Related papers: Wall-crossing, Hitchin Systems, and the WKB Approx…

In 1992, Hitchin used his theory of Higgs bundles to construct an important family of representations of the fundamental group of a closed, oriented surface of genus at least two into the split real form of a complex adjoint simple Lie…

N=2 Seiberg-Witten theories allow an interesting interplay between the Argyres-Douglas loci, singularity structures and wall-crossing formulae. In this paper we investigate this connection by first studying the singularity structures of…

We study mathematical structures on the moduli spaces of BPS structures of $\mathcal{N}=2$ theories. Guided by the realization of BPS structures within type IIB string theory on non-compact Calabi-Yau threefolds, we develop a notion of BPS…

It is well known that in string compactifications on toric Calabi-Yau manifolds one can introduce refined BPS invariants that carry information not only about the charge of the BPS state but also about the spin content. In this paper we…

On a compact connected Riemann surface $C$ of genus at least $2$, we construct Lagrangian correspondences between moduli spaces of rank-$n$ Higgs bundles (respectively, holomorphic connections) and the Hilbert schemes of points on $T^\ast…

We compute the Witten index of one-dimensional gauged linear sigma models with at least ${\mathcal N}=2$ supersymmetry. In the phase where the gauge group is broken to a finite group, the index is expressed as a certain residue integral. It…

The Bogomol'nyi-Prasad-Sommerfield (BPS) multiwall solutions are constructed in a massive Kahler nonlinear sigma model on the complex quadric surface, Q^N=SO(N+2)/[SO(N)\times SO(2)] in 3-dimensional space-time. The theory has a non-trivial…

For a fixed compact Riemann surface X, of genus at least 2, we count the number of connected components of the moduli space of maximal Higgs bundles over X for the hermitian groups $PSp(2n,R)$, $PSO^*(2n)$, $PSO_0(2,n)$ and $E_6^{-14}$.…

We find a simple relation between two-dimensional BPS N=2 superconformal blocks and bosonic Virasoro conformal blocks, which allows us to analyze the crossing equations for BPS 4-point functions in unitary (2,2) superconformal theories…

Cluster coordinates for a large class of Argyres-Douglas and asymptotical free theories are constructed using network on bordered Riemann surface. Such N = 2 theories are engineered using six dimensional (2, 0) theory on Riemann surface…

We establish a gluing construction for Higgs bundles over a connected sum of Riemann surfaces in terms of solutions to the $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-Hitchin equations using the linearization of a relevant elliptic operator.…

Over the last few years, wall-crossing for Bridgeland stability conditions has led to a large number of results in algebraic geometry, particular on birational geometry of moduli spaces. We illustrate some of the methods behind these result…

The wall crossing formula of Kontsevich and Soibelman gives an implicit relation between the BPS indices on two sides of the wall of marginal stability by equating two symplectomorphisms constructed from the indices on two sides of the…

We give a formula comparing the E-series of the moduli stacks of rank 2 degree 0 semistable Higgs bundles in genus $g \geq 2$ to intersection E-polynomials of its coarse moduli space. A parellel formula holds in various 2-Calabi-Yau…

Using the Morse-theoretic techniques introduced by Hitchin, we prove that the moduli space of $\Sp(2p,2q)$-Higgs bundles over a compact Riemann surface of genus $g\geq 2$ is connected. In particular, this implies that the moduli space of…

BPS vortex systems on closed Riemann surfaces with arbitrary genus are embedded into two-dimensional supersymmetric Yang-Mills theory with matters. We turn on a background R-gauge fields to keep half of rigid supersymmetry (topological…

The ${\cal N}=1$ SUSY nonlinear sigma models in four spacetime dimensions are studied to obtain BPS walls and junctions. A nonlinear sigma model with a single chiral scalar superfield is found which has a moduli space of the topology of…

We investigate the wall-crossing behavior as Bridgeland moduli spaces for some Simpson moduli spaces of Gieseker-semistable torsion sheaves on $\mathbb{P}^1\times \mathbb{P}^1$ with linear Hilbert polynomial. In particular, we recover some…

This thesis contains work which appeared in several papers. Additionally to the results in the papers it contains a detailed introduction and some further proofs and remarks. The dissertation gives a description of the topology and…

Four-dimensional massive N=2 nonlinear sigma models and BPS wall solutions are studied in the off-shell harmonic superspace approach in which N=2 supersymmetry is manifest. The general nonlinear sigma model can be described by an analytic…