Kirk Fellowship Interview: Professor Donatella Marini on virtual element methods, talented women and collaborative working

Designed to support and promote underrepresented groups in mathematics, the Kirk Distinguished Visiting Fellows scheme was launched at the start of 2019 and so far boasts five senior academics amongst its recipients. In this interview from its roster of honourees INI spoke to Professor Donatella Marini of the “Geometry, compatibility and structure preservation in computational differential equations” programme.

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Professor Marini: tell us a little about yourself.
Well, I’m based in Pavia, where I’m sitting now in my office. After I graduated here in Mathematics I began working in numerical analysis, particularly in finite element approximation of various partial differential equations with applications essentially within engineering. And this has been all that I’ve done within my career, which has been very long! I’ve been a researcher of the CNR (“Consiglio Nazionale delle Richerche”), the national council of research, in Pavia for a few years. After I became a full Professor I moved to the University of Genoa for four years and then back to the University of Pavia. Since then I’ve always been teaching at the Engineering faculty here in Pavia.

And tell us about your place within the “Geometry, compatibility and structure preservation in computational differential equations” (GCS) programme you’ll be attending?
Recently I’ve moved to something which is having a lot of success and that we have called “virtual element methods”. The applications are always the same: Maxwell’s equations, fluid mechanics, fluid dynamics, things like that. But the approximation method is a little different from finite elements. “Finite elements” is a very powerful and strong method introduced long ago by engineers and which consists of subdividing the domain where your problem is placed into triangles/quads (tetrahedra/hexahedra in 3D). With  “virtual elements” the approach is about the same but the meshes that we can deal with are made of polygons (or polyhedra in 3D) of arbitrary shapes, a feature which gives you a lot of freedom in treating various applications.

And the programme relates to this specialty?
It is related strongly to my specialty. Although it’s more “complete”, if you want, as it contains more theoretical parts and not only applications of numerical methods. However, I feel that I’m suited very well to the programme. I’d heard about GCS and I’d meant to participate for at least a couple of weeks, in order to be involved in the various workshops and to talk to people. The situation at the Institute is very favourable in terms of having such communications. In the past I’d spent a month at INI (“Computational challenges in partial differential equations”, 2003) and it was very, very nice. The atmosphere both scientifically and personally is very relaxed. So I’d meant to participate in any case and I wasn’t expecting this “award”, and in fact I hadn’t yet heard of it. Then I looked on the website and read a little, including the interview with Dr Kirk which was very nice – he’s a great guy!

We shall pass on your regards! How do you feel about being chose to be a Kirk Fellow?
I was honoured, especially because it was unexpected. I knew about the Rothschild Fellowship as some colleagues of mine received it, but I noticed that there have been very few women that have received the award.

And this is partly why the Kirk Fellowship has been aimed at “underrepresented groups” – how do you feel about this approach?
Well I think it’s a great idea, because there are many very talented women in mathematics. They could compete with men, but for some reasons which are not at all clear to me they are highly underrepresented. I think we have to say that family life takes a lot of time from women.

That’s something we hear a lot from interviewing female mathematicians: that the gender balance at undergraduate level is relatively even and it quickly worsens in favour of males as students progress towards PHD and beyond. This is often, in part, put down to the pressures of family life.
Indeed: It’s a delicate and complicated situation. On the one hand this initiative is great, because it can help women – or other underrepresented groups – to “come out”. On the other hand the ideal situation would be that men and women play in the same league. And probably in the future it will be like that. If you take sport, there it is clear that women and men are different. If you run faster then you win, so it is necessary to have two separate leagues otherwise no woman will ever win. But here, where minds are concerned, that is different. Measuring intelligence and “talent” is more complicated but, according to all scientific studies on the matter, the potential is the same. So, there is no reason that women and men could not “play” together.

Do you think that celebrating high-achieving female mathematicians will help set a precedent for future generations?
Surely initiatives like this one might help a lot to influence future generations. Things have changed already, since I began my career. Perhaps it’s because men are more available to help in a family situation. Take my parents’ generation: my father did nothing and my mother took care of everything. Now the situation is a bit different, many men buy food, cook, take care of the children, so women have a little more time to dedicate to work. But still it’s a long way to go.

Are there any particular people you’re looking forward to working with? Or are you hoping mainly for new contacts and collaborations?
I’ve seen amongst the participants many colleagues and friends that I’m looking forward to speak with. When you’re at your home institution you have so many things to follow, in terms of bureaucracy and administration, that it’s difficult to collaborate. So you have to go abroad, and the situation that Institute provides is the ideal. Because at INI we have nothing else to do but research, to talk with people, to have new ideas and to write new papers – because this is what we like to do. For example, one of the organisers is Doug Arnold (Minnesota) who is a very good friend of mine and a bright mathematician. I’m looking forward to working with him. Ricardo Nochetto (Maryland) is another. There are many, many people I’m looking forward to talk to.