Research
Research
Research
Research
20,034+ open-access research outputs.
We classify fillable contact structures on all negative-definite star-shaped plumbings. Along the way, we show that such Seifert fibred spaces admit a unique negative maximal twisting number, and comp…
We derive a class of inner-extremal regular black hole solutions characterized by a degenerate inner horizon. These geometries arise as polymerized vacuum configurations inspired by loop quantum gravi…
We present a systematic derivation of regular black hole solutions - and their horizonless counterparts - that achieve regularization via an anti-de Sitter core. These geometries emerge as polymerized…
We investigate spin-induced scalarization of Kerr black holes in an Einstein-scalar-Gauss-Bonnet (EsGB) model that does not admit a linear tachyonic instability of the scalar-free solution. The scalar…
We give a self-contained, modern exposition of \'Edouard Goursat's 1887 theorem on pseudo-elliptic integrals -- those integrals of the form $\int F(t)\,\d t/\sqrt{R(t)}$ with $R$ a cubic or quartic po…
We study the problem of understanding where two populations differ within a feature space, which we formalize in the concept of a differential subgroup: a subset of individuals from both populations w…
We construct a Lagrangian Floer homology whose chain complex is generically generated by the inscriptions of isosceles trapezoids in a smooth Jordan curve. This is an extension of Greene and Lobb's Jo…
It is not known whether the realisation part of the $s$-cobordism theorem holds for smooth 4-manifolds, nor whether every pair of smoothly $h$-cobordant 4-manifolds is also smoothly $s$-cobordant. We …
Choosing the optimal observable to model dynamical systems for which we do not know the driving equations is nearly always an ad hoc art. Takens' Delay Embedding Theorem guarantees a diffeomorphism be…
We establish two consequences of the Kawamata--Morrison--Totaro cone conjecture, and prove them unconditionally in all dimensions. First, for a K-trivial variety, the natural action of its automorphis…
Connectivity of temporal graphs has been widely studied both as graph theory and as gossip theory. In particular, it is well known that in order to connect every vertex to every other, a temporal grap…
Hybrid-thinking language models expose explicit think and no-think modes, but current designs do not separate them cleanly. Even in no-think mode, models often emit long and self-reflective responses,…
Quantum state tomography provides a fundamental framework for reconstructing quantum states. When the measurement data are not informationally complete, the observed statistics admit multiple compatib…
We establish that $C^\infty$ three-dimensional flows with positive topological entropy admit only finitely many ergodic measures of maximal entropy, even when singularities (zero-velocity points) are …
Establishing the precise computational boundary between classically tractable fermionic systems and those capable of genuine quantum advantage is a central challenge in quantum simulation. While injec…
Core-nilpotent endomorphisms over an arbitrary vector space form the largest subset of the ring of endomorphisms over that arbitrary vector space which admit a decomposition as sum of two endomorphism…
We introduce the finite-horizon first-order rank profile of a language $L \subseteq \Sigma^*$: the least quantifier rank needed by an $\mathrm{FO}[<]$ sentence to classify membership in $L$ correctly …
While most classical NP-hard graph problems cannot be solved in time $2^{o(n)}$ on general graphs under the Exponential Time Hypothesis (ETH), many exhibit the square-root phenomenon and admit optimal…
This article presents a brief account of Amir O. Caldeira's contributions to the theory of quantum Brownian motion. Motivated by its importance, we outline the description of Brownian motion in the qu…
The medial axis $M_X$ of a closed set $X\subset \mathbb{R}^n$ is the set of points from the ambient space that admit more than one closest point in $X$. We study the problem of reaching the singularit…
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