Interview with Eleonora Di Nezza

Eleonora Di Nezza is a young mathematician who has been a post-doc at IHES since September 1. She will work at the Institute for one year, as part of the William Hodge Fellowship program funded by the UK’s Engineering and Physical Sciences Research Council (EPSRC).
In this interview she discusses her career so far but also her working environment at IHES and the place of women in fundamental research.

You have just arrived at IHES, what are your first impressions?

I just arrived and I like everything. I feel taken care of. The secretaries are very efficient and they help us in everything, in the cafeteria we eat very well, the library is beautiful, my accommodation is well equipped and if ever I have a problem I can call the logistics manager and he comes right away. It is paradise!
IHES gives me the possibility to live in the Institute’s residence, l’Ormaille, which has significantly simplified my arrival here: I did not have to look for an apartment, everything was already put in place by the Institute. At first I was afraid that Bures-sur-Yvette would be too quiet, but I really appreciate being there. During the week I can enjoy the proximity of the Institute and the forest and on the weekend I can go to Paris. The studio that has been assigned to me has recently been renewed, it is perfectly equipped and very pretty.

What has been your career in research so far?

My PhD was co-supervised by the University of Tor Vergata in Rome and the Paul Sabatier University in Toulouse. At first I traveled extensively between the two, but during my last year I was stable in Toulouse in order to teach, which I was doing part-time.
After that, I started a three-year post-doc at Imperial College in London. I stayed there for three years, between 2014 and 2017, two of which were funded by a Marie Curie Fellowship that I obtained from the European Union. I also spent six months at MSRI, in Berkeley.

What does this postdoc at IHES mean to your career?

For the first time, differently from what was happening in Toulouse or London, I will have no teaching duties and I will be able to devote myself entirely to my research. Until then, I have always taught, even during my post-doc in London, where even though I had no obligations to teaching, I felt it was a way of contributing to the life of the department. The course I taught was a very interesting, but also very demanding, master course – and that inevitably left less time and energy for my research. I appreciate this parenthesis at the IHES, I am happy to finally be able to devote myself completely to my maths!
In addition, I chose to accept this post-doc at IHES for two main reasons: firstly because IHES is a very prestigious Institute, where very high-level researchers work. But also because IHES is very well positioned in France – being also close to Paris, I will have the opportunity to enlarge my network and also integrate myself into the French mathematical community to which I wish to belong.

What is your research topic?

I work on Kähler geometry, at the intersection between complex geometry, differential geometry and complex analysis. This is a field of research that has developed mainly in France, around the work of Sébastien Boucksom, a CNRS research director and a professor at Ecole Polytechnique, Philippe Eyssidieux, a professor at the Grenoble Alpes University in Grenoble, Vincent Guedj, a professor at Université Paul Sabatier in Toulouse and my PhD supervisor, and Ahmed Zeriahi, also a professor at Université Paul Sabatier.
It is the four of them who started the work on degenerate complex Monge-Ampère equations. I study these equations on Kähler manifolds, which are a particular type of complex varieties.

What is it about this topic that makes you keep working on it?

I really like this topic, for several reasons. I find it very interesting to work at the intersection of several branches of mathematics: differential geometry, birational geometry, through the minimal model program (which is at the basis of the classification of projective varieties), complex analysis , complex geometry and finally theoretical physics.
Moreover, this is a very recent research topic: the pluripotential theory has been developed by the French school of Boucksom, Eyssidieux, Guedj and Zeriahi, whom I mentioned earlier, only during the last ten years and so there is still much to understand and do!
It is also true that the very fascinating world of Kähler manifolds is quite competitive and this can be discouraging sometimes. But, thanks to my PhD supervisors and my collaborators, I could focus on my research without feeling the pressure of competition.
It was also the fact of having a very good human relationship with my collaborators that motivated me to continue working on this subject, as well as the interest of the people I meet when I present my work. It can be demoralizing to work on a topic that no one is interested in.

How did you choose mathematics?

It is rather mathematics that chose me. I found myself having to make my choice about which courses to take at university just before they started. I had been a good student and I was successful in all subjects, but it was the scientific ones that I was most passionate about. I visited some departments in Sapienza University, in Rome, where I knew I wanted to go, to meet students and get some information before making my choice. There were courses for which the registrations had already been closed – and I realize today how lucky I was! Actually, it must be said that I have always been very lucky in life.

