Related papers: Calabi-Yau Geometries: Algorithms, Databases, and …
By introducing a more flexible notion of convexity, we obtain a new Omori-Yau maximum principle for harmonic maps. In the spirit of the Calabi-Yau conjectures, this principle is more suitable for studying the unboundedness of certain…
Calabi-Yau algebras are particularly symmetric differential graded algebras. There is a construction called `Calabi-Yau completion' which produces a canonical Calabi-Yau algebra from any homologically smooth dg algebra. Homologically smooth…
During the last years we have generated a large number of data related to Calabi-Yau hypersurfaces in toric varieties which can be described by reflexive polyhedra. We classified all reflexive polyhedra in three dimensions leading to K3…
We develop a new and efficient method to systematically analyse four dimensional effective supergravities which descend from flux compactifications. The issue of finding vacua of such systems, both supersymmetric and non-supersymmetric, is…
We study geometric transitions on Calabi- Yau manifolds from the perspective of the $B$ model. Looking toward physically motivated predictions, it is shown that the traditional conifold transition is too simple a case to yield meaningful…
While Calabi-Yau hypersurfaces in toric ambient spaces provide a huge number of examples, theoretical considerations as well as applications to string phenomenology often suggest a broader perspective. With even the question of finiteness…
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…
This is a survey article on mirror symmetry and Fourier-Mukai partners of Calabi-Yau threefolds with Picard number one based on recent works by the authors [HoTa1,2,3,4]. For completeness, mirror symmetry and Fourier-Mukai partners of K3…
We present a generalization of the complete intersection in products of projective space (CICY) construction of Calabi-Yau manifolds. CICY three-folds and four-folds have been studied extensively in the physics literature. Their utility…
Kreuzer and Skarke famously produced the largest known database of Calabi-Yau threefolds by providing a complete construction of all 473,800,776 reflexive polyhedra that exist in four dimensions. These polyhedra describe the singular limits…
We revisit the classic database of weighted-P4s which admit Calabi-Yau 3-fold hypersurfaces equipped with a diverse set of tools from the machine-learning toolbox. Unsupervised techniques identify an unanticipated almost linear dependence…
We review advancements in deep learning techniques for complete intersection Calabi-Yau (CICY) 3- and 4-folds, with the aim of understanding better how to handle algebraic topological data with machine learning. We first discuss…
A construction of Calabi-Yaus as quotients of products of lower-dimensional spaces in the context of weighted hypersurfaces is discussed, including desingularisation. The construction leads to Calabi-Yaus which have a fiber structure, in…
The deformation approach of arXiv:2104.07816 for computing zeta functions of one-parameter Calabi-Yau threefolds is generalised to cover also multiparameter manifolds. Consideration of the multiparameter case requires the development of an…
Large N geometric transitions and the Dijkgraaf-Vafa conjecture suggest a deep relationship between the sum over planar diagrams and Calabi-Yau threefolds. We explore this correspondence in details, explaining how to construct the…
We find that for many Calabi-Yau threefolds with elliptic or genus one fibrations mirror symmetry factorizes between the fiber and the base of the fibration. In the simplest examples, the generic CY elliptic fibration over any toric base…
It was proposed that the Calabi-Yau geometry can be intrinsically connected with some new symmetries, some new algebras. In order to do this it has been analyzed the graphs constructed from K3-fibre CY_d (d \geq 3) reflexive polyhedra. The…
This is the sequel to arXiv:math/0001089. In this paper, we complete the promised description of moduli of abelian surfaces of low degree, covering the cases of degree (1,12), (1,14), (1,16), (1,18) and (1,20). In each case, we describe…
In this paper, we initiate the study of the 2d F-theory landscape based on compact elliptic Calabi-Yau fivefolds. In particular, we determine the boundary models of the landscape using Calabi-Yau fivefolds with the largest known Hodge…
These are introductory lecture notes on complex geometry, Calabi-Yau manifolds and toric geometry. We first define basic concepts of complex and Kahler geometry. We then proceed with an analysis of various definitions of Calabi-Yau…