This is a block course held jointly by the Institute for Mathematics of the Polish Academy of Science (IMPAN) and Berlin Mathematical School (BMS), organized by Tadeusz Januszkiewicz and Michael Joswig.

The course will be held one week in Berlin (Nov 27 - Dec 1, 2017) and one week in Bedlewo (Mar 19 - Mar 23, 2018). There will be lectures and exercises during these two weeks. For the time in-between there will be additional project work. The course is also open for students of TU Berlin, who can get credits equivalent to a regular course "Discrete Geometry III".

It will be assumed that the participants have some basic knowledge in the following subjects: cellular homology and cohomology, polytopes and linear programming, smooth manifolds, group actions.

Topics include the following:

- Topological Toric Varieties, Reflection Groups and Buildings, Symplectic Manifolds, Moment Map
- Lattice Polytopes, Algebraic Toric Varieties, Polytope Combinatorics and f-Vectors, Algorithms
- Abramenko & Brown: Buildings - theory and applications, Springer 2008
- Buchstaber & Panov: Torus actions and their applications in topology and combinatorics, AMS 2002
- Buchstaber & Panov: Toric topology, AMS 2015
- Cox, Little & Schenck: Toric varieties, AMS 2011
- Davis: The geometry and topology of Coxeter groups, Princeton 2008
- Dold: Lectures on algebraic topology, reprint of the 1972 edition, Springer 1995
- Humphreys: Reflection groups and Coxeter groups, Cambridge 1990
- Joswig & Theobald: Polyhedral and algebraic methods in computational geometry, Springer 2013
- Stanley: Combinatorics and commutative algebra, 2nd ed., BirkhĂ¤user 1996
- Warner: Foundations of differentiable manifolds and Lie groups, corrected reprint of the 1971 edition, Springer 1983
- Ziegler: Lectures on polytopes, Springer 1995

Personal application (via email) is mandatory since there is a limit on the number of participants.