Fachvortrag in englischer Sprache

Number fields, i.e. finite extensions of the rationals play a prominent role both in the historical development of algebra [and number theory] as well as in current applications such as cryptography and coding theory. 

In this talk I will focus on multiplicative problems in number fields. Typical examples contain Diophantine equations such as Pell's equation or norm equations. Closely related is the problem on non-unique factorization in the ring of [algebraic) integers that gave rise to the theory of ideals and the ideal class group. The core problems in working with essentially all multiplicative problems are twofold: to linearize one needs logarithms, hence introduces numerical problems, and, a lot of solutions are neces­sarily huge, too huge to represent them in the usual way. 1 will explain some of the techniques used to deal with both problems, borrowing ideas from classical numerical and extending them to the algebraic setting. 

Applications discussed will include traditional ones [Pell, norm equation] as well as representation theory, Galois cohomology and, via transfer to global fields, coding theory.  

Speaker: Prof. Dr. Claus Fieker, TU Kaiserslautern