Constructions and obstructions for extremal polytopes

In the fall of 2001, I was finishing my computer science undergrad studies and Martin Skutella suggested that I take the course " Linear optimization " , a course offered to beginning math grad students and taught by Prof. Günter Ziegler. Following his advice, my fellow student Roman Wagner and I took the course, and failed badly. We lacked the necessary linear algebra and so the teaching assistant had a hard time understanding our " solutions " to the exercises. However, I liked the little that I understood and after the next semester break, which I spent with a linear algebra book, I restarted the ADM-lecture-cycle, this time with " Graph and network algorithms " and more computer scientists: Moritz Hilger and Oliver Wirjadi joined the team. We had a great time spending afternoons at the " beach " solving the exercises. But the best of all was our tutor Vanessa Kääb: In three months from now we will get married and in two more months we will have our first child – ain't that great! The teaching assistant was Frank Lutz who offered me the job as a tutor for the linear optimization course – not a bad setup as I did not have to do the exercises again. He also encouraged me to attend the " Discrete Geometry " course in the 2004 summer term, also taught by Günter. In the following semester break I started working on my diploma thesis under Günter's supervision. I got a desk in the workgroup and I met lots of people to talk about math, including Jakob Uszkoreit, someone who can listen to more math than I'm able to tell. I did a decent job in my thesis and Günter offered me a PhD position, first on his Leibnitz grant and later in the research training group " Methods for Discrete Structures ". That was in October 2005. Now it is May 2008 and the end of the journey. I had a wonderful time. Günter taught me how to do research, how to " write stuff up, " and how to give talks. I enjoyed the frequent morning coffees with him in the " Molotov Depot " (it opens up at 7:20 am, weekends a little later) and I appreciated the fact that he had always time for yet another (stupid) question. I benefited not only from what he is doing in …