The COGENT project aims to tackle a range of scientific challenges including:
Obtaining full explicit information on the cohomology of several families of arithmetic groups.
Circumventing the exponential complexity of current computational methods.
Implementing the action of Hecke operators.
Explicitly studying algebraic K-groups and related conjectures, and connecting elements in algebraic K-groups and in homology.
Testing and refining the integral Langlands Program.
Formally verifying intricate proofs and computer-aided computations.
Identifying suitable applications of motivic cohomology and group theory to cryptography.