Cohomology, Geometry, Explicit Number Theory

The aim of COGENT is to develop, analyze and apply efficient algorithms in three core areas where computer algebra plays an

important role: Cohomology, Geometry and Explicit Number Theory. These will have applications to a broad range of mathematical

problems, and will touch as well upon related topics like cryptography and quantum computing. Such applications of mathematics

are expected to have a wide-ranging impact on economic and societal problems. Recent years have seen a plethora of high-flying

projects and a dazzling variety of applications of methods in computer algebra. One of the emerging challenges is to combine ideas

of different areas of computer algebra, to share expertise between them, and to educate young researchers in theoretical and

practical methods with a focus of transferring knowledge and training software development skills. COGENT provides an innovative

training program to facilitate this and has ambition to stimulate interdisciplinary knowledge exchange between number theorists,

algebraists, geometers, computer scientists and industrial actors facing real-life challenges in symbolic computation in order to

bridge key knowledge gaps. This will address the urgent need for computer assisted investigations of several longstanding

conjectures in mathematics, and EU industry's need for workers with an advanced mathematical and computational skill set. Not only

do we expect to merge the best known tools for these purposes with innovative approaches and ideas to extract previously

inaccessible cohomological information of the underlying arithmetic groups, but we also anticipate finding new hitherto unknown

concepts as we intend to enhance the currently available data pool by a whole order of magnitude. The latter will allow the

researchers to find hidden patterns, with the ambition to form a solid basis for formulating novel cornerstone conjectures, ideally in the spirit of the famous Million-Dollar Birch and Swinnerton-Dyer Conjecture.