The Schedule

Abstract: Suppose you have 10 independent investment opportunities, all with success probability of forty percent. If they fail, you get nothing. If they succeed, you triple your money. You want to maximize the probability that you get 9,000 euros or more and you have 7,500 euros to invest. How do you spread the money? Endre Csoka conjectured that you should always spread your money in equal portions, no matter what. This is related to ancient problems in probability and more recent problems in extremal combinatorics. I will present some results on this conjecture. Joint work with Ludolf Meester and Christos Pelekis.

Abstract: In the paradigm of noncommutative geometry, C*-algebras play the role of generalized topological spaces, often encoding interesting dynamics. In this talk, I will introduce a class of C*-algebras constructed from a special class of polynomials in non-commuting variables and I will discuss some of their properties, including how and why we can interpret them both as algebras of functions on algebraic subsets of noncommutative spheres and as algebras of functions on the boundary of a quantum tree.

Abstract: Sampled Gabor phase retrieval - the problem of recovering a square-integrable function from the magnitude of its Gabor transform sampled on a lattice - is a fundamental problem in signal processing, with important applications in areas such as imaging and audio processing. Recently, it has been shown that, in general, square-integrable functions can not be recovered from such samples. Indeed, for any lattice, one can construct functions which do not agree up to global phase but whose Gabor transform magnitudes sampled on the lattice agree.  As a consequence, a priori knowledge about the functions is necessary to restore uniqueness in sampled Gabor phase retrieval, and the search for proper subspaces enjoying uniqueness has attracted recent attention. We contribute to a better understanding of the fundamental limits of uniqueness in sampled Gabor phase retrieval, which in turn can guide future research towards restoring it, showing that the set of counterexamples is dense in the space of square-integrable functions.

Abstract: I will discuss a new invariant property of topological dynamical systems called Bohr chaoticity. This property means that  the system is not orthogonal to any non-trivial weight sequence.

We establish Bohr chaoticity property for a large class of algebraic dynamical systems -- the so-called principal actions. Tha talk is based on a joint work with Aihua Fan and Klaus Schmidt.