[Facets-of-complexity] Invitation to Monday's Lecture & Colloquium Nov.15 !

["I.Brunke" <i.brunke@fu-berlin.de>]

Dear all,

next Monday's Lecture and Colloquium will take place online via Zoom on November 15.

Please find link to Zoom here:
https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09
No password is required.

You all are cordially invited!

Location:

Online via Zoom.

Monday's Lecture: Tim Netzer (Uni Innsbruck)

Time: Monday, November 15 - 14:15 h

Title: Free Semialgebraic Geometry and Quantum Information Theory

Abstract:

Quantum information theory studies how quantum information can be represented, stored, processed and sent. On the mathematical side this often involves the study of tensor products and decompositions of positive matrices, as well as positive maps. These are also natural objects in free semialgebraic geometry, where positivity of non-commutative objects are studied from a geometric viewpoint. In this talk I will give an introduction to some important concepts in both areas, and demonstrate how results and methods from either field can be successfully employed in the other. This is joint ongoing work between the group of Gemma De las Cuevas and my own research group in Innsbruck.


Break

Monday's Colloquium: Stefan Kuhlmann (Technische Universität Berlin)

Time: Monday, November 15 - 16:00 h s.t.

Title: Lattice width of lattice-free polyhedra and height of Hilbert bases

Abstract:

A polyhedron defined by an integral valued constraint matrix and an integral valued right-hand side is lattice-free if it does not contain an element of the integer lattice. In this talk, we present a link between the lattice-freeness of polyhedra, the diameter of finite abelian groups and the height of Hilbert bases. As a result, we will be able to prove novel upper bounds on the lattice width of lattice-free pyramids if a conjecture regarding the height of Hilbert bases holds. Further, we improve existing lattice width bounds of lattice-free simplices. All our bounds are independent of the dimension and solely depend on the maximal minors of the constraint matrix.
The second part of the talk is devoted to a study of the above-mentioned conjecture. We completely characterize the Hilbert basis of a pointed polyhedral cone when all the maximal minors of the constraint matrix are bounded by two in absolute value. This can be interpreted as an extension of a well-known result which states that the Hilbert basis elements lie on the extreme rays if the constraint matrix is unimodular, i.e., all maximal minors are bounded by one in absolute value.
This is joint work with Martin Henk and Robert Weismantel.

You all are cordially invited!

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