Monday, June 2, 2014
Technische Universität Berlin
Fakultät II, Institut für Mathematik
Str. des 17. Juni 136
room MA 041
Lecture - 14:15
We show that polytopes with centroid at the origin satisfy the so-called subspace-concentration-condition (scd). This has several consequences:
a) the "U-conjecture" regarding cone-volume measures of polytopes is correct,
b) the scd is a necessary condition for the (in general still open) logarithmic Minkowski problem. This extends partially recent results obtained in the symmetric setting by Böröczky et al. ,
c) the sum of the roots of an Ehrhart polynomial of a lattice polytope is bounded from above by the sum of its Minkowskian successive minima.
The main tool for the proof of the scd is a polytopal version of the Gaussian divergence theorem for a special log-concave function.
Most of the presented results are part of a joint work with Eva Linke , and Matthias Henze&Maria Hernadez Cifre .
 Károly J. Böröczky, Erwin Lutwak, Deane Yang, and Gaoyong Zhang, The logarithmic Minkowski problem, JAMS 26(3), 2013.
 Martin Henk and Eva Linke, Cone volume measures of polytopes, Adv. Math 253, 50–62, 2014. (arXiv:1305.5335).
 Martin Henk, Matthias Henze, and Maria Hernandez Cifre, On extensions of Minkowski's theorem on successive minima, arXiv:1405.4993.
Colloquium - 16:00
Proposition model counting (#SAT) is the problem of counting satisfying assignments (models) to a CNF-formula. It is the canonical #P-hard counting problem and is important due to its applications in Artificial Intelligence. There is a growing body of work that successfully applies so-called structural restrictions to #SAT, i.e., restrictions to graphs and hypergraphs associated to CNF-Formulas to isolate tractable classes of instances. In this talk I will give an introduction into the area and discuss some very recent results with Johann Brault-Baron, Florent Capelli and Arnaud Durand.