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Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: o-minimal structures SemesterWiSe 2025 / 26 Lecturer Denis-Charles Cisinski Type of course (Veranstaltungsart) Seminar Contents o-minimal structures have been introduced in logic but have found many applications in geometry: in real algebraic geometry (i.e. the geometry of sets defined by inequalities between polynomial equations with real coefficients), but also in complex geometry as well as in number theory. It is also considered as way to realize Grothendieck's program of a "tame topology", that is a theory whose objects are topological in nature but that avoids pathologies that are far away from any geometric intuitions. In particular the notion of dimension of polytopes is a natural concept in the context of o-minimal structures whereas it is has many pathologies in classical topology. In a nutshell, an o-minimal structure is a first order logic whose formulas define reasonable subsets of suitable affine spaces. The first goal of the seminar will be to learn basics on o-minimal structures: how to construct the easiest example (essentially, real algebraic geometry) and how to construct non-trivial instances of o-minimal structures (adding the exponential map, for instance), which basic concepts can be defined (notion of constructibility, dimension, existence of pullbacks, etc). In the second half of the Wintersemester, we will survey nice applications in geometry and in homotopy theory, depending on the interests of the participants. Recommended previous knowledge This seminar does not require any advanced knowledge beyond basic topology and algebra. Time/Date Wednesday 10-12h, organizational meeting on October 1st at 2.15 pm in room M104 Location PHY 5.0.21 Course homepage https://cisinski.app.uni-regensburg.de/lehre.html (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BV, BSem, MV, MSem ECTS 4,5 |