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Prof. Dr. Stefan Geschke
Hausdorff Center for Mathematics
Universität Bonn
Villa Maria
Endenicher Allee 62
53115 Bonn
Raum: 2.003
Telefon: ++ (49)(228) 73-62221
e-mail:
stefan.geschke@hcm.uni-bonn.de
Research
My research is centered around applications of combinatorial set theory and forcing to geometry, topology, algebra and analysis. However, I am also interested in (finite) combinatorics and complexity.Teaching
Summer 2010
In the summer semester we will have a seminar on descriptive set theory (with Bernhard Irrgang and Philipp Schlicht) that takes place on Tuesdays at 10:15 in Room 0.007 (LWK).The seminar is at least particially devoted to the socalled G_0-dichotomy that was found by Kechris, Solecki, and Todorcevic. We will use Benjamin Miller's notes on his Paris lectures, which can be found here (scroll down to "Forceless, ineffective, powerless proofs").
There will be a lecture (in German) on mathematical logic. Mathematical logic studies the notion of a formal proof using mathematical methods. We will consider some propositional calculus, first order languages and their semantics (meaning), formal proofs in first order logic, the completeness theorem that states that if something follows from a set of axioms, then it is formally provable from this set of axioms and Gödel's incompleteness theorems.
Lecture notes (in German) are here .
Winter 2009/10
This winter semester I am teaching a course in model theory. The lectures take place on Tuesdays and Thursdays from 12 to 2 in Room LWK 006. Office hours are after the class or by appointment, i.e., whenever I am available in my office.Model theory studies mathematical theories from an abstract point of view. After proving the basic theorems, we will consider applications to algebra and the connections between finite model theory and algorithmic complexity. The necessary background in logic can be provided during the lecture.
The exercises that came up in the lecture notes until Thursday are due on Thursday, one week later.
The lecture notes (with exercises) are here.
Here are some additional lecture notes that might be useful for some parts of the course: