PhD graduate Luca Ghidelli received this prestigious award in 2020, as his doctoral thesis was deemed the best in Science and Engineering at the University of Ottawa that year. The award recognizes work that also earned him a post-doctoral fellowship from the Humboldt Foundation.
Luca Ghidelli’s excellent doctoral dissertation touches on many topics, which have been the subject of several research articles in pure mathematics. The core his thesis concerns a classical problem in number theory that had not seen substantial progress over more than a century. Indeed, Luca showed that there exist arbitrarily long sequences of consecutive integers that cannot be written as the sum of three cubes of positive or zero integers. This is surprising as we expect the mean difference between integers of this form to be bounded.
To demonstrate this result, Luca deployed a wide range of methods from analytic number theory and algebra. His thesis also established breakthroughs in other areas of mathematics. For example, in the area of combinatorics, he solved a problem on planar graphs with everywhere positive curvature – a problem he had first approached as an undergraduate student in Italy, and which he managed to solve completely during his PhD. He also made important contributions to the classic theory of quadratic forms, as well as to commutative algebra, where his results have applications to transcendental number theory. This great versatility fueled by his intense curiosity for Mathematics characterizes Luca’s work. It is also reflected in his passion for music and languages.
Completing a PhD thesis is an arduous task. Despite his remarkable scholarly achievements, Luca admits that he faced difficulties. While he had completed most of his research, the final writing proved difficult. Two things helped him overcome this obstacle. The first was the inestimable support of his supervisor, Professor Damien Roy. With his kindness and intelligence, Prof. Roy helped Luca advance his doctoral research and provided encouragement in difficult moments. The second was an informal conversation with a fellow graduate student, Sébastien Lord. They discussed how the act of writing, in addition to conveying academically relevant and top-quality content, should be an enjoyable process for the writer and the written product should be enjoyable for the reader. The most beautiful chapters of Luca’s thesis were written with this conversation in mind.
