Monday, April 20, 2015
Technische Universität Berlin
Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin
room MA 041
Lecture - 14:15
Abstract:
In the first part of this talk we survey results
about representations of planar graphs as contact graphs of
internally disjoint geometric objects in two and three dimensions.
In the course we point to some open problems in the area.
The second part is about characterizations of graphs admitting a
straight line triangle representation (SLTR). It is shown that
if it exists an SLTR can be computed as the solution of a
linear system of equations. As a byproduct we reprove a
characterization of stretchable contact systems of pseudosegments.
(joint work with Nieke Aerts)
Colloquium - 16:00
Abstract:
A Gabor frame is the set of all time-frequency translates of a complex function and is a fundamental tool in utilizing communications channels with wide
applications in time-frequency analysis and signal processing. When the domain of the function is a finite cyclic group of order N , then the Gabor frame
forms a design on the complex sphere in N dimensions; when the N2 unit vectors that constitute this Gabor frame are pairwise equiangular then the Gabor
frame forms a spherical 2-design, and in addition, it has minimal coherence, an
ideal property in terms of compressive sensing (whether such an equiangular set
exists is also known as the SIC-POVM existence problem, which is open since
1999).
In this talk, we will deal with the question of existence of a Gabor frame such
that every N vectors form a basis (the discrete analogue of the HRT conjecture);
such a frame is called a full spark Gabor frame. This question was posed by
Lawrence, Pfander and Walnut in 2005 and was answered in the affirmative by
the speaker in 2013 unconditionally. This result has applications in operator
identication, operator sampling, and compressive sensing.