## On the Variational Theory of Yang-Mills-Higgs Energies and the Structure of the Singular Set of $\mathbb{Z}$$_{2}$-Harmonic Spinors

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This dissertation investigates Yang-Mills-Higgs energies and

In the first part, we present joint work with Alessandro Pigati and Daniel Stern on the variational theory of the self-dual U(1)-Yang-Mills-Higgs functionals on a closed Riemannian manifold (M,g). This natural family of energies associated with sections u: M → L and metric connections ∇ of Hermitian line bundles has long been studied in differential geometry and theoretical physics. We show how its variational theory is related to the one of the (n − 2)-area functional by establishing a Γ-convergence result in the spirit of Modica and Mortola. With this in hand, we study the comparison between the corresponding min-max theories. Therefore, we relate the classical theory for C

In the second part of the dissertation, we focus on the notion of