Abstract

This is a colloquium style talk intended for a general audience (including students). The speaker has previously co-organised several events on the topic (see his website).

Abstract: As a theory and programme, IUT is as important as other main directions in number theory. Unlike the latter, IUT already contains the proof of its main theorems. IUT includes 20 new concepts, many of which are of interest on their own. Applications of IUT ​offer​ proofs of​ the​ ​celebrated​ conjectures​, and more conjectures are to be proved. ​ IUT ’s viewpoints drastically extend the range of methods in modern number theory. IUT addresses such fundamental aspects as to which extent the multiplication and add​i​ti​on​ cannot be separated from one another.​ T​he rigidity aspects of number fields and hyperbolic considerations​ play a major role. ​ I will discuss some of these aspects.