Joé Brendel

Hi I’m Joé, I am a mathematician working in symplectic geometry.

I am currently an SNF Ambizione fellow at ETH Zürich hosted by Paul Biran. I am co-organizer of the ETH symplectic seminar.

My research focuses mostly on the interactions between symplectic geometry and integrable Hamiltonian systems. In particular, I often use toric and almost toric fibrations to study certain properties of symplectic manifolds. Here is a question I particularly like and which I think deserves much more attention: Take your favourite integrable Hamiltonian system. As all integrable systems do, it contains a whole bunch of Arnol’d–Liouville tori, and those are all Lagrangian! Which of them can be mapped to one another by a Hamiltonian isotopy of the ambient space? This is a (somewhat humble, but also somewhat manageable) special case of the general classification question of Lagrangian submanifolds, which is wide open in general.

Before my current position, I was Postdoc at Tel Aviv University under the mentorship of Leonid Polterovich and Yael Karshon. Even before that, I did a PhD under the guidance of Felix Schlenk at Université de Neuchâtel, which I defended in 2022.

Here is my CV.