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 "Weil I" SS24

The lecture is scheduled for Tuesdays and Fridays 14-16ct in room 0.007 Endenicher Allee 60. As there will be no lectures on April 8 or 9 the first lecture will be on Friday April 12. The proof of the Weil conjectures from Deligne's Weil I paper will be presented. Knowledge of etale cohomology, from the basic definitions to proper base change, is a prerequisite. The other needed results from etale cohomology will be stated mostly without proofs. If sufficient time remains at the end of the lecture, some but certainly not all of these omitted proofs may be given.

Lecture "Real algebraic geometry 2"

The lecture is scheduled for Tuesdays 8:00-10:00 and Fridays 10:00-12:00 and the exercises for Mondays 14-16ct, all in room N0.007 Endenicher Allee 60. As there are no lectures or exercises in Endenicher Allee 60 on April 8 or 9, the first lecture will be on Friday April 12. Sheaf cohomology of the real spectrum will be discussed. In particular, it will be shown that the cohomology of locally constant sheaves has the properties expexted by the comparison with algebraic topology. While some basic familiarity with algebraic topology makes it easier to follow the lecture and understand the motivation for these considerations, it is not a prerequisite. However, a knowledge of real closed fields, of the real spectrum and the general theory of spectral spaces is necessary. Previous knowledge of the machinery of sheaf cohomology as a derived functor of the functor of global sections will simplify things, but a crash course on this topic can be given in the exercises if needed.

Seminar "Geometrische Konstruktionen und transzendente Zahlen."

Das Seminar fand 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.


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