MAT773 Topics in convex geometry (HS22)

Lecturer: Dr. Johannes Schmitt
Time and Place: Friday, 10:15 - 12:00, Room Y27H25
Further information can be found in the UZH Course Catalogue.


A polytope is the convex hull of finitely many points in real d- dimensional space. Examples include triangles in the plane, the five platonic solids in three-dimensional space or the so-called permutohedron in d dimensions. Polytopes and other convex objects like cones and polyhedra appear in many areas of mathematics. And even though their definition is simple, it is possible to ask many interesting questions about them, such as:

In the seminar, we will start with introducing the basic notions and results of convex geometry. Based on this foundation, we then have a look at more specialized questions such as the ones described above (in particular concerning their combinatorics and computational approaches). The precise questions can depend on the interests of the participants.

List of talks

Here you find a preliminary list of topics for the talks.
Here is the preliminary assignment of topics and dates:

Topic Date Student
Basic definitions 23.09 Fadil Osmani
Further examples and main theorems 30.09 Argetim Beluli
Proofs of main theorems 07.10 Cagri Camoglu
Farkas lemmas and further basic results 14.10 Yonatan Christoph
Faces of polytopes 21.10 Jenny Pletscher
Polarity and the representation theorem for polytopes 28.10 Blerim Alimehaj
Platonic solids 04.11 Anna Glapka
Linear programming and related concepts 11.11 Weronika Wawrzyniak
More on graphs and polytopes 18.11 Philine Schönenberger
Polyhedral complexes and Schlegel diagrams 25.11 Chiara Romano
Review and exercise session 02.12 Chen Ping
The simplex algorithm 09.12 Özgür Özsu
Further algorithms and practical implementations 16.12 Delia Schüpbach
Ehrhart theory 23.12 Mattia Bottoni

Requirement for passing

In order to pass the seminar and get credit points, you have to:

There is no grade for the seminar, so it is simply pass/fail.

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