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2026
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OpenAlex
Attila Maróti, Kamilla Rekvényi
Abstract Let G be a primitive permutation group acting on a finite set X . The orbital diameter $$\textrm{diam}(X,G)$$ diam ( X , G ) is defined to be the supremum of the diameters of the (connected) orbital graphs of G after …
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2026
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Ulrich Pennig, George Tridimas
Lifting obstructions for group actions, cocycle actions, and $Γ$-kernels admit a cohomological description via topological crossed modules, as recently developed by Izumi, Giron-Pacheco, and the first named author. For a strongly self-absorbing $C^*$-algebra $A$, we show that the classifying spaces $\mathcal{B}^D\mathcal{G}_A$ and …
gb
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2026
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OpenAlex
Joseph P. MacManus, Bobby Miraftab
We show that the separation profile of a hyperbolic planar graph and, more generally, a hyperbolic apex-minor-free graph, grows at most logarithmically, answering a question of Benjamini, Schramm, and Timár in the affirmative.
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2026
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Saul D. Freedman, Hong Yi Huang, Melissa G.Y. Lee, Kamilla Rekvényi
A base for a finite permutation group G ⩽ Sym ( Ω ) is a subset of Ω with trivial pointwise stabiliser in G , and the base size of G is the smallest size of a base for G . Motivated …
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2026
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OpenAlex
Guy Fowler
Let $V \subset \mathbb{A}^2(\mathbb{C})$ be an algebraic curve such that $\mathrm{deg} X \neq \mathrm{deg} Y$, where $X, Y$ denote the coordinate functions on $\mathbb{A}^2(\mathbb{C})$ restricted to $V$. We prove there exists an effectively computable constant $c$, that depends linearly on the height …
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2026
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Gemma Crowe, Islam Foniqi
Abstract In this paper, we construct an implementable algorithm that solves the conjugacy problem in twisted right-angled Artin groups (T-RAAGs). In certain cases, the complexity is known to be linear, by reducing the problem to the twisted conjugacy problem in RAAGs. We …
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2026
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Vladimir Vankov
We construct uncountably many finitely generated, pairwise non-isomorphic torsion-free groups, all of which fall into the same quasi-isometry class. This is done by considering Schur covering groups and group cohomology, with the necessary geometric ingredient coming from the theory of bounded-valued cohomology.
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2026
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Dane Michael Wolf, Endri Mjeku, Mayuko Segawa, Alva M. Casey et autres
Abstract The mitochondrial genome (mtDNA) is essential for oxidative phosphorylation, and mammalian cells typically contain hundreds or thousands of copies. Although specific aspects of mtDNA replication and degradation have been explored, a complete account of the mtDNA life cycle has remained elusive, …
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2026
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Mark J. Crumpton, Francesco Mezzadri
We employ the recently developed Kac-Rice formalism for non-Hermitian random matrices to derive the joint distribution of an eigenvalue and its associated normalised right eigenvector in a Gaussian ensemble that interpolates between complex Ginibre (Class A) and complex symmetric matrices (Class AI$^\dagger$). …
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2026
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Andrew Harrison-Migochi, Raymond McCulloch
Let [Formula: see text] be a lattice and let [Formula: see text] be a definable family in an o-minimal expansion of the real field, [Formula: see text]. A result of Barroero and Widmer gives sharp estimates for the number of lattice points …
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2026
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Jesse Pajwani, Ambrus Pál
Abstract We prove an arithmetic refinement of the Yau–Zaslow formula by replacing the classical Euler characteristic in Beauville’s argument by a motivic Euler characteristic, related to the work of Levine. Our result implies similar formulas for other related invariants, including a generalisation …
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2026
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OpenAlex
Christopher W. Parker, Jack Saunders
Abstract Let be a finite group and a normal subset consisting of odd‐order elements. The rational closure of , denoted , is the set of elements with the property that for some in . If , we prove that is soluble.
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