To be given later 9.4.2019
Gabor Analysis is an important branch of time-frequency analysis. It describes signals or distributions through their series expansions, using time-frequency shifted copies of some {\it Gabor Atom} or window function. A good choice (for the abstract discussion) is a Gaussian atom because it has optimal decay in both the time and the frequency domain. Very often, Gabor analysis is reduced to the question, whether for a given atom a lattice of the form $\Lambda = a Z\times b Z$ allows to generate a Gabor frame resp. allows to expand any $L^2(R^d)$-function $f$ in a Gabor series, with square summable coefficients.

However, Gabor Analysis has a much wider scope. It allows to characterize a family of function spaces, the
so-called modulation spaces, some of which are useful for certain PDEs, while others, like the Banach Gelfand
triple $(S_0,L_2,S_0')$ are useful for Abstract Harmonic Analysis and Engineering Applications, from
mobile communication to classical system theory.

Although we know - after almost 40 years of research in this area - a lot about Gabor Analysis, and many
fundamental facts have been obtained in the last decades, there are still many practical and theoretical
questions unsolved. In our presentation we plan to address some of these questions.

One of the main topics will be the application of the general idea of ``Conceptual Harmonic Analysis''
to the domain of Gabor Analysis. Among other we may ask: What is the best fit of a Gabor atom and
a corresponding multi-dimensional lattice, given one of the two ingredients. How well can Anti-Wick
operators be approximated by Gabor multipliers, or who can one discretize a given operator, starting
from the Kohn-Nirenberg or Weyl calculus or the spreading definition, just to mention a few topics.