arXiv subjects

Paula Naomi Pilatus

Publications and source records attributed to Paula Naomi Pilatus.

4 recordsLinked to original sources

arXiv2026

Deformations of generalized complex structures on $\mathcal{G}$-flat transitive Courant algebroids

We extend Gualtieri's deformation theorem for generalized complex structures on exact Courant algebroids to the more general class of $\mathcal{G}$-flat transitive Courant algebroids. Our approach relies on the framework of tame Fréchet spaces and Hamilton's Nash-Moser (implicit function) theorem. As an important step of the proof of our deformation theorem, we endow the group of autoequivalences of a $\mathcal{G}$-flat transitive Courant algebroid with a tame Fréchet Lie group structure and show that there exists a tame subgroup of exact autoequivalences, whose infinitesimal action is by inner derivations.

math.DG↗

arXiv2026

Deformation theory of complex structures via Hamilton-Nash-Moser theory

We revisit the classical proof by Kuranishi on the existence of a locally complete family of complex deformations on a compact complex manifold using Hamilton's Nash-Moser implicit function theorem. This is relevant to existing and future extensions of this theorem to generalized complex structures on Courant algebroids.

math.DG↗

arXiv2025

Geometry of effective field theory positivity cones

Positivity bounds are theoretical constraints on the Wilson coefficients of an effective field theory. These bounds emerge from the requirement that a given effective field theory must be the low-energy limit of a relativistic quantum theory that satisfies the fundamental principles of unitarity, locality, and causality. The task of deriving these bounds can be reformulated as the geometric problem of finding the extremal representation of a closed convex cone~$\mathcal C_W$. More precisely, in the presence of multiple particle flavors, the forward-limit positivity cone $\mathcal C_W$ consists of all positive semi-definite tensors in $W =\left\{ S \in \mathrm{Sym}^2 (\mathrm{Sym}^2\, V^*)\oplus \mathrm{Sym}^2 \left(Λ^2 V^*\right) : τS = S \right\} \subset \mathrm{Sym}^2(V^*\otimes V^*)$, where $τ$ denotes transposition in the second and fourth tensor factor and $V\cong\mathbb{R}^n$, where $n$ is the number of flavors. In this work, we solve this question up to three flavors, i.e.~$n=3$, proving a full classification of all extremal elements in these cases. We furthermore study the implications of our findings, deriving the full positivity bounds for amplitudes with and without additional symmetries. In the cases with additional symmetries that we consider, we find that the so-called elastic bounds are sufficient to give rise to the full positivity bounds.

math-ph↗

arXiv2025

Born Lie algebras

We show that every Born Lie algebra can be obtained by the bicross product construction starting from two pseudo-Riemannian Lie algebras. We then obtain a classification of all Lie algebras up to dimension four and all six-dimensional nilpotent Lie algebras admitting an integrable Born structure. Finally, we study the curvature properties of the pseudo-Riemannian metrics of the integrable Born structures obtained in our classification results.

math.DG↗