Number Theory via Algebra, Geometry and Experimentation

The research group carries out fundamental research in number theory and arithmetic geometry and it explores relations with cryptography. A particular feature is the development and the use of computer algebra tools. Experimental data often lead to unexpected observations and give the necessary insights for a deeper theoretical understanding.

Two domains of expertise

Antonella Perucca’s research group focuses on Kummer theory for fields and for algebraic groups, investigating also related problems like Artin’s conjecture on primitive roots or the arithmetic of abelian varieties.

The research portfolio of Gabor Wiese’s group includes theoretic and experimental work on modular and automorphic forms, Galois representations, the inverse Galois problem, elliptic curves and abelian varieties, as well as relations to cryptography.