Symmetries occur everywhere in nature, and this is where mathematics and physics meet. Remarkably, symmetry also appears to play a major role in the world of numbers. In the 1970s, the mathematician Robert Langlands formulated a coherent set of unproven conjectures suggesting that the behaviour of prime numbers is largely determined by hidden symmetries. These conjectures are now known as the Langlands programme. Langlands' ideas are highly revolutionary and visionary, suggesting unprecedentedly deep connections between geometry and number theory. The progress already achieved has already led to stunning applications in number theory. The most famous example is the proof of Fermat's so-called Last Theorem, by British mathematician Andrew Wiles. Recently, a geometric version of the Langland programme was formulated, which builds new bridges between mathematics and physics. The Langland programme is so challenging and broad that many mathematicians worldwide are working on it. The Netherlands has a unique combination of expertise in the Langland programme, making us ideally placed to make high-quality contributions to these important international research efforts.
Connecting character
The question primarily gives rise to very basic research and builds bridges between mathematics and physics. Prime numbers play an important role in cryptography, for example in encrypting data during online banking.
