Interview with Lauren Williams

Lauren Williams is Dwight Parker Robinson Professor of Mathematics at Harvard and Sally Starling Seaver Professor at the Radcliffe Institute. She studied mathematics at Harvard University and completed her PhD at MIT, under the supervision of Richard Stanley. After post-doctoral fellowships at the University of California, Berkeley, and Harvard University, she moved back to UC Berkeley in 2009, first as an Assistant Professor, then Associate Professor and became full Professor in 2016. She obtained a new professorship from Harvard University and the Radcliffe Institute in 2018. Her research interests are in algebra and combinatorics. Prof. Williams spent almost a year at IHES as a visiting professor between August 2022 and July 2023. Her visit was funded by the ENGIE Foundation, which has committed to supporting the visits of women researchers at IHES. This interview is published on the occasion of the International Day of Women and Girls in Science (Feb 11th).

Yours is an impressive career path. Have you always known that you wanted to be a mathematician?

In high school I already liked mathematics very much, but I did not know what sort of careers existed out there. There is a particular program that was very important for me and that I attended after my second year of high school, called the Research Science Institute (RSI). It takes place every summer at MIT and welcomes high school students from all over the US as well as some international students. All the students were paired with mentors and I was matched with a math graduate student who gave me a research problem in combinatorics to think about, together with some references to read to learn combinatorics and how to program. That was very intensive, but extremely interesting and fun. It was my first experience doing research and I really enjoyed the freedom and the creativity that it involved. After that summer I wanted to continue working on my project, but I was going back home to California, so my mentor got me in touch with a researcher at UCLA who agreed to meet with me to help me continue my project, which was very rewarding.

How did you find out that research in mathematics was a possibility and that was what you wanted to do?

After RSI, I understood that it was possible to have a career in math and I decided that I would try to be a researcher. Despite my limited experience, I thought I might enjoy a career doing research and teaching. I knew the path might be difficult though, so during my summers as an undergraduate, I explored various career options: I spent one summer at a math research program in Minnesota, one summer at the National Security Agency doing cryptography, and another summer in New York doing financial consulting. After these experiences I understood that if in the future I didn’t manage to get a job as a professor then there were other possibilities.

A pivotal moment for me was in graduate school, during the second year of my PhD. I had recently started on a research problem, and after several months, had formulated a conjecture that I really wanted to prove. I was working almost every day all day but for nine months nothing really seemed to work. I was completely stuck and I was starting to feel depressed and discouraged. I had to wonder whether I should give up and find another problem, or continue, knowing that I might not ever prove my conjecture. That was a period of time that was quite difficult for me. But I did find the solution to my problem eventually. After those nine months I started making progress, and once I started on the right path it took me another three or four months to prove the conjecture. Finding the solution gave me some confidence in my abilities, and with every new problem I solved and every paper I wrote I gained more confidence that I could continue on this path. In retrospect, I know now that my experience was not unusual — nearly everyone I know who went through graduate school had times when they felt lost. One has to realize that in research we are stuck most of the time, and that there will be many days when we work, not knowing if our efforts will take us anywhere. But then, when one finally finds the result, the feeling is very rewarding!

How would you describe your experience as a woman in mathematics?

I realized that there were not many girls in mathematics already in high school. I was doing some math competitions and attending math summer programs where there were not many girls. During the summer after my third year of high school, I participated in the Math Olympiad Summer Program, a residential 3.5-week program that trained students for the International Math Olympiad. There were 24 participants, and I was the only girl. Everyone was friendly, but the experience was strange and isolating; moreover I felt a tremendous pressure that if I did badly, it would reflect badly on all females.

In the math departments that I have been part of (as a student or faculty member), the proportion of professors who are women has ranged from 0% to about 15%, which is obviously not ideal. On the other hand, I think there can be a very nice community among women mathematicians. I have been lucky to have had multiple extremely good women collaborators, some of whom I have worked with for nearly two decades. I am thinking of Sylvie Corteel, who is now at Université Paris Cité and UC Berkeley, and of Konstanze Rietsch, who is at King’s College London. I have been collaborating with them for perhaps seventeen years and it has been really nice to have these very strong women collaborators that I am also good friends with. I have also had some exceptional female undergraduate and graduate students, which makes me optimistic about the future.

Which conditions or factors do you think would help more women choose a career in mathematics?

I think it is helpful for younger women to see more senior women having a successful career in mathematics who are also happy in their job.

Providing opportunities for girls in middle school and high school to experience the joy of discovering mathematics, of creating mathematics, could help with the “pipeline” problem. Girls Angle is an excellent example of such program. There are other great co-educational programs including MIT Primes.

Childcare is another key factor, as childcare in the US can be extremely expensive. That can make it difficult for academics, especially women, to continue their career in research once they start a family. So grants that cover childcare can be helpful: for example, the Alfred Sloan research fellowship can be used to cover childcare costs, which was very helpful to me when I had my first child.

Another thing that can make it hard for young researchers to pursue a career in academia is the length of time it takes to obtain a permanent position. In the United States, many people spend 3 to 5 years as a postdoctoral fellow, then get a tenure-track position (if they are lucky!), and then wait six or seven years until they have a tenured (permanent) position. While I know it’s also difficult in France, it seems to me that there are more positions available and the length of time from obtaining a PhD to obtaining a permanent position is shorter. In this way France makes it easier for people (especially women) to choose a career in academia.

How have you heard about IHES and what has your experience been as a visiting researcher?

Although I have been to France many times, particularly during a sabbatical in 2014, August 2022 was my very first time setting foot in Bures-sur-Yvette. I had heard a lot about IHES from many different colleagues who would wax eloquent about the Institute, but I had never applied before.
I am very happy with my year at IHES, which is a wonderful place to do research. The offices are comfortable and there is a room with huge blackboards and a smartboard which is nice for collaboration. Everything here is designed to make the life of a researcher as easy as possible. IHES is also very international and over the course of this past year I have unexpectedly run into colleagues from the US who I was not expecting to see; this has been very nice.

Additionally, I have found IHES to be a very tranquil place to work. This year I have been living in Paris, and it always feels like a retreat in the countryside whenever I get out of the train at Bures- sur-Yvette, breathe the fresh air, and hear the birds singing rather than the noise of the city.

Finally, my children like IHES too! I have come to France with my family, and have taken my children to the Institute multiple times on weekends. They have enjoyed drawing on my blackboard, spinning in my rotating chair, drinking hot chocolate from the coffee machine, and doing cartwheels in the hallways. They think the life of a researcher is great!

What do you think that IHES could do to ensure that more women mathematicians apply to come to the Institute?

I had heard about IHES almost exclusively through word of mouth. I doubt that everyone knows about IHES and its visiting program: I think that it would be important to make it more visible.