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 Advanced Algebra II (Rigid Analytic and Adic Geometry) WS2627

The lecture is a continuation of my summer 2026 lecture on the same topic. In particular, knowledge of the material about spectral spaces, topological rings, the topological spaces Spa(A) and their structure presheaves introduced in the previous term is necessary. Since the exposition differs from the one in the classical texts you will have to consult me in the first lecture if you did not follow my lecture in the previous term but want to attend the lecture in the current term and have the necessary knowledge to do so.

Knowledge of the machinery of derived functors is also desirable although a brief outline may be given in the lecture.

Topics of the current lecture will be affinoid algebras, cohomology of the structure sheaf and of sheaves of modules as well as relation with other types like classical rigid analytic spaces, ordninary schemes and formal schemes.

A first lecture has been scheduled for Monday October 12 18:00ct in Großer Hörsaal Wegelerstraße 10. We will use this to schedule the other lectures in a way which will hopefully be suitable for everyone. It is therefore highly desirable that you attend this lecture or tell a friend attending it about your scheduling requirements.

Lecture Algebra II WS2627

The lecture takes place on Mondays 16:00-18:00ct and Thursdays 14:00-16:00ct in Zeichensaal. The Hilbert Nullstellensatz as well the Positivstellensätze of Real Algebraic Geometry will be covered, as well as the basic results of algebraic geometric dimension theory. A good knowlegde of the topics covered by the typical "Introduction to Algebra" lecture is required. This includes field extension, Galois theory, modules over rings and the classification of finitely generated modules over principal ideal domains.

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