# Prof. Günter M. Ziegler

#### Discrete Geometry Group, Freie Universität Berlin

Günter M. Ziegler has been President of Freie Universität Berlin since July 2018.

He is an internationally respected mathematician who has become known, among other things, for the construction and analysis of complex geometric structures, as well as by the development and the successful use of deeper topological methods for problems stemming from different areas such as for division problems and in optimization.

Günter M. Ziegler was awarded, among others, the Leibniz Prize of the German Research Foundation (DFG) and an Advanced Grant of the European Research Council (ERC). He is a board member of the German Mathematical Society, a board member of the Berlin-Brandenburg Academy of Sciences and Humanities (BBAW), a member of the German National Academy of Sciences (Leopoldina) and the German National Academy of Science and Engineering (acatech), a Fellow of the American Mathematical Society and a member of the Senate of the DFG.

# Research fields

#### Discrete Mathematics / Geometry, Topology and Optimization

- Discrete Geometry, Polytopes
- Combinatorics, Topological Methods
- Discrete Differential Geometry, Polyhedral Surfaces
- Linear and Integer Optimization

My current work in Discrete Geometry focuses on 4-dimensional polytopes, constructions, enumerative properties (such as f-vectors, see [1]), their graphs, as well as inscribability questions, cf. [2]. Our topological investigations deal with the existence of equivariant maps, in order to solve problems in Discrete Geometry, such as the existence of hyperplane mass partitions [3]. The Topological Tverberg Problem is another outstanding problem, where the recent counter-examples — see [4] — raise a lot of new questions.

[1] Philip Brinkmann & Günter M. Ziegler: A flag vector of a 3-sphere that is not the flag vector of a 4-polytope, Preprint, November 2015, 12 pages, http://arxiv.org/abs/1506.08148

[2] Arnau Padrol & Günter M. Ziegler: Six topics on inscribable polytopes, to appear in Alexander I. Bobenko, editor, Advances in Discrete Differential Geometry, Springer, Heidelberg, 2016. http://arxiv.org/abs/1511.03458

[3] Pavle V.~M. Blagojevic, Florian Frick, Albert Haase & Günter M. Ziegler: Topology of the Grünbaum—Hadwiger—Ramos hyperplane mass partition problem, Preprint, 27 pages, February 2015, http://arxiv.org/abs/1502.02975

[4] Pavle V. M. Blagojevic, Florian Frick & Günter M. Ziegler: Counterexamples to the Topological Tverberg Conjecture and other applications of the constraint method, Preprint, 6 pages, Oktober 2015, http://arxiv.org/abs/1510.07984

# Video

#### Prof. Günter M. Ziegler about "Our Mathematical Future“ at the Symposium 2016

(video in German)

More videos from the Hector Fellow Academy on YouTube.