# Johan Asplund is looking forward to mathematical conversations

6 april 2021

Johan Asplund, who will soon defend his doctoral thesis in symplectic geometry, has received a postdoctoral position at Columbia University in New York, funded by the Knut and Alice Wallenberg Foundation. He is looking forward to exciting mathematical conversations and to finding himself as a mathematician.

Johan Asplund has always liked thinking in pictures. He remembers the time when he went to high school and heard about string theory which was said to exist in 11 dimensions.

“I became obsessed with trying to understand how to visualize a room with a dimension larger than 3,” he says.

But his interest in geometry became more concrete when he took the course Special Course in Mathematics I here at Uppsala University, with Magnus Jacobsson as lecturer.

“Among other things, we learned about knot theory and about different geometric spaces. Two years later, I did my bachelor thesis with my current supervisor Tobias Ekholm. The thesis was about links (a knot consisting of several circles) and flows of a certain type of vector field, and from then on I continued studying geometry.”

According to Johan Asplund, there is a widespread belief among young mathematics students that one must be a genius to do research in mathematics. But he thinks this is a myth that absolutely does not correspond to reality.

“The two most important qualities for success are motivation and hard work. Doctoral studies are great for people who are interested in immersing themselves more in mathematics.”

After the undergraduate education, Johan Asplund went on to doctoral studies in mathematics and now he has received a postdoctoral position at Columbia University in New York, funded by the Knut and Alice Wallenberg Foundation.

**What are you most looking forward to?**

“The change of environment. Even though I like it here and feel at home in Uppsala, it will be very exciting to move to New York and meet new people. I look forward to many exciting mathematical conversations with others, but I also look forward to finding myself as a mathematician.”

**What will the project be about?**

“In symplectic and contact geometry, there are special subspaces called Legendre subspaces and Lagrangian subspaces. My project is largely about better understanding subspaces that are allowed to be singular. Such subspaces can be associated with an algebraic object called the Chekanov-Eliashberg algebra. This algebraic object provides a mathematical invariant for the subspace; if you move around or deform the subspace, the invariant remains the same. It is basically a matter of deciding whether two seemingly different subspaces are equal or not, and such an invariant can be an important tool in deciding this”, says Johan Asplund and continues:

“The project is about understanding this Chekanov-Eliashberg algebra by chopping the subspace into smaller pieces and understanding the Chekanov-Eliashberg algebra for each small piece. The idea is that you can then understand the Chekanov-Eliashberg algebra for the whole subspace if you understand it for each small piece and how the pieces are put together."

*Alma Kirlic*

More about Johan Asplund's project on KAW's website (in Swedish)