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Interview: special edition with EMS Prize winner Cristiana De Filippis

25 July 2024
As part of the outreach committee, Raffaella Mulas regularly interviews colleagues and visitors to our department. In this special edition, she sits down with Cristiana de Filippis, a recipient of the 2024 EMS Prize. Raffaella and Cristiana first met through the inaugural cohort of the European Mathematical Society Young Academy (EMYA), where they both serve as elected members.

Cristiana De Filippis is an Assistant Professor in the Department of Mathematics at the University of Parma, where she will become an Associate Professor starting from November 2024. Born in Bari, Italy, in 1992, Cristiana obtained her bachelor's degree in mathematics at the University of Turin and her master's degree at the University of Milan-Bicocca. Then, she completed her PhD at the University of Oxford. Following her PhD, Cristiana held a postdoctoral position at the University of Turin from 2020 to 2021, after which she moved to the University of Parma.

Throughout her career, Cristiana has been awarded several prestigious recognitions, including appearing on Forbes' list of the 100 most successful Italian women in 2023 and being one of the top-cited mathematicians for her PhD year (2020). In 2024, she received the Bartolozzi Prize by the Italian Mathematical Union. In the same year, during the 9th European Congress of Mathematics, Cristiana was awarded the EMS Prize, which is considered the most prestigious mathematics prize in Europe and is referred to as the "Fields Medal's little sister."

Cristiana, congratulations on receiving the EMS prize! It is a great honor for me to interview you. 

Many thanks to you Raffaella for the interview, the honor is mine!

I would like to start from the beginning, by asking you how you discovered your passion for mathematics, and in particular how old you were.

I discovered my passion for mathematics right after primary school: I realized that studying was pleasant and exercises/problems were easy, so I also deepened some aspects of the subject by myself.

Well, that turned out to work out very well! Now, you were awarded the EMS prize for your "outstanding contributions to elliptic regularity, in particular Schauder estimates for nonuniformly elliptic equations and non-differentiable variational integrals, and minima of quasiconvex integrals." How would you explain this to someone who thinks that "elliptic regularity" is a type of workout routine?

“Workout routine” is very nice, I will use it somewhere! Let’s say that an “elliptic PDE (Partial Differential Equation)” is an equation driven by a differential operator that is a (possibly degenerate) generalization of the Laplacian. Investigating the regularity of solutions means finding out how “good” they are. Two basic questions may be for instance, “Can their graph be drawn with a continuous line that has no holes?” or “How many derivatives solutions have?”. To answer, it is in general necessary to design delicate iteration schemes aimed at showing that certain features of solutions improve at each step, in a controlled way. This in general requires a deep understanding of the problem, very fine techniques as well as a bit of luck.

You have all three! What is your creative process? How do your mathematical ideas take shape?

My creative process is rather visual, I tend to imagine what are the right paths towards the outcome and the main obstructions, leaving details aside. Sometimes it works, others a super small parameter appears in the wrong place and nullifies months of work.

Does this mean that also an EMS Prize winner can have difficulties?

Of course! I feel stuck for so many things in my research, and what comes out is just the tip of the iceberg.

Can you share a specific moment or breakthrough in your research that was particularly exciting for you?

When I obtained the first set of Schauder estimates for nonuniformly elliptic PDE, in collaboration with Giuseppe Mingione. This was probably the first “big” problem I’ve heard about at the very beginning of my PhD, with the warmest recommendation of not wasting my time working on it, as nothing would have come out.

Great that you didn't listen! Cristiana, I looked at your CV and I am impressed by the breadth and depth of your activities and achievements. How do you manage your time to balance research, teaching, and the various other professional commitments that you have?

You are very generous, thank you! I focus the majority of my time on research, and try to optimize teaching in such a way that the efforts required remain reasonable. 

What advice would you give to younger researchers who are just starting their journey in mathematics?

My advice would be to always be curious, willing to study, and not be afraid of hard work and failures.

Great advice! Since we are friends on social media, I have to ask you: Do you manage your accounts, or have your cat taken over as the real influencer behind the scenes?

That’s right, you spotted the real social network mastermind, the king of perfect shots, the nightmare of the average influencer, the terrible cat Anakin!

I knew it! Who have been your greatest supporters throughout your career?

My horse and my cat, of course! And my friends (colleagues) at the University of Parma. We made a very strong and supportive group, so it’s natural in such a nice environment to try to do our best.

This sounds wonderful. Besides research, your friends, and your beloved animals, what makes you happy?

I like running and doing sports in general!

And what are you looking forward to in the future?

I look forward to continuously improving my work and the results I obtain. I also hope to be able to build a research group to share ideas, approaches and perspectives and, above all, to learn from other researchers with different backgrounds from mine.

I’m sure it will happen!

Photo by Giovanni Calori / University of Parma, from Corriere.it

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