Related papers: Variations of BPS structure and a large rank limit
A version of the Donaldson-Thomas invariants of a Calabi-Yau threefold is proposed as a conjectural mathematical definition of the Gopakumar-Vafa invariants. These invariants have a local version, which is verified to satisfy the required…
We show that there exist flat surface bundles with closed leaves having non-trivial normal bundles. This leads us to compute the Abelianisation of surface diffeomorphism groups with marked points. We also extend a formula of Tsuboi that…
Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 5-folds. We find recursions for meeting numbers of genus 0 curves, and we determine the contributions of moving multiple covers of genus 0 curves to the…
We define Donaldson-Thomas invariants of Calabi-Yau orbifolds and we develop a topological vertex formalism for computing them. The basic combinatorial object is the orbifold vertex, a generating function for the number of 3D partitions…
We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact Calabi-Yau…
Gross-Pandharipande-Siebert have shown that the 2-dimensional Kontsevich-Soibelman scattering diagrams compute certain genus zero log Gromov-Witten invariants of log Calabi-Yau surfaces. We show that the $q$-refined 2-dimensional…
Let $X\subset \mathbb P^r$ be a projective factorial variety of dimension $3$, degree $n$, with at worst isolated singularities. Assume that the Picard group of $X$ is generated by the hyperplane section class. Let $C\subset X$ be a…
Generating functions $h_r(\tau)$ of D4-D2-D0 BPS indices, appearing in Calabi-Yau compactifications of type IIA string theory and identical to rank 0 Donaldson-Thomas invariants, are known to be higher depth mock modular forms satisfying a…
In a previous paper, we introduced quasi-BPS categories for moduli stacks of semistable Higgs bundles. Under a certain condition on the rank, Euler characteristic, and weight, the quasi-BPS categories (called BPS in this case) are…
The classical Beauville-Bogomolov Decomposition Theorem asserts that any compact K\"ahler manifold with numerically trivial canonical bundle admits an \'etale cover that decomposes into a product of a torus, and irreducible,…
This is the author's PhD thesis. Two main sections address various aspects of mirror symmetry for compact Calabi-Yau threefolds and the roles that classically modular varieties play in string theory compactifications. The main results…
In this paper, we propose a mathematical definition of a new ``numerical invariants" of Calabi--Yau 3-folds from stable sheaves of dimension one, which is motivated by the Gopakumar-Vafa conjecture in M-theory. Moreover, we show that for…
Topological string theory partition function gives rise to Gromov-Witten invariants, Donaldson-Thomas invariants and 5D BPS indices. Using the remodeling conjecture, which connects Topological Recursion with topological string theory for…
We study properties of the recently established refined topological recursion for some simple spectral curves associated to quadratic differentials. We prove explicit formulas for the free energy and Voros coefficients of the corresponding…
We study geometric engineering of Argyres-Douglas superconformal theories realized by type IIB strings propagating in singular Calabi-Yau threefolds. We use this construction to count the degeneracy of light BPS states under small…
We show that the stringy K\"ahler moduli space of a generic genus one curve of degree $N$, for $N\le 5$, is the $\Gamma_1(N)$ modular curve $X_1(N)$. This implies a correspondence between the cusps of the modular curves and certain large…
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…
We consider Donaldson-Witten theory on four-manifolds of the form $X=Y \times {\bf S}^1$ where $Y$ is a compact three-manifold. We show that there are interesting relations between the four-dimensional Donaldson invariants of $X$ and…
We examine the problem of counting bound states of BPS black holes on local Calabi-Yau threefolds which are fibrations over a Riemann surface by computing the partition function of q-deformed Yang-Mills theory on the Riemann surface. We…
We introduce limit categories for cotangent stacks of smooth stacks as an effective version of classical limits of categories of D-modules on them. We develop their general theory and pursue their relation with categories of D-modules. In…