Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

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Andreas Paffenholz Technische Universität Darmstadt Permutation Polytopes DMV Tagung 2011 - Köln, 19. - 22. September A permutation polytope is the convex hull of the permutation matrices of a subgroup of Sn. These polytopes are a special class of 0/1-polytopes. A well-known example is the Birkhoff polytope of all doubly-stochastic matrices. This polytope is defined by the full symmetric group Sn. Much less is known for general groups. I will introduce basic properties of permutation polytopes, characterize faces, and discuss connections between the group and the polytope. The main focus of my presentation will be on recent results for permutation polytopes defined by cyclic groups. Their face structure depends on the cycle structure of the generator, and I will describe exponential families of facets. The class of cyclic permutation polytopes contains the class of marginal polytopes. (This is joint work with Barbara Baumeister, Christian Haase, and Benjamin Nill.) Raman Sanyal University of California, Berkeley Deciding Polyhedrality of Spectrahedra Spectrahedra are to semidefinite programming what polyhedra are to linear programming. Spectrahedra form a rich class of convex bodies with many of the favorable properties of polyhedra. It is a theoretical interesting and practically relevant question to decide when a spectrahedron is a polyhedron. In this talk I will discuss an algorithm for doing that which requires a good understanding of the geometry of spectrahedra and some linear algebra. Only knowledge of the latter will be assumed. (This is joint work with Avinash Bhardwaj and Philipp Rostalski.) Margarita Spirova Technische Universität Chemnitz Translative Coverings of Convex Bodies We discuss arrangements of proper translates of a convex body K in R n sufficient to cover this body. We call such an arrangement a t-covering (a covering by translates) of K. First we investigate relations between t-coverings of the whole of K and t-coverings of only its boundary. Refining the notion of tcovering in several ways, we discuss, particularly for centrally symmetric convex bodies and n = 2, how such coverings relate to the classical theorems of ¸Ti¸teica and Miquel as well as to notions like Voronoi regions. We also compare t-coverings with coverings in the spirit of Hadwiger, using smaller homothetical copies of K instead of proper translates. Finally we give upper bounds on the cardinalities of t-coverings. (The talk is based on a joint work with Marek Lassak and Horst Martini.) 142
Jonathan Spreer Universität Stuttgart Slicings of Combinatorial 3-Manifolds DMV Tagung 2011 - Köln, 19. - 22. September We investigate slicings of combinatorial manifolds as properly embedded co-dimension 1 submanifolds. Focus is given to the case of dimension 3, where slicings are (discrete) normal surfaces. The talk will be about three particular questions: 1. Is there a connection between the number of quadrilaterals of a slicing and its genus? 2. Which weakly neighborly polyhedral maps can be embedded into combinatorial 3-manifolds? 3. How can we use slicings to construct combinatorial 3-manifolds with a transitive automorphism group? Gennadiy Averkov Otto-von-Guericke-Universität Magdeburg Compact Polynomial Representations of Special Semialgebraic Sets Bosse, Grötschel and Henk conjectured that every d-dimensional polytope in R d can be determined by a system of d nonstrict polynomial inequalities. Recently this conjecture has been confirmed in a joint work with Ludwig Bröcker. We also present further results on compact polynomial descriptions of special classes of semialgebraic sets. Christian Wagner Eidgenössische Technische Hochschule Zürich Maximal Lattice-Free Polyhedra in Mixed-Integer Cutting Plane Theory A polyhedron with non-empty interior is maximal lattice-free if it is inclusion-maximal with respect to the property of not containing integer points in its interior. In this talk, I will explain the relation between maximal lattice-free polyhedra and cutting plane generation in mixed-integer linear optimization. Günter M. Ziegler Freie Universität Berlin Polytopes with Few Degrees of Freedom 143
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Ken Ono Emroy University, Atlanta A
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Frank Kutzschebauch Universität Be
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Ulrich Derenthal Ludwig-Maximilians
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Eleutherius Symeonidis Katholische
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Martino, Maurizio, 15 Maruhn, Jan H
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Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

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