Parma Cristiana De Filippis is among the best young mathematicians

Parma, Cristiana De Filippis is among the best young mathematicians on the continent Gazzetta di Parma

The Academy of the European Mathematical Society was founded to bring together the best of the new generations in Europe. And among the thirty members, chosen from among the best young mathematicians on the continent, is Cristiana De Filippis from the University of Parma. For De Filippis, this is an international recognition of great prestige, even if one considers that the most important prizes in mathematics are often reserved for not-so-mature people. Keep in mind that the Fields Medal, considered by many to be the equivalent of the Nobel Prize for the discipline, has an age limit of 40 years.

In recent years, Professor De Filippis, who had become one of the best known and most invited mathematicians of her generation worldwide, was not new to major awards, although not yet of this importance. A few years ago she was awarded the G-Research Prize in Great Britain for her contributions to the calculus of variations. In 2021 she received the Iapichino Prize from the Accademia Nazionale dei Lincei from the hands of the Nobel Prize winner Giorgio Parisi. After completing her research doctorate at Oxford University, De Filippis had received numerous offers for professorships at various prestigious universities in Europe and the United States, but then decided to return to Italy and more specifically to Parma, convinced of the quality of research at Parmesan University, in Consistently at the top of the international rankings for mathematics in recent years.

Today, the impact of De Filippis’ research and work has resulted in her being the world’s most-cited person in her PhD year, according to the American Mathematical Society database. Publications taking up her ideas now appear every week in the most important international journals, while the requests from young European and non-European researchers who want to come to Parma to collaborate with her are multiplying.

Thanks to the work of De Filippis, some difficult questions of contemporary mathematical analysis have been answered, such as the validity of Schauder’s theory for non-uniformly elliptic equations. This is a classic question that has its roots in the tragic climate of Europe in the 1930s, when, among others, the Polish mathematician Juliusz Schauder and the Italian Renato Caccioppoli were building the foundations of the topological theory of differential equations and proving what they have been in the world ever since literature as Schauder estimates for linear equations. A line of research shaped by the dramatic events of that time: Schauder is murdered by the Nazis, Caccioppoli is sent to a mental institution by the fascists. Schauder’s estimates are today one of the basic and most used tools in the analysis of partial differential equations, since they allow to demonstrate the regularity and therefore the approximation of the solutions, which is fundamental for applications. Many physical problems are in fact governed by differential equations, whose explicit solutions can almost never be calculated. It only remains to approximate them with the help of powerful electronic calculators. This is done in the major applied research labs around the world, from NASA to Dallara. At this point, the approximation algorithms fulfill their intention, namely to return a graph of the solution, the better the more partial and qualitative information about the solutions is known a priori, even if this cannot be written down to the end. Schauder’s estimates provide this step as a basic tool. After the war, the theory was developed and extended to nonlinear equations, the most complicated and important, starting from the initial intuitions of De Giorgi and Nash, by various big-name research groups such as that of Smirnov and Ladyzhenskaya in St. Petersburg. Gilbarg and Trudinger in Stanford and Hildebrandt in Bonn.

The non-uniformly elliptic case, which has been the subject of research by St. Petersburg and Stanford mathematicians for years and has been at the center of many extremely partial developments in the last decade, remained open. The first general reactions came from Parma thanks to the work of De Filippis and her collaborators who, together with their work devoted to regularity theory, brought the young mathematician instant international fame until her European nomination.

The election of De Filippis to the Academy is undoubtedly one of the most important scientific awards that the University of Parma has received in the last decade, allowing the University of Parma to appear in this case alongside institutions such as the Max Planck Institute, Paris Dauphine , Princeton and New York University. The process has been long and difficult, and has gone through a careful analysis of the different sectors with the greatest impact on world mathematics. The idea is that the role of the newly elected is destined to lead European mathematics towards a renewal aimed at quality and competitiveness.

Today Cristiana De Filippis is divided in her work between Parma and the rest of the world and is invited by institutions and research bodies practically every month. Only in his final program are there invitations to give lectures from Australia, Belgium, Korea, Germany, Great Britain, Poland, Portugal, the Czech Republic, Russia, Spain and Sweden.

Commentary on acknowledgments to De Filippis by Susanna Terracini, Full Professor of Mathematical Analysis at the University of Turin and world-renowned researcher. Terracini is a member of the ten-member Executive Committee of the European Mathematical Society and for many years was one of the seven members of the Governing Council of Anvur, the government body responsible for evaluating the Italian university system. «An important acknowledgment for De Filippis, who was chosen for its excellent curriculum, and for the entire University of Parma. A vocation that also represents a great responsibility. The Academy will play a proactive and advisory role, it will take care of the promotion of meetings, activities, conferences, congresses and the appointment of the various scientific committees at European level. Cristiana represents the future of math with her incredible curriculum and a particularly brilliant mind.”

There was also great satisfaction at the University of Oxford, where the Director of the Department of Mathematics, Professor Jan Kristensen, one of the leading living experts in the calculus of variations, commented: «De Filippis did his PhD in mathematics with us at Oxford in 2020, on regularity theory. This is notoriously one of the more technical and difficult areas of mathematics and one with a long tradition. Since then, De Filippis has achieved a number of notable results and established himself as one of the leading experts in the industry. The nomination to the Academy recognizes these achievements and is a great honor for the Universities of Oxford and Parma and for the Italian mathematical community more generally.”