Michael Hartz

Title: Quotients of multipliers in complete Pick spaces.

Abstract: Every function in the Hardy space on the unit disc is a quotient of two functions in $H^\infty$. I will talk about a generalization of this result, which says that every function in a complete Pick space is a quotient of two multipliers. Moreover, I will explain applications to the Corona problem and to extremal functions.This is joint work with Alexandru Aleman, John McCarthy and Stefan Richter.

Volker Runde (University of Alberta, Edmonton)

Title: Dual Banach algebras: a survey

Martin Michajlow

Title: Hilbert Sudokus

Abstract: Given a sudoku, i.e. a N^2xN^2-matrix filled with numbers 1,...,N^2, we can replace every number by the projection onto the span of the standard basis vector of C^{N^2} with the respective index. Distinct projections of the same row, column or N-block will then be orthogonal. Furthermore, the projections in each row, column or N-Block sum up to the identity. More generally, we consider Hilbert sudokus, i.e. square matrices whose entries are projections on subspaces of an arbitrary Hilbert space s.t. the above orthogonalilty-/sum conditions hold for rows and columns. One main question is: Given a partially filled Hilbert sudoku - can we always fill it up to a complete Hilbert sudoku? In our Bachelor's thesis, we looked at different types of Hilbert sudokus and discuss a similiarity relation for Hilbert sudokus.

Miguel Pluma

Title: Bi-free probability theory

Abstract: In 2013, Voiculescu introduced bi-free probability in order to study simultaneously left and right representations of algebras. This gives rise to a notion of bi-free independence and bi-free convolution. In this talk we will give an exposition of the basic concepts of the theory, and explain how can we use bi-freenes to define a bi-free convolution for complactly suported proability measures in the plane R^2.

Sebastian Langendörfer

Title: to be announced.