I am a mathematician based at the Department of Mathematics of the American University of Beirut.



Teaching



Research
Interactions between symbolic dynamics (cellular automata and tilings),
probability theory (probabilistic cellular automata and Gibbs measures), ergodic theory,
computation theory, information theory, and combinatorics,
particularly problems originated from statistical physics and computer science.



Events of Interest







Slides of Recent Talks



Preprints
[2024]
(with Yahya Ayach, Anthony Khairallah, Tia Manoukian, Jad Mchaimech, and Adam Salha),
Zeroone laws for events with positional symmetries,
Preprint.
[2023]
(with Léo Gayral and
Mathieu Sablik),
Characterisation of the set of ground states of uniformly chaotic finiterange lattice models,
Preprint.



Publications
[2022]
(with Sem Borst, Frank den Hollander
and Francesca Nardi),
Crossover times in bipartite networks with activity constraints and timevarying switching rates,
Annals of Applied Probability, 32(6): 4279–4314, 2022.
[ preprint]
[2022]
(with Nazim Fatès and
Irène Marcovici),
Selfstabilisation of cellular automata on tilings,
Fundamenta Informaticae, 185(1): 27–82, 2022.
[open access]
[2021]
Reversible cellular automata in presence of noise rapidly forget everything,
in Proceedings of AUTOMATA2021, 90, 3:1–3:15, OASIcs 90, Schloss Dagstuhl, 2021.
[open access]
[2021]
(with Sebastián Barbieri, Ricardo Gómez, Brian Marcus and Tom Meyerovitch),
Gibbsian representations of continuous specifications:
the theorems of Kozlov and Sullivan revisited,
Communications in Mathematical Physics, 382(2), 1111–1164, 2021.
[ preprint]
[2020]
(with Sebastián Barbieri, Ricardo Gómez and Brian Marcus),
Equivalence of relative Gibbs and relative equilibrium measures for actions of countable amenable groups,
Nonlinearity, 33(5), 2409–2454, 2020.
[ preprint]
[2019]
(with Nazim Fatès and
Irène Marcovici),
Cellular automata for the selfstabilisation of colourings and tilings,
in Proceedings of RP2019,
LNCS 11674,
121–136, Springer, 2019.
[ preprint]
[2019]
(with Irène Marcovici and
Mathieu Sablik),
Ergodicity of some classes of cellular automata subject to noise,
Electronic Journal of Probability, 24, paper #41, 44pp, 2019.
[open access]
[2018]
(with Frank den Hollander
and Francesca Nardi),
Metastability of hardcore dynamics on bipartite graphs,
Electronic Journal of Probability, 23, paper #97, 65pp, 2018.
[open access]
[2018]
Statistical equilibrium in deterministic cellular automata,
in Probabilistic Cellular Automata: Theory, Applications and Future Perspectives, 145–164, Springer, 2018.
[ preprint]
[2017] (with Silvio Capobianco and
Jarkko Kari),
Postsurjectivity and balancedness of cellular automata over groups,
Discrete Mathematics & Theoretical Computer Science, 19(3), 2017.
[open access]
[2016]
(with Silvio Capobianco and
Jarkko Kari),
An "almost dual" to Gottschalk’s conjecture,
in Proceedings of AUTOMATA2016,
LNCS 9664,
77–89, Springer, 2016.
[2016]
(with Nazim Fatès and
Irène Marcovici),
Twodimensional traffic rules and the density classification problem,
in Proceedings of AUTOMATA2016,
LNCS 9664,
135–148, Springer, 2016.
[2015]
Restricted density classification in one dimension,
in Proceedings of AUTOMATA2015,
LNCS 9099, 238–250, Springer, 2015.
[ preprint]
[2015] (with Jarkko Kari),
Statistical mechanics of surjective cellular automata,
Journal of Statistical Physics, 160(5):1198–1243, 2015.
[open access]
[2013] (with Amir Daneshgar and Alireza Rahimi),
Function Simulation, Graph Grammars and Colourings,
International Journal of Computer Mathematics, 90(7):1334–1357, 2013.
[2012] (with Aernout C. D. van Enter and Giulio Iacobelli),
Potts model with invisible colours: Randomcluster representation and PirogovSinai analysis,
Reviews in Mathematical Physics, 24(2):1250004, 2012.
[2012] (with Jarkko Kari),
Conservation laws and invariant measures in surjective cellular automata,
in Proceedings of AUTOMATA2011,
DMTCS, 113–122, 2012.
[2012] (with Enrico Formenti, JeanPaul Comet, and Gilles Bernot),
On the impact of distance between two genes on their interaction curve,
Journal of Mathematical Biology, 64(1–2):131–147, 2012.
Preliminary results presented in MTNS2010.
[2012] Conservation Laws in Cellular Automata,
in G. Rozenberg et al. (Eds.), Handbook of Natural Computing (Vol I), 259–286, Springer, 2012.
[2011] (with Aernout C. D. van Enter and Giulio Iacobelli),
Firstorder transition in Potts models with ``invisible'' states: Rigorous proofs,
Progress of Theoretical Physics, 126(5):983–991, 2011.
[2011] (with Enrico Formenti and Jarkko Kari),
On the hierarchy of conservation laws in a cellular automaton,
Natural Computing, 10(4):1275–1294, 2011.
[2010] (with Amir Daneshgar and Hossein Hajiabolhassan),
On the Complexity of Unique List Colourability and the Fixing Number of Graphs,
Ars Combinatoria, 97, 2010.
[2008] (with Jarkko Kari),
Combinatorics of Conservation Laws,
Bulletin of the EATCS, 95:183–197, June 2008.
[2008] (with Jarkko Kari),
A Particle Displacement Representation for Conservation Laws in TwoDimensional Cellular Automata,
in Proceedings of JAC2008, B. Durand (Ed.), 65–73, 2008.
[2008] (with Enrico Formenti and Jarkko Kari),
The Most General Conservation Law for a Cellular Automaton,
in Proceedings of CSR2008, E. A. Hirsch et al. (Eds.), LNCS 5010, 194–203, 2008.
[2008] (with Tim Boykett and Jarkko Kari),
Conservation Laws in Rectangular CA, Journal of Cellular Automata, 3(2):115–122, 2008.
[2007] Cellular Automata Reversible over Limit Set,
Journal of Cellular Automata, 2(2):167–177, 2007.



Theses
[2009] Conservation Laws in Cellular Automata, Ph.D. thesis, University of Turku, 2009.
Supervisor: Professor Jarkko Kari. Opponent: Professor Bruno Durand.
Errata to be added.
[2004] Multiparty Interactive Protocols and Some Applications (in Persian), Master's Thesis,
Department of Mathematical Sciences, Sharif University of Technology. Supervisor: Professor Amir Daneshgar.



Other writings



Coauthors
Yahya Ayach,
Sebastián Barbieri,
Gilles Bernot,
Sem Borst,
Tim Boykett,
Silvio Capobianco,
JeanPaul Comet,
Amir Daneshgar,
Aernout van Enter,
Nazim Fatès,
Enrico Formenti,
Léo Gayral,
Ricardo Gómez,
Hossein Hajiabolhassan,
Frank den Hollander,
Giulio Iacobelli,
Jarkko Kari,
Anthony Khairallah,
Tia Manoukian,
Irène Marcovici,
Brian Marcus,
Tom Meyerovitch,
Jad Mchaimech,
Francesca Nardi,
Alireza Rahimi,
Mathieu Sablik,
Adam Salha







Resources for Mathematicians






