# First children, then career

Kathryn Hess is a mathematician with a foot in neuroscience

Her favorite number is 7, and her professional life revolves around numbers and shapes: Kathryn Hess teaches and conducts research at the École polytechnique fédérale de Lausanne (EPFL) in topology, the mathematics of shape and connectivity. As a mother of four children, her academic career has its own unconventional arc.

When Kathryn Hess came to Switzerland in 1991, she was 24 years old. Two years earlier, the American-born researcher had earned a doctorate in mathematics at the prestigious Massachusetts Institute of Technology (MIT) in Cambridge, USA, at an age when others finish their undergraduate studies. It was also at MIT that she met her husband, a Swiss national, with whom she eventually moved to western Switzerland, where she found her new academic home at EPFL. In Lausanne, she first became an assistant, then was given a permanent position in 1998, followed a year later by the title of professor. In 2015 she became an associate professor and finally a full professor in 2019. Kathryn Hess was then 52 years old, a relatively advanced age for this career step.

**A special career pattern**

"I had a fairly unusual career path," the scientist tells us in the video chat. The reason for this is the four boys she gave birth to between 1992 and 2002 and then raised with her husband. When asked how raising four children has influenced her academic career, Kathryn Hess breaks into a cheerful laugh, as if to say: "I can tell you a lot about that!" Then she says: "The four children meant that I was much less productive in research for ten or fifteen years! If you have young children and want to spend time with them, there's no other way, because there are only 24 hours in a day." And after a pause, she adds, "I don't regret it at all!"

But that's only one side of Kathryn Hess' unusual academic career. For when the youngest boy was old enough that he no longer needed so much of his mother's immediate attention, something unexpected happened: "All the energy for research from those ten, fifteen years was stored up in me, and that energy has now really exploded. What followed was an incredibly creative and productive time," Kathryn Hess recalls. Anyone who wants to understand what she means can take a look at the researcher's CV: The number of scientific publications skyrockets. In the years that followed, she supervised a good 20 doctoral students and just as many postdocs. In addition, she gives 20 to 30 talks a year. All this, of course, in addition to teaching at EPFL.

**Researching homotopies**

Over the past few years, Kathryn Hess has given so many talks that she can almost appreciate the restrictions due to the Corona pandemic. "The quieter Corona months give me time to think, and I've made good progress on various projects," she reports. "Often, you've been mulling over a math problem for a long time, but you're still missing the key element to solving it. Then when I allow myself to relax, take a walk or have a meal, suddenly it goes 'Boom!' - and the solution is there!"

What those solutions look like is not easy for non-mathematicians to understand. That's because topology, Kathryn Hess's focus, is not taught in schools. Among other things, topology deals with homotopies, which describe the continuous deformation of one geometric object with any number of dimensions into another. Topology describes such deformations in mathematical language and formulates the associated laws, such as the necessity that any continuous deformation of a donut (formed from plasticine) have exactly one hole. The hole is an 'invariant', as mathematicians say, a property that does not change with deformation.

**Applications in neuroscience**

The study of homotopies is 'pure' mathematics. But the mathematical descriptions have tangible practical applications. For example, they help in materials science in the search for so-called nanoporous crystalline materials that are particularly efficient at storing greenhouse gases. A graduate student of Kathryn Hess uses topological methods for genetic analysis of cancer cells. The lab itself specializes in applications in neuroscience: At her initiative, among others, a new field of research has emerged here in recent years that uses topology, for example, to describe signal transmission in nerve cells of the brain.

It is not surprising that Kathryn Hess is now working across disciplinary boundaries. At the age of ten, she had already developed a fascination for stars and their life cycles, and initially wanted to become an astronomer. Then, during her studies, she switched to mathematics. She once told how that came about: "I took a course in electricity and magnetism with the only woman professor who was in the department at the time. In the middle of the semester, the professor called me into her office and told me that she thought my success in the physics course was mainly due to my mathematical talent, and less to a good intuition for physical facts. I realized she was right."

**Communicating good content well**

Kathryn Hess was encouraged by her parents as a girl; it is no coincidence that one of her sisters is a physicist and the other a chemist. She attended a course for young math talents set up by her parents, based on the program developed at the well-known Johns Hopkins University in Baltimore, which also served as the blueprint for the Euler course that the scientist founded at EPFL a decade ago. For adult female scientists, Kathryn Hess was one of the founders of a women's research network in the field of topology. She also keeps an eye on the next generation: around half of her doctoral students are women.

When asked for advice for aspiring scientists, Kathryn Hess, an eloquent university lecturer, says: "Learn to give good talks!" It's not enough to have fresh ideas, she says; you have to be able to pass them on. She also has tips on how to do that: Take advantage of every opportunity that comes your way! Practice in front of colleagues of the same age! Ask for feedback! Put yourself in the listeners' shoes! Kathryn Hess believes that female junior researchers speak at least as well as their male colleagues: "In my experience, women are excellent speakers!"

*Author: Benedikt Vogel*

*Portrait #3 of Women in science in the fields of MAP (2021)*