From analysis to arithmetic via the Langlands program The grand vision of Langlands has revealed connections between various fields within mathematics. This proposal focuses on a particular, conjectural link between on the one hand number theory and on the other hand symmetry groups and analysis. A proof of this single conjecture will provide more insight to at least three fields - a contribution to the unity of pure mathematics.

Post-quantum signatures are digital signatures that can be run on classical computers but with the promise of being secure even for adversaries with a quantum computer. The quantum computer being close to reality has urged the world to start standardization processes for stadardizing post-quantum signatures. This project aims at aiding this process by providing new cryptanalytic methods and techniques for scrutinizing the proposed designs and improving the confidence in the security of the chosen standards. It will help evaluate both the security of the algorithms and the security of their physical implementations and propose appropriate countermeasures.

In our everyday life our brain is constantly bombarded with sensory information. Since only a small amount of this information is directly relevant for our behaviour, we have to select the relevant and ignore irrelevant incoming information. The combination of new neuroimaging techniques holds the promise of advancing our understanding of how the stream of incoming information is routed through the human brain. This project entails an integrated analysis of data from multiple neuroimaging techniques. This is in particular needed in the quest to understand the role of sub-cortical structures and the role of layer specific computations. I will integrate data from simultaneously recorded EEG and (high and normal resolution) fMRI with information about anatomical connections between brain regions obtained from diffusion tensor imaging (DTI). By recording these different types of data during, and in relation to a task in which subjects have to attend to information in one sensory modality, while ignoring information in another sensory modality, I try to answer the following questions: (I) Which brain networks provide top-down control and through which mechanisms do they influence the information flow in earlier sensory brain regions? (II) How is the layer specific information flow between early and later sensory regions controlled by top-down control? (III) Are there direct anatomical connections between cortical control networks, or are they mediated through other, possibly sub-cortical, brain regions? (IV) Do the same attentional networks modulate information processing in different sensory modalities, or are there sensory specific networks? This project will therefore address both anatomical and functional aspects of how routing of information in the working brain is controlled. It therefore will provide knowledge that is essential for our understanding when attentional control fails, like for instance in individuals with ADHD who have pervasive difficulties in maintaining focussed attention, and ignoring irrelevant information.

Moraliteit is de lijm die menselijke samenlevingen bij elkaar houdt. Recente ontwikkelingen als #MeToo, Zwarte Piet en JustStopOil laten zien dat onze morele waarden in de loop van de tijd kunnen veranderen en dat moraliteit tussen individuen kan verschillen. In deze studie willen we begrijpen hoe ons brein morele waarden berekent. We ontwikkelen een computationeel model dat nabootst hoe onze hersenen morele besluitvorming implementeren. Vervolgens testen we dit model bij gezonde vrijwilligers, gebruiken we het om te bestuderen hoe ons brein morele waarden berekent, en om te bestuderen hoe morele besluitvorming verkeerd kan uitpakken bij mensen met psychopathie.