## Mathematics as an artwork: Juliette Kennedy

Here we go with another interview to introduce a lady rocking science here at University of Helsinki: Juliette Kennedy. Juliette is a Lecturer at HY, currently visiting the Isaac Newton Institute in Cambridge, UK. Beside working in mathematical logic, she is an active participant of the academic life and promoter of interdisciplinary activities.

Could you introduce yourself?

I am a university lecturer in the Department of Mathematics and Statistics. My area(s) is (are) logic and the foundations of mathematics. This encompasses mathematical logic, set theory, and the history and philosophy of logic.

Right now I am working on a kind of invariance, and this is how you detect it: if you take your favorite canonical mathematical structure most of the time it is built out first order logic, the logic in which the quantifiers range over elements of a given domain. I ask the question, what happens if you change the logic? To, say, second order logic, in which the quantifiers range over subsets of the domain.

Sometimes you get the same thing back, but sometimes you get a new structure.

How did you fall in love with mathematics?

I was not interested in it as a teenager. I wanted to write novels! But I happened to take a math course at NYU while I was an undergraduate there. The teacher was really great! From then on my fate was sealed.

One occasion on which mathematics really amazed you…

Hard to choose just one! Recently I was amazed by Åsa Hirvonen’s lectures on the Main Gap Theorem of Saharon Shelah, which she gave in her model theory course last summer as part of the Scandinavian Logic Society Summer School in Logic. To simplify the statement of the theorem just a little bit, it says that countable theories are either “classifiable”, which means that they have relatively few models and admit “geometric” invariants—like the basis of a vector space; or, in the nonclassifiable case, they have the maximum number of models possible. Also in the nonclassifiable case the models are very entangled with eachother, meaning that it is very hard to tell them apart. The mathematical statement of this entanglement is really beautiful, and the proof itself is majestic. The theorem took many years and about one hundred papers to prove—or so I have heard—but Åsa gave everyone a real sense of the proof in one week. That was amazing!

You publish papers on art as well. Does that relate to mathematics still or is it a parallel passion and research?

I think the answer is that both are true. I think it is very important to engage with the culture of your time, so for me the form this takes is art and curating. I believe art tells us something very important about what it means to be human; tells us where we are in our consciousness. On the other hand as a theorist I ask myself the question, can mathematical constructions be treated as artworks? Most of my curating is about this question in some form or other.

What was the biggest obstacle you had to face? And the achievement you are most proud of?

Biggest obstacle: Being a girl, no doubt!! I felt like a real “fish out of water” while I was an undergraduate (in the 1980s), even so that I had wonderful professors and I really loved my courses. Then in graduate school at CUNY I had to deal with a professor who decided he was in love with me. Phone calls morning, noon and night, and lots of other bad stuff went on. He stole years of my life.

Achievement I am most proud of: I asked a question in 2009 that nobody had asked before. It turned out to be a very good question, in that it has led to some deep results—at least my collaborators and I think the results are deep! Something else I am proud of is that my niece went into mathematics, getting her Ph.D.  in statistical methods related to public health, specifically water-born diseases. When she was a child we played a lot of math games, like generating sequences of values related to the Collatz conjecture (also called the 3n+1 conjecture), just for fun. I guess it was no surprise that on her first day of university she declared a math major! Still I take some credit for that.

What mathematician of the past has most inspired you?

Julia Robinson. She was a wonderful mathematician, worked on so-called decision problems. She is the “R” of the celebrated MRDP Theorem, which gives a negative answer to Hilbert’s Tenth Problem: is there an algorithm that tells you, if you input a Diophantine equation, whether it has solutions in the integers? I admire her as a person very much. In her public life she was politically active (working on left-wing causes), also her character was very modest. She struggled with all kinds of obstacles, one being that she was in poor health most of her life. But she always met these obstacles with grace and optimism. I highly recommend the biography of her written by her sister, Constance Reid.

Can you describe your perfect day off work?

Do you mean a day off, away from math? Or day of work? A perfect day off work is walking along the coast of Ireland with my husband. A perfect day OF work is making progress on a paper, whether it is by working alone or at the blackboard with my collaborators Menachem Magidor and Jouko Väänänen.

Do you have a message for girls who are mathematics students or are considering to study mathematics?

This is a great time to enter mathematics for women, so don’t hesitate to follow your interest! If you decide to become a mathematician though, please marry somebody who is willing to follow you to YOUR job, not insist that you have to follow them to THEIR job. In my case moving to where my husband’s job is worked out really well, because I had a job (of assistant) waiting for me. But I have seen too many women pass up great opportunities, or not apply for positions they would otherwise be in the running for, because it entails living abroad, and the partner is not willing to move, or because there is a perception that his job is more important. I can say though, that from what I have observed,  young Finnish men are generally very enlightened when it comes to gender equality. And the older ones aren’t so bad either.

## Recycling manifolds: Kirsi Peltonen

I am proud to present another fellow mathematician, now working as a Senior Lecturer at Aalto University and as Docent at University of Helsinki, Kirsi Peltonen. Kirsi will also be the speaker at the seminar Women in Mathematics in Finland on November 9th at 4 p.m. in Exactum CK112 (info to come soon).

