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We systematically construct a class of two-dimensional $(2,2)$ supersymmetric gauged linear sigma models with phases in which a continuous subgroup of the gauge group is totally unbroken. We study some of their properties by employing a…
Understanding which effective field theories are consistent with an ultraviolet completion in quantum gravity is an important theoretical question. Therefore, it is important to know the structure of the 4D effective theory associated with…
We attempt to define a new invariant I of (almost) Calabi-Yau 3-folds M, by counting special Lagrangian rational homology 3-spheres N in M in each 3-homology class, with a certain weight w(N) depending on the topology of N. This is…
We study the quasimap invariants of elliptic and K3 fibrations. Oberdieck and Pixton conjectured that the Gromov-Witten potentials of elliptic fibrations are quasi-modular forms. Analogously, we propose similar conjecture for the quasimap…
The study of the geometry of Calabi-Yau fourfolds is relevant for compactifications of string theory, M-theory, and F-theory to various dimensions. In the first part of this thesis, we study the action of mirror symmetry on two-dimensional…
We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We prove this conjecture in several special…
We present a new class of dualities relating non-geometric Calabi-Yau compactifications of type II string theory to T-fold compactifications of the heterotic string, both preserving four-dimensional $\mathcal{N}=2$ supersymmetry. The…
We compute exactly the partition function of two dimensional N=(2,2) gauge theories on S^2 and show that it admits two dual descriptions: either as an integral over the Coulomb branch or as a sum over vortex and anti-vortex excitations on…
In a previous paper, we presented a matrix model reproducing the topological string partition function on an arbitrary given toric Calabi-Yau manifold. Here, we study the spectral curve of our matrix model and thus derive, upon imposing…
Let $(F,J,\omega)$ be an almost K\"ahler manifold, $\alpha$ a $J$-holomorphic action of a compact Lie group $\hat K$ on $F$, and $K$ a closed normal subgroup of $\hat K$ which leaves $\omega$ invariant. We introduce gauge theoretical…
We study the enumerative geometry of stable maps to Calabi-Yau 5-folds $Z$ with a group action preserving the Calabi-Yau form. In the central case $Z=X \times \mathbb{C}^2$, where $X$ is a Calabi-Yau 3-fold with a group action scaling the…
Gauging isometries of four-dimensional N=2 supergravity theories yields an N=2 supersymmetric theory with a scalar potential. In this note, we study the well-known constraints for four-dimensional N=2 Minkowski vacua of such theories. We…
In this work we analyze F-theory and Type IIB orientifold compactifications to study $\alpha '$-corrections to the four-dimensional, $\mathcal{N} = 1$ effective actions. In particular, we obtain corrections to the K\"ahlermoduli space…
Mirror symmetry gives predictions for the genus zero Gromov-Witten invariants of a closed Calabi--Yau variety in terms of period integrals on a mirror family of Calabi-Yau varieties. We deduce an analogous mirror theorem for the open…
Achieving full moduli stabilisation in type IIB string compactifications for generic Calabi-Yau threefolds with hundreds of K\"ahler moduli is notoriously hard. This is due not just to the very fast increase of the computational complexity…
Modular invariance is known to constrain the spectrum of 2d conformal field theories. We investigate this constraint systematically, using the linear functional method to put new improved upper bounds on the lowest gap in the spectrum. We…
The predictions of the Mirror Symmetry are extended in dimensions n>3 and are proven for projective complete intersections Calabi-Yau varieties. Precisely, we prove that the total collection of rational Gromov-Witten invariants of such…
We prove the KKV conjecture expressing Gromov-Witten invariants of K3 surfaces in terms of modular forms. Our results apply in every genus and for every curve class. The proof uses the Gromov-Witten/Pairs correspondence for K3-fibered…
This is the second part of the project toward an effective algorithm to evaluate all genus Gromov-Witten invariants of quintic Calabi-Yau threefolds. In this paper, the localization formula is derived, and algorithms toward evaluating these…
We investigate mirror symmetry for toric Calabi-Yau manifolds from the perspective of the SYZ conjecture. Starting with a non-toric special Lagrangian torus fibration on a toric Calabi-Yau manifold $X$, we construct a complex manifold…