A native of Albacete, Spain, José Pablo Llano Gómez is a mathematician from the University of Valencia, with a master's degree as a Secondary Mathematics Teacher at the same university, and is currently in his last year of his doctoral studies at the University of Castilla - La Mancha (UCLM) in his hometown. 

His research interests are Boolean networks, which, he explains “are any system in which you can differentiate different entities or individuals and relationships between those entities, which evolve over time, with a characteristic of those individuals, and you can model it using a Boolean network”.  

“From a mathematical perspective,” he details, ”you simply study the object you don't have to look at the applications and there is a whole theoretical analysis behind to understand the properties of those systems and how they evolve over time which is called and basically my research focuses on studying the properties or the dynamics of those systems.”  

International networks  

José Carlos Valverde and Juan Ángel Aledo are his thesis directors, both academics from the Department of Mathematics at UCLM, and his stay in Concepción was motivated by his interest in collaborating with members of the Center for Mathematical Engineering, CI²MA, of the University of Concepción Lilian Salinas Ayala from the Faculty of Engineering and Julio Aracena Lucero from the Faculty of Physical and Mathematical Sciences. “I knew about their work, because they have several joint and very important works in the area and because of the project I am working on, which finances my doctorate, I had the opportunity to make an international stay, so I contacted them and we talked about it and agreed that I would stay for three months”, he explained.  

In this regard, Dr. Aracena, also a researcher at the Center for Mathematical Modeling (CMM) of the U. of Chile, commented that “they work on similar research and we have always known each other's work, but we have never had the opportunity to collaborate so closely”.  

“We were working for more than three months”, the UdeC academic added, ‘and we not only showed what we were doing, but, based on what he was doing, we showed him different results that gave him a different look at his work, and I think he learned a lot from what we were doing’. 

“We looked for a link between the topics they were researching in recent years and what I was doing, particularly in my thesis”, said José Pablo and explained that ‘we were working on several topics, which deal with Boolean networks and the analysis of the properties and dynamics of these systems, to find dynamic equivalences, or different networks that behave in the same way and how, from different perspectives, this problem can be analyzed’. 

“In a first phase, we tried to find dynamic equivalences by means of the switch operator, which is a very particular mathematical object that makes transformations in the system in a certain way, this from the basis of a master's work of Victor Cartes, which was directed by Professor Aracena”, commented José Pablo.  

“I have learned a lot from both professors (Aracena and Salinas), the way they work, how to face the problems and the questions you have to ask yourself, which are very important in the doctorate, because many times, especially in mathematics, if you don't have a good question, then, no matter how good you are at solving the questions, you don't do a good job”, commented Dr. (c) Llanos.  

“I am very happy with the experience now and I am looking forward to the work we can do together in the future,” he emphasized.  

Meanwhile, the director of CI²MA, Dr. Rodolfo Araya Durán emphasized that “it is always very encouraging for the work in our Center to have international collaborations, because these speak of the quality of our researchers and the interest of centers abroad in collaborating with us”.  

Continuing collaboration 

In this sense, Prof. Aracena detailed that José Pablo “obtained good results, worked well and took a lot of problems to finish his doctoral thesis and even to be able to continue in that, with problems that are different from his laboratory and although, many times they are the same questions, they are different methodologies and techniques that enrich his work”. 

The idea is that José Pablo becomes a bridge of collaboration and that he is already starting to take his first steps in the sense that there are scholarships offered by them so that our students can go to do internships now”, emphasized Dr. Aracena and added that ‘our students who interacted with him and got to know his work, also have the opportunity to participate in his work’.

 Continuing to collaborate 

In this sense, Prof. Aracena detailed that José Pablo “obtained good results, worked well and took a lot of problems to finish his doctoral thesis and to be able to continue in that, with problems that are different from his laboratory and although, many times they are the same questions, they are different methodologies and techniques that enrich his work”. 

“The idea is that José Pablo becomes a bridge of collaboration and that he is already starting to take his first steps in the sense that there are scholarships offered by them for our students to go and do internships now”, emphasized Dr. Aracena and added that ‘to our students who interacted with him and got to know his work, it also brings them the fact of highlighting what they are doing, because it is different from me telling them as a guiding professor, to someone from outside telling them that what they are doing is important’. 

“That he came to UdeC” said the CI²MA researcher”, speaks well of what we do here, because he could have chosen several other places and it seemed to him that here was also a good place to continue growing in the field of his training, he knew our work and had cited some of them”.