Since September 2024, I am a PhD student of Johan Martens at the University of Edinburgh, funded by the EPSRC Centre for Doctoral Training in Algebra, Geometry, and Quantum Fields. I did my masters under the supervision of Florent Schaffhauser.
My masters thesis was on canonical reductions of principal bundles, which is now a preprint with Florent Schaffhauser. It generalizes Harder-Narasimhan filtrations to symplectic and orthogonal bundles. My bachelors thesis was on the Mitchell embedding theorem.
My email is ERoth2 [at] ed [dot] ac [dot] uk, but I also use E [dot] Roth [at] sms [dot] ed [dot] ac [dot] uk.
Preprints and papers
Jordan-Hölder theory for complementary polyhedra and moduli of parahoric Higgs torsors (2026), on arxiv.
Harder-Narasimhan filtrations of decorated vector bundles (2025), on arxiv, with Florent Schaffhauser.
Other material
Poster on my Jordan-Hölder theory paper.
QuiverCombinatoricsTools, a SageMath package for computing symplectic leaves of quiver varieties, joint with Tudor Caba and Mia Lam.
Nonabelian Hodge theory, a report joint with Shing Tak Lam.
Bachelor thesis on the Mitchell embedding theorem.