#
Monday Lecture and Colloquium

**Monday, June 2, 2014**

Technische Universität Berlin

Fakultät II, Institut für Mathematik

Str. des 17. Juni 136

10623 Berlin

room MA 041

** Lecture - 14:15**

### Martin Henk -
Universität Magdeburg

### Polytopes, successive minima,
and the Gaussian divergence theorem

*Abstract:*

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. [1],

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 [2],
and Matthias Henze&Maria Hernadez Cifre [3].

[1] Károly J. Böröczky, Erwin Lutwak, Deane Yang, and Gaoyong Zhang, *The logarithmic Minkowski problem*,
JAMS 26(3), 2013.

[2] Martin Henk and Eva Linke, *Cone volume measures of polytopes*,
Adv. Math
253, 50–62, 2014. (arXiv:1305.5335).

[3] Martin Henk, Matthias Henze, and Maria Hernandez Cifre, *On extensions of
Minkowski's theorem on successive minima*,
arXiv:1405.4993.

** Colloquium - 16:00**

### Stefan Mengel-
Ecole Polytechnique Paris

### Tractable Propositional Model Counting by Structural Restrictions

*Abstract:*

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.

Letzte Aktualisierung:
22.05.2014