Prof. Dr. Jens Franke

Material related to Mihailescu's CIDE primality proof

In a first use of these ideas of Mihailescu, certificates for the Leyland numbers 311063+633110 and 86562929+29298656 were calculated in late 2012. The description of the format, together with a (in my opinion) complete mathematical proof that it is indeed a valid primality proof, is here. While the terminology in fmt-0.1.pdf has been chosen to be disjoint from the terminology of the Mihailescu preprints quoted there, all crucial ideas are Mihailescu's.

Lecture "Rigid analytic geometry I" WS24/25

The lecture has been moved to Tuesdays and Thursdays 18ct-20 in Großer Hörsaal Wegelerstraße 10. Rigid analytic geometry will be introduced in the classical framework of Tate and the Grauert school but additional points will be introduced early, using the definition of van der Put. Knowledge of topology, homological algebra and basic commutative algebra at a level similar to the prerequisites for a basic algebraic geometry course is required.

Lecture "Algebra II" WS24/25

The lecture is scheduled for Mondays 16:00-18:00ct and Thursdays 14:00-16:00ct in Kleiner Hörsaal Wegelerstraße 10. The theory of Dedekind rings will be developed and applied to the theory of algebraic number fields and their local fields. In particular, the ideal group and the ideal class group will be introduced and the finiteness of the ideal class group and Dirichlet's theorem about the structure of the group of units will be shown. A good knowledge of Galois theory and the other Introduction to Algebra topics, as well as some familiarity with Noetherian rings and knowledge of the analysis lectures from the first year will be required. The exercise sheets will be published on this home page:

Seminar "Geometrische Konstruktionen und transzendente Zahlen."

Das Seminar fand erstmalig im Sommersemester 2016 für Studenten des zweiten Semesters statt. Um einen guten Anschluß an die Vorlesung "Lineare Algebra I" sicherzustellen, diente ein von mir selbst verfaßter Text als Grundlage des Seminares. Dieser soll hier weiterhin zur Verfüfung gestellt werden.

Sprechstunden

In der vorlesungsfreien Zeit sind die Sprechstunden nach Vereinbarung.

Vorlesungen "Mathematik für Physiker I-III"

Die Javascript-Programme zu den Anwesenheitsübungen dieser Vorlesungen, die ich zwischen 2008 und 2011 gehalten habe, sind weiterhin online:

Selected Publications