Dr Reem Yassawi

Research

Topological dynamics, Automata sequences, Substitutional dynamics, Ergodic theory, Cellular automata, Aperiodic order

Interests

After completing her PhD in Mathematics at McGill University, Reem was a tenured Associate Professor (Senior Lecturer) at Trent University, Canada, until 2014. During part of this time, she was a Van Vleck fellow at Wesleyan University (in the United States). She then moved to France, worked for the CNRS at Université Claude Bernard Lyon 1, and was a visiting researcher at IRIF, Université Paris-Cité. In 2019 she accepted a position as a Lecturer in Applied Mathematics at the Open University, before joining QMUL as a Senior Lecturer in 2022.

Her research is at the active interface between topological and symbolic dynamical systems, number theory (particularly numeration systems and formal power series), and theoretical computer science (particularly automata theory). Finite state automata generate important sequences, which are of interest both in dynamics and in number theory. In dynamics, these sequences lead to low-complexity dynamical systems such as substitution shifts, odometers and adic systems, around which a vibrant theory has developed. In number theory, these sequences include prime-power projections of well-known combinatorial sequences, such as the Catalan numbers and Apéry numbers.

The underlying automata give a numeration-based description of important dynamical phenomena, such as how far the associated dynamical systems are from being equicontinuous. She uses this information to compute topological invariants of these systems, such as the symmetry group and the Ellis semigroup.
In number theory, she uses automata to describe the congruence and algebraic structure of these sequences in a p-adic setting. This is done via Christol’s and Furstenberg’s beautiful theorems, which characterise these sequences as roots of algebraic equations, and diagonals of rational functions. This part of her research makes essential use of computer experiments to identify subtle patterns that would be not otherwise be discernible; this leads to conjectures and eventually theorems.

She also studies cellular automata as dynamical systems, in particular, their (shift)-invariant measures and their topological factors.

Publications of specific relevance to the Centre for Complex Systems

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Grants