"It was like a game,” Pol said. “I've always enjoyed the challenge of mathematics."

She is particularly fascinated by the interaction of algebraic equations with the physical shapes of geometry.

“One of things that I like in mathematics is that sometimes you have deep relations between objects that at first glance look very different,” Pol said.

Now, as an Alexander von Humboldt Fellow at Technical University of Kaiserslautern working with Professor Mathias Schulze, she is tackling much more complicated puzzles — singularities.

Algebraic equations, once solved, can translate into geometric objects, including lines, circles, and surfaces. Sometimes the solutions translate into a smooth geometric object, but sometimes there are some points where, for example, an edge, a corner or a spike appear -- this is a singularity. For example, a single spike in a smooth curve is called a cusp singularity. These singular points have to be taken into account to fully understand these objects as well as the equations that gave rise to them.

Pol and her collaborators at TUK, University of Western Ontario in Canada and Purdue University in the U.S. are seeking to understand the properties of particular algebraic equations called configuration polynomials. These polynomials appear in the study of graphs called Feynman graphs, which are used by physicists to describe interactions between particles.

Pol first became interested in singularities while studying mathematics at the University of Angers. It combined the aspects of math that she likes most: algebra and geometry. She went on to earn a PhD in singularity theory. For part of her thesis, she visited TUK for a week to work with Professor Schulze, so it was a natural step to return to TUK for a two-year post doc, thanks to the Humboldt Fellowship.

Being at TUK has offered several opportunities to collaborate with others who are working on similar questions. An open-source computer algebra software, called SINGULAR, that Pol uses regularly to run computations was developed by a TUK-led team. While her tools are mostly a pen and paper, or chalk and a blackboard, the computer program can save a lot of time running calculations.

“It would take me several days probably if I wanted to compute them by hand,” Pol said. “Using SINGULAR is very useful and I am very happy to be here to learn more about it.”

Pol says she feels very lucky to obtain the Humboldt Fellowship. Besides making it possible to work at TUK, she appreciates the events that the Humboldt Foundation organizes to enable the fellows from all over the world to meet and network.

She notes that she didn’t speak a word of German when she arrived in October 2018. But she is grateful that the TUK community was patient and helpful as she learns the language. She also enjoys the Rhineland-Palatinate’s quiet atmosphere that allows her to stay focused.

“Kaiserslautern is a very nice place, I feel good here,” she said.

This is Pol’s second international fellowship. She also received a Japan Society for the Promotion of Science (JSPS) Fellowship for a postdoc at Hokkaido University in Sapporo, Japan. Living and working overseas has been eye-opening.

“Sometimes I am anxious about it because I don’t know what to expect, but in the end it is always very interesting to meet different people and discover other cultures,” Pol said.

Her lab in Japan had researchers from all over the world, including Italy, Vietnam and China. Similarly at TUK, she has developed collaboration with researchers from several countries, including Canada, USA and Germany.

In her free time, Pol likes to bake. Whipping up a cheesecake or pan of muffins helps take her mind off math, at least until the oven timer buzzes.

“When I am cooking, I do not think about anything else,” she said. “Sometimes it is good to make a stop; my ideas are often clearer after.”