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#### Can you describe your education leading up to your PhD?

I have been passionate about mathematics since childhood, and have always enjoyed its puzzle-like nature. As a 10th grader, I placed first in the mathematical olympiad of Kosovo, and this achievement marked the beginning of my serious interest in the discipline. I decided to study mathematics at the University of Prishtina in Kosovo, and while still in high school I began studying university books on mathematical analysis.

My first year in university coincided with the appointment of a young professor of mathematics, Qendrim Gashi. Inspired by his experience in various international universities, he helped instill an enthusiastic atmosphere for the community in our small department of mathematics, of which I was very lucky to be a part of. In Prishtina I learned the foundations of various disciplines of mathematics, and slowly my interests shifted from mathematical analysis to algebra, which would remain my main area of study all the way to my PhD.

After my undergraduate studies, I pursued my master's studies in mathematics at the University of Bonn in Germany. The mathematics department in Bonn is exceptional and staffs many world-renowned professors, and the students are very motivated and hardworking. All these aspects made Bonn a wonderful and challenging place to study mathematics. There I deepened my interest in algebra, focusing on its sub-discipline of representation theory, and I wrote my master's thesis in this area under the supervision of professor Catharina Stroppel. As per her recommendation, I decided to pursue a doctorate in mathematics. During my time in Bonn I had the pleasure of discovering the German country, culture, and language, and I was interested in experiencing these aspects of life in France too, thus I chose to go to Lyon for the next step in my academic journey.

### How would you describe the time during your PhD?

I did my doctorate in mathematics at the Université Claude Bernard Lyon 1 under the supervision of professors Stéphane Gaussent and Philippe Malbos. The topic of my thesis was at the intersection of my professors' respective research areas: representation theory and rewriting theory. While I was already familiar with representation theory from my studies in Bonn, rewriting theory was a completely new domain to me. However I found great pleasure in discovering it, and as an area rooted in theoretical computer science, it served as a gateway to me learning more about computers and programming.

A common technique in solving questions in theoretical mathematics consists of identifying a candidate answer, then proving its correctness. The first part can often be very challenging. During my doctorate, through programming I modelled certain combinatorial notions from my research, and using the brute force of the computer I identified a candidate answer to my problem. I then introduced a mathematical framework suited to this candidate answer, and proved its correctness. In broad terms, in my thesis I introduced certain combinatorial objects which facilitate topological computations of certain algebraic objects called plactic monoids.

During my PhD I was an invited researcher for a trimester at the Institut Henri Poincaré in Paris, and attended several conferences in France and abroad. I found this aspect of the PhD great, as one gets to travel, meet new people, and talk to experts in the field. Another nice part of the PhD is teaching – it gives us a chance to revisit the foundations of our discipline, and greatly improves our communication skills.

#### How did you transition from research in mathematics to working in the industry?

Theoretical mathematics is a very rich and fascinating subject, though it is often very disconnected from everyday life. This can sometimes create a feeling of professional loneliness for mathematicians. I was lucky to stumble upon computer science during my thesis, and after having employed computing as an aid for my research problem, my like and interest for programming increased. I thus learned to program using different resources: reading books, solving online problems, and doing small personal projects.

Finding a job in the industry with a doctorate in pure mathematics is not trivial. Companies seem to value the expertise of such candidates, but have doubts over their lack of formal experience in the profession. Luckily I broke this status quo through a program of the French government called POEI, via which I found a short-term internship at M2iFormation, where I was trained as a Java full-stack developer.

What do you do on your current job, and how does it relate to your previous experience?

Today I am a consultant software engineer at Atos, a French IT services and consultancy company that provides digital services to a broad spectrum of international industries. Currently, as an Atos consultant, I am assigned at the Centre de l’Énergie Atomique (CEA) in Grenoble on a project on magnetic anomaly detection. My work consists of researching the theoretical nature of different probabilistic models, and implementing adapted versions of them for our practical needs. I find working for Atos wonderful, as it provides fantastic working conditions, and they have found a very interesting and well-suited project for me to work on. Moreover working at the CEA shows me how the industry pairs up cutting-edge research with the development of solutions to real life problems.

My work now is unrelated to my work during the PhD, and to my work during the internship. However a long education in mathematics has given me the tools and understanding to learn about and tackle new problems in different areas, particularly in data science and in programming.

#### What advice would you give to people considering embarking on a PhD?

Doing a doctorate has great benefits. We learn the scientific methodology through research, we improve our critical thinking through writing, and our communication skills through teaching. We also meet people with shared interests, and we can discover new cultures and languages. Moreover the doctorate is a period of self-discovery and the not-so-strict daily schedule of academia allows for plenty of time to learn about and develop ourselves in whatever interests us.

However the experience also depends on how interesting we find our research topic and how much support we receive from our advisors. Going for a PhD is a decision that requires thought, though generally I think it is easier to do it right after a master's degree, since life tends to pile up responsibilities as we grow older. I would say that if you are doing a doctorate in pure mathematics, think about investing some time in learning programming. It is a skill of high value in our increasingly technological world, and it will serve your professional activity regardless if you continue in academia or move to the industry.

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