I asked some students in electronic engineering if they were doing any maths, and they showed me two books. I was very disappointed because I knew that two books could not satisfy me, so I went to the mathematics department. It was a beautiful building, squared, with a circular inner court, and a very nice library. I studied there a lot during the years that followed and even worked as a librarian in the evening, happy to be able to take advantage of the archives of the library, which include works of Galileo that I could leaf through, from time to time.
At the department of mathematics, they welcomed me with open arms: the registrations were so rare that mine cost me almost nothing. The department fit me well from the beginning. I had worked well enough in high school to understand things without too much effort and, as I was getting good results, I kept going. For my third year project I worked in analysis. I continued with the master. For the final project, I spent one year in Germany working on a complex analysis project, before returning to Italy for my PhD, at the University of Rome Tor Vergata, in collaboration with Université Paul Sabatier, where I started working on complex geometry.

Maybe mathematics chose you, but you chose it at your turn and you keep on choosing it.

Yes, that’s it. I admit I keep asking myself if this is really what I want. The life of a mathematician, especially at this stage of her career, is not simple: it requires the flexibility to travel often, without the security of a permanent position.
But every time my answer is yes. Although it can be tiring at times, this is what I want to do. This job is very fulfilling. It was mathematics that allowed me not only to travel to a number of  different places, but also to meet beautiful people in any place where I worked. They have become my family and their friendship accompanies me, from near and far, wherever I go. So yes, I chose maths and I keep choosing it.

We decided to publish this interview on Ada Lovelace Day, which celebrates women working in science and maths. At IHES there are unfortunately few women: among the permanent members there is only one woman, Fanny Kassel, who is a CNRS researcher, and even among the visitors women are rare. Is that what you are used to, or is IHES an isolated case?

IHES is unfortunately not an isolated case and the too small presence of women in the departments of mathematics is something I have become accustomed to. For example, at Imperial College, which, unlike IHES, is a university and where therefore there are many more permanent professors than at IHES, there is only one woman who is a full professor in the whole department of mathematics.
This is in contrast to the fact that in the first year at the faculty of mathematics, at least in Italy, where I started my studies, the percentage of women is about the same as that of men. Afterwards, during the years, women often stop. But we have to make a difference. In Italy there is a good proportion of women in research, even at the level of professors. In France there are many women working as lecturers or CNRS researchers, but much less among professors or research directors. In the United States there are very few women who have permanent positions and they are now compensating for this gap with positions dedicated only to women. I do not have a solution and I understand that it is a way to ensure a greater presence of women, but it saddens me to think that a condescending attitude is the only way possible.

What do you think is the reason for this gap?

I think it is mostly the difficulty of successfully balancing family and career. Being a mathematician requires dealing with periods of great instability, not only before obtaining a permanent position, but also at the moment of advancing in one’s career, which may involve a change of affiliation, and therefore a move. In our society it is still seen as normal that a man be followed by his family when he moves for work. I often meet men who are accompanied by their wives and children during their research stays. It is much rarer to see the opposite, but it gives hope to see couples, where it is the man who sometimes follows his partner during his research stay at MSRI rather than at the IHES .
There are also ‘super-women’ who get to do everything, have a family and children and do very high level maths  they are also an example for me.

This reminds me of one afternoon during my first year as a post-doc in London, where I used to share my office with another Italian post-doc, Enrica Floris. We were discussing about the shortage of women in research and we reflected on the fact that the fewer women there are, the more women who are there may want to leave in their turn. Sometimes I’ve been the only woman at a conference and I found it very uncomfortable, wondering if I was really fitting in, even if there was no reason for me to doubt that.
It was with this in mind that, during our discussion, Enrica and I came to the conclusion that it is important to stay, to resist, even if that can be uncomfortable at times. If we stay, the young women who will arrive will be able to count on our presence. It is important to have examples that show that it is possible and that we can have it all. It is not just a dream.
Enrica has kept her promise and this year she got a position as a lecturer in Poitier.

To conclude, could you tell us what are the qualities that you think brought you here and that pushed you forward in your career?

First, as I always say, I’m lucky. But luck alone is not enough, one must help it a little. I am determined in my choice to continue doing mathematics, and I have a lot of optimism and hope, which I keep alive by focusing my attention on the positive side of things.
It is also the way I position myself in life that helps me: for example, here at IHES, when I have lunch at the cafeteria, I do not stay in my corner, I introduce myself to everyone. This is what makes it possible that to an “Eleonora, nice to meet you” follows a “Laurent Lafforgue, nice to meet you” (!!)
I put a lot of enthusiasm into what I do. That’s what I try to convey every time I get an interview for a position: I’m not a genius, I’m rather like a little craftsman studying and doing her calculations little by little, but I have plenty of enthusiasm. That’s what allows me to move on. Maybe that’s exactly what brought me here.