Ten years ago, in February 2011, I joined the group of Günter M. Ziegler at Freie Universität Berlin. Now, ten years later, I will show you some of the problems in Geometric and Topological Combinatorics that intrigued us, some of which we managed to solve, and sketch some of the crucial ideas, methods, and the tools we had to develop in order to answer them. 

We will see how 

-- work on the Bárány-Larman conjecture on colored point sets in the plane   gave birth to the Optimal colored Tverberg theorem, 

-- the constraint method collected all classical Tverberg type results under one roof    and opened a door towards counter-examples to the topological Tverberg conjecture.

Furthermore, we will illustrate how the search for convex partitions of a polygon into pieces of equal area and equal perimeter forced us to 

-- study the topology of the classical configuration spaces, 

-- construct equivariant cellular models for them, 

-- prove a new version of an equivariant Goresky-MacPherson formula for complements of arrangements, 

-- revisit a classical vanishing theorem of Frederick Cohen, and explain why these answers are related to the existence of highly regular embeddings and periodic billiard trajectories.

Finally, we will talk about 

-- equi-partitions of convex bodies by affine hyperplanes, and 

-- greedy convex partitions of many measures.

These results are joint work with, in chronological order, Günter M. Ziegler, Benjamin Matschke, Florian Frick, Albert Haase, Nevena Palić, Günter Rote, and Johanna K. Steinmeyer.