相关论文: Classifying divisor topologies for string phenomen…

The study of topological band structures have sparked prominent research interest the past decade, culminating in the recent formulation of rather prolific classification schemes that encapsulate a large fraction of phases and features.…

We prove the Integral Hodge Conjecture for curve classes on smooth varieties of dimension at least three with nef anticanonical divisor constructed as a complete intersection of ample hypersurfaces in a smooth toric variety. In particular,…

We determine all toric phases for the $2d$ $(0,2)$ theories on D1-branes probing the complex cones over the 18 smooth Fano 3-folds, whose toric diagrams correspond to the regular reflexive polytopes in 3 dimensions. These results…

We present a complete intersection Calabi-Yau manifold Y that has Euler number -72 and which admits free actions by two groups of automorphisms of order 12. These are the cyclic group Z_12 and the non-Abelian dicyclic group Dic_3. The…

We investigate the modularity constraints on the generating series $h_r(\tau)$ of BPS indices counting D4-D2-D0 bound states with fixed D4-brane charge $r$ in type IIA string theory compactified on complete intersection Calabi-Yau…

Heterotic string models in $4$-dimensions are the hybrid theories of a left-moving $N=1$ fermionic string whose additional $6$-dimensions are compactified on a $N=2$ SCFT theory with the central charge $9$, and a right-moving bosonic…

In this paper, we will study the arithmetic geometry of rank-2 attractors, which are Calabi-Yau threefolds whose Hodge structures admit interesting splits. We will develop methods to analyze the algebraic de Rham cohomologies of rank-2…

Integrals of characteristic classes of tautological sheaves on the Hilbert scheme of points on a surface frequently arise in enumerative problems. We use the K-theoretic Donaldson-Thomas theory of certain toric Calabi-Yau threefolds to…

The moduli space of multiply-connected Calabi-Yau threefolds is shown to contain codimension-one loci on which the corresponding variety develops a certain type of hyperquotient singularity. These have local descriptions as discrete…

We investigate the compactification of D=11 supergravity to D=5,4,3, on compact manifolds of holonomy $SU(3)$ (Calabi-Yau), $G_2$, and $Spin(7)$, respectively, making use of examples of the latter two cases found recently by Joyce. In each…

We obtain a detailed classification for a class of non-simply connected Calabi-Yau threefolds which are of potential interest for a wide range of problems in string phenomenology. These threefolds arise as quotients of Schoen's Calabi-Yau…

We develop some methods to construct normal crossing varieties whose dual complexes are two-dimensional, which are smoothable to Calabi--Yau threefolds. We calculate topological invariants of smoothed Calabi--Yau threefolds and show that…

This thesis aims at concluding the classification results for topological phases with symmetry in 2+1 dimensions. The main result is that topological phases are classified by a triple of unitary braided fusion categories $\mathcal…

In this paper we find an explicit formula for the number of topologically different ramified coverings $C\to\CP^1$ (C is a compact Riemann surface of genus g) with only one complicated branching point in terms of Hodge integrals over the…

We develop a combinatorial approach to the construction of general smooth compact base surfaces that support elliptic Calabi-Yau threefolds. This extends previous analyses that have relied on toric or semi-toric structure. The resulting…

We study cohomologies and Hodge theory for complex manifolds with twisted differentials. In particular, we get another cohomological obstruction for manifolds in class $\mathcal{C}$ of Fujiki. We give a Hodge-theoretical proof of the…

We show that there is a natural perverse sheaf on the moduli space of semistable sheaves on a smooth projective Calabi-Yau 3-fold which is locally the perverse sheaf of vanishing cycles for a local Chern-Simons functional. This gives us a…

We propose conjectural semiorthogonal decompositions for Fano schemes of linear subspaces on intersections of two quadrics, in terms of symmetric powers of the associated hyperelliptic (resp. stacky) curve. When the intersection is…

We consider type IIA string theory on a Calabi-Yau 2-fold with D6-branes wrapping 2-cycles in the 2-fold. We find a complete set of conditions on the supergravity solution for any given wrapped brane configuration in terms of SU(2)…

We investigate holomorphic anomalies of partition functions underlying string compactifications on Calabi-Yau fourfolds with background fluxes. For elliptic fourfolds the partition functions have an alternative interpretation as elliptic…