By Matteo Bechere – April 2026
In the fall of 2025 I moved to Antibes, a town close to Nice in the southeast of France, to join the Aromath team at Inria. I was to spend 10 months, under the supervision of Bernard Mourrain, to work on my PhD project. So far I am 6 months in. These have been among the most humbling, yet instructive and joyful months of my life. I love the small, close-knit group of young researchers; it is invaluable being surrounded by such great people willing to help each other, whether it is a math question, or a coffee to be shared. I am very grateful for this.
Math-wise, I was immediately surprised to realize that algebraic geometry was going to be such a central and powerful tool for studying tensor decomposition problems, I severely underestimated them in the past. At the beginning I didn’t know it, but these new methods (new for me, but not for everyone else) were there to stay. In fact, I spent a good chunk of the first months catching up with classical facts and apolarity theory 101: it was really necessary. With newfound understanding and helpful guidance, I was able to generalize a sub-project I first got into during spring 2025, about Hankel tensors. In December 2025 I started writing down my notes in a draft which is constantly evolving and being refined, but I am confident it will be out in the coming weeks, together with a Julia package supporting the theoretical tensor decomposition findings we have. The bit of coding experience was a new and fun challenge that I totally did not anticipate going into 2026… and who knows what else awaits me!
Hoping whatever is awaiting you is very awesome, I sign off.