Prof. Martin Grötschel (Zuse Institute, Technische Universität, and Matheon Berlin, Germany)
Polyhedra: Their Description and Use

April 28, 2015


Polyhedra have fascinated humans since they have begun recognizing and understanding geometric objects. Together with numbers, plane curves and figures, polyhedra stand at the beginning of mathematics, but they have also played particular roles in the arts, sciences and even in religion and mysticism. After centuries of investigation, is there still anything interesting to study? Are polyhedra of any practical use? In my lecture, I will briefly survey some wonderful results on polyhedra and a few simple looking problems, open for a long period of time. I will particularly focus on various techniques to describe polyhedra and discuss their usefulness. I will explain several algorithms to solve ?polyhedral problems? that arise in various applications and I will mention which of these methods work theoretically and which in practice. I will conclude my lecture with a survey of large-scale real-world applications (such as telecommunication, logistics, public transport, energy,?), investigated in my research group, where linear programming and polyhedral results play important roles for the solution.

Short bio

Martin Grötschel holds the Chair for Information Technology at the Institute of Mathematics of Technische Universitat Berlin and is the President of the Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB). He served ZIB as Vice President from 1991 to September 2012. From November 2002 till May 2008 he chaired the DFG Research Center MATHEON "Mathematics for key technologies", a scientific institution involving about 200 applied mathematicians from the three large Berlin universities and two research institutes. Martin Grötschel's main areas of scientific interest are discrete mathematics, optimization and operations research. His special focus in the last 15 years is on the design of theoretically and practically efficient algorithms for hard combinatorial optimization problems. He has deep interest in real applications. He has been working with scientists from other disciplines and, in particular, with engineers and economists from industry to mathematically model challenging problems of their domain of expertise. He has contributed to application areas such as telecommunication, chip design and very large scale integration, production planning and flexible manufacturing, logistics, planning of public transportation systems and energy. He has also been leading several projects on electronic information and communication. Before coming to Berlin in 1991, Grötschel was Full Professor of Applied Mathematics at Augsburg University (1982 - 1991) and held several visiting positions abroad. He received a Master's Degree in Mathematics from Bochum University (1973), a Doctoral Degree (1977) and a Habilitation (1981) from Bonn University. Grötschel's scientific achievements were honored with several distinctions including the John von Neumann Theory Prize (2006), the EURO Gold Medal (2004), the Leibniz Prize (1995), the Dantzig Prize (1991), the Beckurts Prize (1990), and the Fulkerson Prize (1982). He is a member of the Berlin-Brandenburg Academy of Sciences and Humanities (BBAW), of Acatech the "German Academy of Sciences and Engineering", and of the German Academy of Sciences Leopoldina. He is also a Foreign Member of the National Academy of Engineering, USA and a SIAM Fellow. He received Honorary Doctorates from the University of Karlsruhe (2006), Magdeburg (2008), Augsburg (2011) and the Vietnamese Academy of Science and Technology (2007). Grötschel has written and edited 15 books and published more than 150 scientific papers. He has been on the editorial boards of 16 scientific journals. Martin Grötschel has served the academic community in many administrative functions. In particular, after having served as a member-at-large of the Executive Committee of the International Mathematical Union (IMU) from 1999 to 2006, Martin Grötschel was elected IMU's Secretary for the period 2007 to 2014. Moreover, Martin Grötschel has been the Chairman of the Executive Board of the Einstein Foundation Berlin since June 2011.