Related papers: Improved statistics for F-theory standard models
We study equisingular deformation problems for curves and surfaces in algebraic families, with particular emphasis on situations where nodal behavior is no longer generic. Extending classical Severi theory, we develop deformation--theoretic…
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…
We consider tautological bundles and their exterior and symmetric powers on the Quot scheme over the projective line. We prove and conjecture several statements regarding the vanishing of their higher cohomology, and we describe their…
We consider universal statistical properties of systems that are characterized by phase states with macroscopic degeneracy of the ground state. A possible topological order in such systems is described by non-linear discrete equations. We…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
Identical quantum particles exhibit only two types of statistics: bosonic and fermionic. Theoretically, this restriction is commonly established through the symmetrization postulate or (anti)commutation constraints imposed on the algebra of…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
Studying degenerations of moduli spaces of semistable principal bundles on smooth curves leads to the problem of constructing and studying moduli spaces on singular curves. In this note, we will see that the moduli spaces of…
What kind of reduced monomial schemes can be obtained as a Gr\"obner degeneration of a smooth projective variety? Our conjectured answer is: only Stanley-Reisner schemes associated to acyclic Cohen-Macaulay simplicial complexes. This would…
Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively…
Variational models with coupling terms are becoming increasingly popular in image analysis. They involve auxiliary variables, such that their energy minimisation splits into multiple fractional steps that can be solved easier and more…
For a projective curve $C\subset\mathbf{P}^n$ defined over $\mathbf{F}_q$ we study the statistics of the $\mathbf{F}_q$-structure of a section of $C$ by a random hyperplane defined over $\mathbf{F}_q$ in the $q\to\infty$ limit. We obtain a…
We introduce a new moduli stack $\mathscr{E}_{g,n}$ of ``equinormalized curves," closely related to the moduli space of all reduced, connected algebraic curves. We construct a stratification $\bigsqcup_\Gamma \mathscr{E}_\Gamma$ of…
We derive recursive equations for the characteristic numbers of rational nodal plane curves with at most one cusp, subject to point conditions, tangent conditions and flag conditions, developing techniques akin to quantum cohomology on a…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
We develop a combinatorial theory of vector bundles with connection on locally ordered simplicial complexes. This is a first step towards a discrete exterior calculus for bundle-valued forms. The basic building block is the discrete…
We develop a general framework for the quantization of bosonic and fermionic field theories on affine bundles over arbitrary globally hyperbolic spacetimes. All concepts and results are formulated using the language of category theory,…
Elliptic curves play a natural and important role in elliptic cohomology. In earlier work with I. Kriz, thes elliptic curves were interpreted physically in two ways: as corresponding to the intersection of M2 and M5 in the context of (the…
Rational algebraic curves have been intensively studied in the last decades, both from the theoretical and applied point of view. In applications (e.g. level curves, linear homotopy deformation, geometric constructions in computer aided…
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…