Thema der Dissertation:
Donaldson-Uhlenbeck type moduli spaces for principal bundles over higher dimensional manifolds Thema der Disputation:
On a Conjecture of Gaiotto
Donaldson-Uhlenbeck type moduli spaces for principal bundles over higher dimensional manifolds Thema der Disputation:
On a Conjecture of Gaiotto
Abstract: Let $E$ be a vector bundle of rank $n$ over a smooth projective algebraic curve of genus $g$, denoted by $C$. Further, let $(E,\phi)$ be a stable Higgs bundle in the Dolbeault moduli space and $\nabla$ a connection on $E$. Locally, the Higgs field $\phi$ and the $1$-form associated to $\nabla$, denoted by $A$, are both $r\times r$ matrices of $1$-forms, but satisfying different with respect to the transition functions of the vector bundle. It is not obvious, starting from a Higgs bundle $(E,\phi)\in\mathcal{M}_{Dol}$, how to obtain a connection $(V,\nabla)\in\mathcal{M}_{De Rham}$ in the De Rham moduli space. Gaiotto's conjecture constructs a connection $\nabla$ as the scaling limit of a $2$-parameter family of connections that arises naturally from a stable Higgs bundle $(E,\phi)$.
The goal of this document is to present all the required elements in the conjecture and finally to give the special properties that turn the limiting connection into an oper.
The goal of this document is to present all the required elements in the conjecture and finally to give the special properties that turn the limiting connection into an oper.
Time & Location
Oct 29, 2024 | 04:00 PM
Seminarraum 007/008
(Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin)