From September 2024, I am a PhD student of Johan Martens at the University of Edinburgh. I was previously at the University of Heidelberg, where I completed my masters under the supervision of Florent Schaffhauser.
In 2025, I thought about nonabelian Hodge theory, moduli spaces of Higgs bundles, vector bundles, and principal bundles, along with their stability conditions. Now, I think about complentary polyhedra to generalize Jordan-Hölder filtrations to parahoric Higgs torsors.
My masters thesis was on canonical reductions of principal bundles, which is now a preprint with Florent Schaffhauser. It explains how Harder-Narasimhan filtrations of vector bundles can be generalized to principal bundles, and works out some examples (symplectic and special orthogonal versions).
My bachelors thesis was on the Mitchell embedding theorem, explaining how the Yoneda embedding can be used to embed certain abelian categories into module categories.
Harder-Narasimhan filtrations of decorated vector bundles (2025), on arxiv, with Florent Schaffhauser.
My email is E [dot] Roth2 [at] ed.ac.uk.
I also use E [dot] Roth [at] sms.ed.ac.uk.