Callum R. Brodie
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View article: Cohomology Chambers on Complex Surfaces and Elliptically Fibered Calabi–Yau Three-Folds
Cohomology Chambers on Complex Surfaces and Elliptically Fibered Calabi–Yau Three-Folds Open
We determine several classes of smooth complex projective surfaces on which Zariski decomposition can be combined with vanishing theorems to yield cohomology formulae for all line bundles. The obtained formulae express cohomologies in term…
View article: Branes and bundles through conifold transitions and dualities in heterotic string theory
Branes and bundles through conifold transitions and dualities in heterotic string theory Open
The authors study transitions of particular string compactifications (heterotic theories with $N=1$ supersymmetry in four dimensions) that change the topology and other nonpertubative properties of the internal manifold. This is part of tr…
View article: Branes and Bundles through Conifold Transitions and Dualities in Heterotic String Theory
Branes and Bundles through Conifold Transitions and Dualities in Heterotic String Theory Open
Geometric transitions between Calabi-Yau manifolds have proven to be a powerful tool in exploring the intricate and interconnected vacuum structure of string compactifications. However, their role in N=1, 4-dimensional string compactificat…
View article: Flops for Complete Intersection Calabi-Yau Threefolds
Flops for Complete Intersection Calabi-Yau Threefolds Open
We study flops of Calabi-Yau threefolds realised as Kaehler-favourable complete intersections in products of projective spaces (CICYs) and identify two different types. The existence and the type of the flops can be recognised from the con…
View article: Recent Developments in Line Bundle Cohomology and Applications to String Phenomenology
Recent Developments in Line Bundle Cohomology and Applications to String Phenomenology Open
Vector bundle cohomology represents a key ingredient for string phenomenology, being associated with the massless spectrum arising in string compactifications on smooth compact manifolds. Although standard algorithmic techniques exist for …
View article: Swampland conjectures and infinite flop chains
Swampland conjectures and infinite flop chains Open
We investigate swampland conjectures for quantum gravity in the context of M-theory compactified on Calabi-Yau threefolds which admit infinite sequences of flops. Naively, the moduli space of such compactifications contains paths of arbitr…
View article: Topological Formulae for the Zeroth Cohomology of Line Bundles on del Pezzo and Hirzebruch Surfaces
Topological Formulae for the Zeroth Cohomology of Line Bundles on del Pezzo and Hirzebruch Surfaces Open
We show that the zeroth cohomology of effective line bundles on del Pezzo and Hirzebruch surfaces can always be computed in terms of a topological index.
View article: Flops, Gromov-Witten Invariants and Symmetries of Line Bundle Cohomology\n on Calabi-Yau Three-folds
Flops, Gromov-Witten Invariants and Symmetries of Line Bundle Cohomology\n on Calabi-Yau Three-folds Open
The zeroth line bundle cohomology on Calabi-Yau three-folds encodes\ninformation about the existence of flop transitions and the genus zero\nGromov-Witten invariants. We illustrate this claim by studying several Picard\nnumber 2 Calabi-Yau…
View article: Cohomology Chambers on Complex Surfaces and Elliptically Fibered Calabi-Yau Three-folds
Cohomology Chambers on Complex Surfaces and Elliptically Fibered Calabi-Yau Three-folds Open
We determine several classes of smooth complex projective surfaces on which Zariski decomposition can be combined with vanishing theorems to yield cohomology formulae for all line bundles. The obtained formulae express cohomologies in term…
View article: Topological Formulae for the Zeroth Cohomology of Line Bundles on Surfaces
Topological Formulae for the Zeroth Cohomology of Line Bundles on Surfaces Open
We identify a set of transforms on the Picard lattice of non-singular complex
projective surfaces that map effective line bundles to nef line bundles, while
preserving the dimension of the zeroth cohomology. These transforms can often
be u…
View article: Machine learning line bundle cohomology
Machine learning line bundle cohomology Open
We investigate different approaches to machine learning of line bundle cohomology on complex surfaces as well as on Calabi-Yau three-folds. Standard function learning based on simple fully connected networks with logistic sigmoids is revie…
View article: Aspects of string model building and heterotic/F-theory duality
Aspects of string model building and heterotic/F-theory duality Open
In this thesis, we develop tools for model building in heterotic string theory and F-theory. We focus in particular on heterotic line bundle models and their F-theory duals. The first reason for this is that line bundle models are particul…
View article: NS5-branes and line bundles in heterotic/F-theory duality
NS5-branes and line bundles in heterotic/F-theory duality Open
We study F-theory duals of heterotic line bundle models on elliptically\nfibered Calabi-Yau threefolds. These models necessarily contain NS5-branes\nwhich are geometrised in the dual F-theory compactifications. We initiate a\nsystematic st…