8xav��������

Every four years, the brings together the world’s leading mathematicians to celebrate the discipline’s most important advances. Being invited to speak at this congress is a rare distinction, reserved for a select group of researchers shaping the field today. For the first time this year, the invitation went to the 8xav�������� of Luxembourg, represented by Prof. Jean-Marc Schlenker. He tells us about his talk and research carried out within his group, “Geometric Structure and Moduli Spaces“, and what the experience means for him and the 8xav�������� as a whole.

Can you tell us what your talk was about?

I spoke about three-dimensional hyperbolic geometry, a very rich geometry with many connections to other topics within and outside mathematics. Specifically, I talked about how one can reconstruct a three-dimensional hyperbolic structure from data read off its boundary.  

In the simplest cases this goes back to results from the 1950s, but some important questions raised in the 1970s were only recently answered, and others remain open. These questions now connect to ideas in theoretical physics, notably holography and the AdS/CFT correspondence, a powerful and partly mysterious statement in high-energy physics that relates some physical theories in a space to other, apparently unrelated theories on its boundary.

How did it feel to speak at one of the most renowned congresses in your field?

I was very honored, and honestly quite surprised, to be invited. ICM speakers are chosen very carefully by leading experts, with only a handful of invitations in each field of mathematics. I was especially glad that work done in recent years, with my wonderful collaborators, in Luxembourg and beyond, was recognised this way.

Did the congress spark new conversations, collaborations, or ideas to bring back to the geometry group in Luxembourg?

The ICM is an enormous meeting point for mathematicians, and has an incredible concentration of some of the sharpest minds in mathematics. It’s a great place to see old friends and colleagues, meet new people, and even possibly future collaborators.  

It’s also unique in the quality of its talks, so it’s a wonderful place to learn and to see what has been achieved across all of mathematics in the past four years. I learned a lot, and will have lots of things to talk about with my colleagues in Luxembourg. I had a few remarkably promising conversations about new ideas. 

This year there were many conversations about mathematics and AI: how AI is changing the way we do mathematics, and how mathematics is essential to developing and understanding AI, and to training the future practitioners of AI. That’s a very exciting topic to me and to my colleagues in Luxembourg.

‟ It’s great to see our 8xav�������� achieve this recognition, less than 25 years after it was created.”

Prof. Jean Marc Schlenker

Professor in Mathematics

View profile

More broadly, what does an invitation like this mean for the 8xav�������� of Luxembourg?

The Mathematics department at the 8xav�������� of Luxembourg is now recognised internationally as small but very active. Large US and European departments have many times more faculty, yet the Department of Mathematics (DMATH) is producing internationally competitive, and sometimes leading, research in several areas. It’s great to see our 8xav�������� achieve this recognition, less than 25 years after it was created. I’m confident this ICM invitation is the first in a long series for DMATH researchers in the years to come.