The results described above are all going beyond the state of the art in the research directions that they address, as also witnessed by the fact that two of the results were accepted in highly competitive international conferences on theoretical computer science, which allowed the researcher to present them to the wider research community, and that two other results appeared in peer-reviewed high-quality specialized mathematics journals.
The researcher made significant progress on the research in both finite and profinite semigroup theory in the collaboration with Steinberg during the outgoing phase. Steinberg is an international expert on semigroup theory, and he has helped the researcher to acquire new skills and knowledge in the highly technical field of semigroup theory. One important implication of this is that the researcher will be able to transfer this knowledge to the scientific community in Europe during the return phase of the project. This knowledge transfer will take place through conferences, local seminars, and research visits within Europe. Moreover, the results with European collaborators mentioned above will have a positive impact on both the researcher's career opportunities and on the European scientific activity on logic in theoretical computer science. The research in this project is of a fundamental mathematical nature, with the potential for applications in computer science. In particular, the decidability results that were obtained in collaboration with Steinberg are mathematical descriptions of algorithms which could be implemented in the future.
During the return phase, the project saw a continuation of the international collaborations established during the outgoing phase of the project, by working remotely and by organizing research visits at the host institution. Moreover, the researcher has set up new scientific collaborations at the host institution during the return phase, where he benefited from the local expertise in coalgebra and modal logic, which are likely to lead to new research publications in the near future. The researcher has successfully disseminated the results at several conferences and international meetings in Europe: the researcher has become a frequently invited speaker at several such meetings. Finally, the researcher has spent considerable time and effort on his future career development, grant acquisition, and networking.
