theory,
- noncommutative geometry in a finite-dimensional setting,
- finite matrix geometries with Lorentzian signature,
- covariant quantum spaces and symmetries

**Organizers:**

Denjoe o’Connor, Jun Nishimura, Harold Steinacker, and Asato Tsuchiya