In the 20th century two remarkable mathematical areas were born. Firstly, John von Neumann introduced his eponymous algebras of quantum observables and constructed a solid theory behind quantum mechanics. These von Neumann algebras became a standard tool in many branches of mathematics and mathematical physics. Secondly, in a parallel development the theory of commutative harmonic analysis was broadly established through singular integrals and Calderón-Zygmund theory which had broad impact on differential geometry, PDE’s and functional analysis. Although both areas are well-established nowadays, there is a substantial gap between the vast theory of commutative harmonic analysis and the yet underdeveloped theory of harmonic analysis on von Neumann algebras (‘non-commutative measure spaces’). This is particularly unsatisfactory because tools from harmonic analysis have recently made their way in the classification of von Neumann algebras beyond Connes’ Fields medal awarded work on amenable factors. Moreover, several new von Neumann algebras have emerged from quantum symmetries and their structure is largely shrouded in mystery. Non-commutative harmonic analysis would shed considerable light on these quantum symmetries. This Vidi proposal bridges this gap by developing the theory of non-commutative harmonic analysis in three projects: (A) Harmonic analysis on Lie groups and an attack at Connes’ rigidity conjecture (B) Operator algebras of compact quantum groups (C) Quantum Markov semi-groups It is quite remarkable that these three aspects can be connected in the first place and exactly these connections potentially give powerful tools in general von Neumann algebra theory and their classification/distinction beyond the fundamental work of Connes. If successful, this proposal has a lasting impact on general operator theory and neighbouring areas as geometric group theory, free probability, quantum information theory and non-commutative geometry.

Delft is a city of thinking and making. TU Delft’s technical profile lends itself entirely to contributing to the major societal challenges. The wicked problems of today demand scientific research and technological innovation. However, societal factors determine the applications. TU Delft educates students as socially engaged engineers who collaborate broadly. Including the technical talents at all levels of education! Central question is how to integrally involve the entire education chain at MBO, HBO and WO levels, and opening up a local space n Delft-West that focuses mainly on issues around health, sustainability and liveable neighbourhoods.

Dutch residents experience a diminishing sense of control over their lives and living environment. Besides, their trust in government institutions has decreased. At the same time, society faces multiple crises (housing, liveability, climate change, energy transition). Citizen collectives may be part of the solution, while they help communities to respond, resist and adapt to changes in their direct living environments. ECCO will develop models, methods, digital and non-digital tools that stimulate equal partnerships between governments and citizen collectives. These will provide them with practicable knowledge and skills, and show the value, credibility, and long-term impact of citizen collectives to governments.

The TU Delft Digital Competence Centre (DCC) is an on-campus initiative, which has been supported by N.W.O. funding, to help researchers make research data FAIR, improve research software, and apply computing practices to increase the efficiency of the research process. The DCC is also an initiative of the Open Science Programme at TU Delft designed to benefit researchers at all levels.

RenoDat accelerates energy renovations by addressing data governance, ownership, privacy, and harmonization gaps in the implementation of Renovation Passports. By uniting social, technical, pedagogic, and economic expertise, the project develops a reliable data infrastructure to improve renovation quality, streamline processes, and help meet critical climate and societal well-being goals in the Netherlands.