6 papers
Universal Hitchin moduli spaces
Luis Álvarez-Cónsul, Mario Garcia-Fernandez, Oscar García-Prada +1
We study metric aspects of the universal moduli space of solutions to Hitchin's equations as the complex structure varies over the Teichmüller space of a closed s…
Gandalf the Red: Adaptive Security for LLMs
Niklas Pfister, Václav Volhejn, Manuel Knott +23
Current evaluations of defenses against prompt attacks in large language model (LLM) applications often overlook two critical factors: the dynamic nature of adversarial behavior an…
The hyperkähler metric on the almost-Fuchsian moduli space
Samuel Trautwein
Donaldon constructed a hyperkähler moduli space associated to a closed oriented surface with . This embeds naturally into the cotangent…
Complex structures, moment maps, and the Ricci form (Extended Version)
Oscar Garcia-Prada, Dietmar Salamon, Samuel Trautwein
The Ricci form is a moment map for the action of the group of exact volume preserving diffeomorphisms on the space of almost complex structures. This observation yields a new appro…
Convergence of the Yang-Mills-Higgs flow on gauged holomorphic maps and applications
Samuel Trautwein
The symplectic vortex equations admit a variational description as global minimum of the Yang-Mills-Higgs functional. We study its negative gradient flow on holomorphic pairs $(A,u…
A survey of the GIT picture for the Yang-Mills equation over Riemann surfaces
Samuel Trautwein
The purpose of this paper is to give a self-contained exposition of the Atiyah-Bott picture for the Yang-Mills equation over Riemann surfaces with an emphasis on the analogy to fin…