Titel: "Unconditional Class Group Computation and Applications"

Abstract: Class groups of number fields have been studied since the time of Gauss, and in modern times have been used in applications such as integer factorization and public-key cryptography. Computing class groups and a system of fundamental units is a challenging problem for classical computers, for which no polynomial time algorithm is currently known. In addition, the fastest-known algorithm for computing these invariants has the shortcoming that the output is only correct under the assumption of the generalized Riemann hypothesis. This is fine for some cryptographic applications, but in computational number theory applications such as tabulating class groups for testing unproved conjectures and solving Diophantine equations, unconditional results are typically required. In this talk, I will discuss some of the applications where unconditional results are required, as well as recent results and on-going work on computing class groups and fundamental units unconditionally.

Der Vortrag findet statt am
Mittwoch, den 30.11.2022 um 17.15 - 18.45 Uhr im Raum W01 0-006
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