A researcher working in frame theory will naturally be led to consider matrices (the Gram matrix, the analysis operator and the synthesis operator), and many problems in frame theory have a re-casting in operator theory. The most celebrated example of this is the Kadison-Singer problem. By now, there are many mathematicians familiar with the basics of the two areas, and there is a fruitful collaboration. Less obvious is the relationship between frame theory and maps between operator algebras. Very recent work in this area by Han, Larson, Lu, and Lu indicate that this may be a relationship that is ripe for exploiting. The goal of this concentration week is to bring together researchers in these two fields so that they may learn from one another and build networks of potential collaborators. The following introductory lecture series will be given:

• Frame theory, Ole Christensen
• Maps on operator algebras, Vern Paulsen
• Bridging the gap between frame theory and maps on operator algebras, Deguang Han

This concentration week will also lead into a separate conference on the following weekend celebrating the 70th birthday of David Larson.

This concentration week is designed to bring together two groups of experts: those specializing in complex and harmonic analysis an those working in spectral theory of differential operators and mathematical physics. The main goals are to study new relationships and to widen participation in this area in the United States. Introductory series of lectures are planned to acquaint non-experts with these topics with the expectation that some the participants in the larger Workshop will be attracted to this program and inject new ideas into the field.