# MS-15 Matrix techniques in operator algebra theory (Operator Algebra)

### Organizers: Vern Paulsen (University of Waterloo) and Hugo Woerdeman (Drexel University)

This mini-symposium is intended to highlight the interplay between Operator Algebra and Matrix Theory. Clearly, a problem in Operator Theory can first be explored in the finite dimensional setting, and thus becomes a matrix theory problem. But, the interplay goes well beyond this. A recent example is the 1959 Kadison-Singer conjecture, where a reformulation as the Paving conjecture was crucial to its solution. The Paving conjecture is one stated in matrix terms, and a clever use of interlacing families of polynomials led to its solution in 2013. Another intriguing conjecture, due to Crouzeix, found its origin in numerical linear algebra, but its solution will have an impact on Operator Algebra theory. These are just two examples illustrating the interplay. The mini-symposium will provide more examples of this interplay, and may also include the latest developments of the Crouzeix conjecture.

### Speakers

**Radu Balan**, *On a Feichtinger Problem for trace-class operators*

**Lawrence Fialkow**, *The core variety and representing measures in multivariable moment problems*

**John Haas**, *Constructions of optimal like packings with DFT matrices*

**Scott McCullough**, *Matrix convex sets defined by non-commutative polynomials*

**Eric Weber**, *Boundary Representations of Reproducing Kernels in the Hardy Space*

**Hugo Woerdeman**, *Complete spectral sets and numerical range*