Date: thursday, 17.12.2020,10:00
Speaker: prof. Günter M. Ziegler
Title: Semi-algebraic sets of integer points
Abstract: We look at sets of integer points in the plane, and discuss possible definitions of when such a set is "complicated": One interesting criterion is whether it is the set of integer solutions to some system of polynomial equations and inequalities. Let's together work out lots of examples, and on the way let's try to develop criteria and proof techniques...
The examples that motivated our study come from polytope theory: Many question of the type "What is the possible pairs of
(number of vertices, number of facets) for 4-dimensional polytopes?" have been asked, many of them with simple and complete answers, but in other cases the answer looks complicated. Our main result says: In some cases it IS complicated!
(Joint work with Hannah Sjöberg and Moritz Firsching).
Video
Speaker
Günter M. Ziegler started his studies at LMU Munich. He received his PhD in Mathematics at M.I.T. in 1987. Since 1995 he has been Professor of Mathematics at TU Berlin, since 2011 at FU Berlin, where since 2018 he serves as the President. He is a member of the Berlin-Brandenburg Academy of Sciences and Humanities, of the German National Academy Leopoldina, and of the German Academy of Engineering Sciences acatech. From 2006 to 2008 Ziegler was president of the German Mathematical Society (DMV). He has received numerous awards, including a DFG Leibniz prize, an ERC Advanced Grant, the Communicator Award, and the Berlin Science Prize of the Governing Mayor of Berlin.
In mathematics Ziegler deals with aspects of discrete geometry, especially the theory of polyhedra, with algebraic and topological methods in combinatorics, and with problems of optimization. He is committed to promoting a diverse and lively public image of mathematics. He was an initiator of the Year of Mathematics in 2008 and currently continues his promotional work, i.a. directing the DMV’s Media Bureau of Mathematics. Ziegler has published numerous essays and books, among which Das Buch der Beweise (Proofs from the BOOK) was co-authored by Martin Aigner and translated into 14 languages. The book is dedicated to the mathematician Paul Erdõs and contains 32 theorems related to a broad range of mathematical fields.
