Martin Bies
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FTheoryTools: Advancing Computational Capabilities for F‐Theory Research Open
A primary goal of string phenomenology is to identify realistic four‐dimensional physics within the landscape of string theory solutions. In F‐theory, such solutions are encoded in the geometry of singular elliptic fibrations, whose study …
FTheoryTools: Advancing Computational Capabilities for F-Theory Research Open
A primary goal of string phenomenology is to identify realistic four-dimensional physics within the landscape of string theory solutions. In F-theory, such solutions are encoded in the geometry of singular elliptic fibrations, whose study …
Improved statistics for F-theory standard models Open
Much of the analysis of F-theory-based Standard Models boils down to computing cohomologies of line bundles on matter curves. By varying parameters one can degenerate such matter curves to singular ones, typically with many nodes, where th…
Machine learning and algebraic approaches towards complete matter spectra in 4d F-theory Open
Motivated by engineering vector-like (Higgs) pairs in the spectrum of 4d F-theory compactifications, we combine machine learning and algebraic geometry techniques to analyze line bundle cohomologies on families of holomorphic curves. To qu…
Toric Geometry in OSCAR Open
We report on the computer implementation for toric geometry in the computer algebra system $\texttt{OSCAR}$. The main architectural feature of $\texttt{OSCAR}$ is that its four fundamental tools $\texttt{Antic}$ (Hecke, Nemo), $\texttt{GAP…
Root bundles: Applications to F-theory Standard Models Open
The study of vector-like spectra in 4-dimensional F-theory compactifications involves root bundles, which are important for understanding the Quadrillion F-theory Standard Models (F-theory QSMs) and their potential implications in physics.…
Statistics of limit root bundles relevant for exact matter spectra of F-theory MSSMs Open
In the largest, currently known, class of one quadrillion globally consistent F-theory Standard Models with gauge coupling unification and no chiral exotics, the vectorlike spectra are counted by cohomologies of root bundles. In this work,…
Root bundles and towards exact matter spectra of F-theory MSSMs Open
A bstract Motivated by the appearance of fractional powers of line bundles in studies of vector-like spectra in 4d F-theory compactifications, we analyze the structure and origin of these bundles. Fractional powers of line bundles are also…
Tensor products of finitely presented functors Open
We provide explicit constructions for various ingredients of right exact monoidal structures on the category of finitely presented functors. As our main tool, we prove a multilinear version of the universal property of so-called Freyd cate…
Cohomologies of coherent sheaves and massless spectra in F-theory Open
In this PhD thesis we investigate the significance of Chow groups for zero mode counting and anomaly cancellation in F-theory vacua. The major part of this thesis focuses on zero mode counting. We explain that elements of Chow group descri…