# Members & Former Members

## M.Ed. Maximilian Holdt

### Researcher

Christian-Albrechts-Universität zu Kiel

E-mail: holdt(at)math.uni-kiel.de
Telephone: 0431/8803669
Homepage: https://www.math.uni-kiel.de/geometrie/d…

## Project

77Asymptotic geometry of the Higgs bundle moduli space II

## Publications within SPP2026

We use the theory of Gaiotto, Moore and Neitzke to construct a set of Darboux coordinates on the moduli space $$\mathcal{M}$$ of weakly parabolic $$SL(2,\mathbb{C})$$-Higgs bundles. For generic Higgs bundles$$(\mathcal{E},R\Phi)$$ with $$R\gg 0$$ the coordinates are shown to be dominated by a leading term that is given by the coordinates for a corresponding simpler space of limiting configurations and we prove that the deviation from the limiting term is given by a remainder that is exponentially suppressed in $$R$$.

We then use this result to solve an associated Riemann-Hilbert problem and construct a twistorial hyperkähler metric $$g_{\text{twist}}$$ on $$\mathcal{M}$$. Comparing this metric to the simpler semiflat metric $$g_{\text{sf}}$$, we show that their difference is $$g_{\text{twist}}-g_{\text{sf}}=O\left(e^{-\mu R}\right)$$, where $$\mu$$ is a minimal period of the determinant of the Higgs field.