# Dr Reem Yassawi

PhD, Mcgill UniversitySenior Lecturer in Mathematical Sciences

Director of Graduate Studies

School of Mathematical Sciences

Queen Mary University of London

Queen Mary University of London

## 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

### 2024

Yassawi R and Berthé V (2024).

01-01-2024

**Meyer sets, pisot numbers, and self-similarity in symbolic dynamical systems.**41-73.01-01-2024

### 2023

Yassawi R (2023).

04-09-2023

**Torsion-free S-adic shifts and their spectrum.**, Editors: Lemanczyk M.*Studia Mathematica*,*Instytut Matematyczny*04-09-2023

Yassawi R, Fuhrmann G and Kellendonk J (2023).

18-08-2023

**Tame or Wild Toeplitz Shifts.***Ergodic Theory and Dynamical Systems*,*Cambridge University Press*18-08-2023

### 2022

Allouche J-P, Shallit J and Yassawi R (2022).

03-03-2022

**How to prove that a sequence is not automatic.***Expositiones Mathematicae*,*Elsevier*vol. 40 (1), 1-22.03-03-2022

### 2021

Kellendonk J and Yassawi R (2021).

20-12-2021

**The Ellis semigroup of bijective substitutions.***Groups, Geometry, and Dynamics*,*EMS Press*vol. 16 (1), 29-73.20-12-2021

### 2020

MÜLLNER C and YASSAWI R (2020).

20-02-2020

**Automorphisms of automatic shifts.***Ergodic Theory and Dynamical Systems*,*Cambridge University Press*vol. 41 (5), 1530-1559.20-02-2020

### 2019

Rowland E and Yassawi R (2019).

05-09-2019

**Automaticity and Invariant Measures of Linear Cellular Automata.***Canadian Journal of Mathematics*,*Cambridge University Press*vol. 72 (6), 1691-1726.05-09-2019

### 2018

Baake M, A. G. Roberts J and Yassawi R (2018).

01-11-2018

**Reversing and extended symmetries of shift spaces.***Discrete and Continuous Dynamical Systems - Series A*,*American Institute of Mathematical Sciences (AIMS)*vol. 38 (2), 835-866.01-11-2018

Fokkink R and Yassawi R (2018).

11-07-2018

**Topological rigidity of linear cellular automaton shifts.***Indagationes Mathematicae*,*Elsevier*vol. 29 (4), 1105-1113.11-07-2018

BERTHÉ V, STEINER W, THUSWALDNER JM and YASSAWI R (2018).

24-01-2018

**Recognizability for sequences of morphisms.***Ergodic Theory and Dynamical Systems*,*Cambridge University Press*vol. 39 (11), 2896-2931.24-01-2018

### 2017

Rowland E and Yassawi R (2017).

17-01-2017

**p -adic asymptotic properties of constant-recursive sequences.***Indagationes Mathematicae*,*Elsevier*vol. 28 (1), 205-220.17-01-2017

### 2016

Rowland E and Yassawi R (2016).

09-12-2016

**Profinite automata.***Advances in Applied Mathematics*,*Elsevier*vol. 85, 60-83.09-12-2016

Janssen J, Quas A and Yassawi R (2016).

31-10-2016

**Bratteli diagrams where random orders are imperfect.***Proceedings of the American Mathematical Society*,*American Mathematical Society (AMS)*vol. 145 (2), 721-735.31-10-2016

Bezuglyi S and Yassawi R (2016).

04-07-2016

**Orders that yield homeomorphisms on Bratteli diagrams.***Dynamical Systems*,*Taylor & Francis*vol. 32 (2), 249-282.04-07-2016

Yassawi R, Quas A and Coven E (2016).

01-03-2016

**Computing automorphism groups of shifts using atypical equivalence classes.***Discrete Analysis*,*Alliance of Diamond Open Access Journals*01-03-2016

### 2015

Rowland E and Yassawi R (2015).

01-02-2015

**A characterization of p-automatic sequences as columns of linear cellular automata.***Advances in Applied Mathematics*,*Elsevier*vol. 63, 68-89.01-02-2015

Rowland E and Yassawi R (2015).

01-01-2015

**Automatic congruences for diagonals of rational functions.***Journal de Theorie des Nombres de Bordeaux*,*Universite de Bordeaux*vol. 27 (1), 245-288.01-01-2015

### 2014

Bezuglyi S, Kwiatkowski J and Yassawi R (2014).

01-02-2014

**Perfect Orderings on Finite Rank Bratteli Diagrams.***Canadian Journal of Mathematics*,*Canadian Mathematical Society*vol. 66 (1), 57-101.01-02-2014

### 2009

PIVATO M and YASSAWI R (2009).

15-10-2009

**Embedding Bratteli–Vershik systems in cellular automata.***Ergodic Theory and Dynamical Systems*,*Cambridge University Press (CUP)*vol. 30 (5), 1561-1572.15-10-2009

Coven EM and Yassawi R (2009).

01-01-2009

**Embedding odometers in cellular automata.***Fundamenta Mathematicae*,*Instytut Matematyczny*vol. 206, 131-138.01-01-2009

### 2006

Coven EM, Pivato M and Yassawi R (2006).

15-09-2006

**Prevalence of odometers in cellular automata.***Proceedings of the American Mathematical Society*,*American Mathematical Society (AMS)*vol. 135 (3), 815-821.15-09-2006

MAASS A, MARTÍNEZ S, PIVATO M and YASSAWI R (2006).

03-07-2006

**Asymptotic randomization of subgroup shifts by linear cellular automata.***Ergodic Theory and Dynamical Systems*,*Cambridge University Press (CUP)*vol. 26 (4), 1203-1224.03-07-2006

PIVATO M and YASSAWI R (2006).

03-07-2006

**Asymptotic randomization of sofic shifts by linear cellular automata.***Ergodic Theory and Dynamical Systems*,*Cambridge University Press (CUP)*vol. 26 (4), 1177-1201.03-07-2006

### 2004

PIVATO M and YASSAWI R (2004).

01-12-2004

**Limit measures for affine cellular automata II.***Ergodic Theory and Dynamical Systems*,*Cambridge University Press (CUP)*vol. 24 (6), 1961-1980.01-12-2004

### 2003

YASSAWI R (2003).

01-08-2003

**Multiple mixing and local rank group actions.***Ergodic Theory and Dynamical Systems*,*Cambridge University Press (CUP)*vol. 23 (4), 1275-1304.01-08-2003

### 2002

PIVATO M and YASSAWI R (2002).

01-08-2002

**Limit measures for affine cellular automata.***Ergodic Theory and Dynamical Systems*,*Cambridge University Press (CUP)*vol. 22 (4), 1269-1287.01-08-2002

### 2000

del Junco A and Yassawi R (2000).

01-04-2000

**Multiple Mixing and Rank One Group Actions.***Canadian Journal of Mathematics*,*Canadian Mathematical Society*vol. 52 (2), 332-347.01-04-2000

## Grants

Grants of specific relevance to the Centre for Complex Systems

**Maths DTP 2021/22**

**Reem Yassawi**

£411,852

*EPSRC Engineering and Physical Sciences Research Council*(01-10-2021 - 31-01-2026)

**Computing algebraic invariants of symbolic dynamical systems-GRANT TRANSFER**

**Reem Yassawi**

£216,599

*EPSRC Engineering and Physical Sciences Research Council*(01-11-2022 - 31-12-2024)