I am currently working at Aalto University Science School Mathematics department as a Senior Lecturer. I am also docent in Mathematics at Helsinki University. I do research in geometric analysis in pure mathematics. At Aalto I am responsible on activities related to differential geometry and applications. This is a broad field with exciting connections not only to research inside mathematics but also physics, computer science, engineering and arts. At the moment I live in Järvenpää together with my husband and two cats. Our 3 children have already moved away from home and started their own careers and live together with their spouses.

When did you start getting interested about mathematics?

It is hard to pinpoint any particular time or event for a start of getting interested in mathematics. I found natural sciences in general the most interesting subjects at school. I also enjoyed all sorts of handcrafts at the same time. The passion for mathematics is difficult to explain, but it has been a crucial part of all my activities as far as I remember.

In the heart of my research are mapping problems between abstract shapes with certain geometric constraints. The principles of this process could be compared to recycling textiles. You take for example men’s shirt and would like to change it to women’s skirt. If the material, size and other properties are appropriate, you cut and sew to perform the needed changes according to your plan. In my research I take different types of manifolds instead of shirts and skirts which I suppose they could be transformed to each other and try to prove it by making use of the properties they have. I use techniques like cutting and sewing for abstract entities. Sometimes the outcome is a beautiful example but more often the constructions fail. This does not mean failure, but like often happens in sewing, you get something completely different as planned but still something useful. You also learn why certain things do not work and this is important as well.

Up to now, what do you regard as your most satisfying professional achievement?

I think it is the fact that I have been able to find the joy of doing mathematics over and over again. I am privileged to have so many talented collaborators and colleagues that have inspired and encouraged me over the years.

What was your hardest professional period and how did you overcome it?

Without no doubt it was almost 10 years ago when I found myself in the middle of hostile bureaucrat acts and almost lost my health. Thanks to my family, Finnish healthcare and great colleagues in Finland and abroad, I am now completely recovered. I am also happy that this process did not make me a bit bitter or cynical but made me more aware of unconscious bias and the fact that your true friends are those who also tolerate your success.

Did you face any obstacles – direct or indirect – in your work because of your being a woman?

This is a tough question as being a mathematician is equally hard to everybody working in the field. Good collaboration is an essential ingredient of this profession and   I think this has been most challenging to me, especially when I was younger.

Crisp sunny day in the forests together with my husband to pick up some mushrooms.

Be active, go to seminars, listen broadly what other people are doing and share your problems and ideas with others. Do not take it personally if you do not get the grant you applied. It is not all about you, but most often about politics and circumstances. Just make the next application and continue working persistently.

What would you tell to girls who are thinking to study or work in mathematics?

Just go ahead! Math is fun and always useful ! And when you get the grant you applied be happy and continue working persistently no matter other people might say.

(Picture: Eeva Lehtinen)

## Laura Venieri, from Italy to Finland for love of mathematics

I interviewed Laura Venieri, an Italian postgrad student working at the Department of Mathematics and Statistics in the Geometric Measure Theory research group, with Prof. Pertti Mattila.

When did you move to Finland and what brought you here?

“I came for my Erasmus study period in 2012, motivated by the curiosity to see some country different from Italy and to study in some courses I noticed. It was my first time in Finland. I felt really at home and decided to stay: Prof. Pertti Mattila had an open position for a doctoral student and after my master graduation I moved to Helsinki permanently.”

Were doctoral studies part of your master plan? What are your future perspectives?

“I have started thinking about doctoral studies during my master. Now I am half-way in my studies. I would like to continue working in academia, but the job instability and the mobility scare me. Anyway I am open to possibilities also outside the academia.”

Do you plan to stay in Finland?

“I am integrated here now, I have a boyfriend, friends… I like to travel but moving abroad for longer periods does not sound nice. My boyfriend is still studying here in Finland.”

Can you explain in simple words what you work on?

(she laughs) “Well, I study the Hausdorff dimension of some sets, called Kakeya sets, in Heisenberg groups and other metric spaces. These sets in Euclidean spaces are defined as sets of zero Lebesgue measure containing a segment of length 1 in every direction. In the plane, it has been proved that such sets have Hausdorff dimension 2, that is quite surprising since they have measure zero. One standing conjecture is: is this true in R^n, that is, do Kakeya sets in R^n have Hausdorff dimension n? This conjecture is connected to many problems in other areas of mathematics, such as harmonic analysis. I do not work on this particular conjecture, but I use Kakeya sets in my own research project, generalizing and studying them in other spaces.”

What do you love about mathematics?

“I like its logical structure and I love that many times logic leads you to less intuitive conclusions, like the Kakeya sets I have talked about.

I have always liked mathematics. When I was in high school I liked it as a challenge, a game. During university years I started seeing something deeper in it.”

Professionally speaking, what are you bringing from Italy to Finland? And viceversa, what would you export from Finland to Italy?

“Mathematics studies at University of Bologna are very theoretical, I was trained not to be scared by highly theoretical contents. On the other hand, I appreciated all the exercise classes here in Helsinki, they are useful and needed in Bologna. I also like the more relaxed university environment: in Italy everything is very formal.”

Did you have to face obstacles as a woman in mathematics? And in general?

“No, as a woman no. In general I found the passage from master to postgraduate studies hard. All of sudden I was not sure if a problem had a solution and how to find it. Luckily my supervisor has helped me get through this.”

What would you tell to girls who are thinking to study or work in mathematics?

“If you like it, just try to follow this path. Don’t be discouraged: hard times are very usual in mathematics.”