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Preprint Sep 2026

Quantitative asphericalization and Gromov's linear bordism problem

We prove a PL bordism version of Gromov's linearity conjecture over a broad class of asphericalization groups for manifolds endowed with faithful representations in all dimensions. Since every group embeds into an asphericalization group, this bordism version of the conjecture holds after allowing the target group to b...

Geunho Lim · 0 citations
Preprint Aug 2026

Generic spherical unitary dual for Chevalley groups over local fields

We prove that a generic spherical parameter for the graded affine Hecke algebra with equal parameters is unitary if and only if its normalized intertwining forms are positive on the reflection representation and on the irreducible constituents of its second symmetric power. The proof combines a signature formula for th...

D. Ciubotaru · 0 citations
Preprint Aug 2026

The Twist Conjecture and the Isomorphism Problem for Coxeter groups

We prove M\"uhlherr's Twist Conjecture: any two angle-compatible Coxeter generating sets of a Coxeter group differ by a finite sequence of elementary twists and a conjugation. Combined with earlier work of Howlett-M\"uhlherr and Marquis-M\"uhlherr, this completes the resolution of the Isomorphism Problem for Coxeter gr...

Elia Fioravanti · 0 citations
Preprint Sep 2026

Comparison and Almost Finiteness for Actions of Amenable Groups

We prove that every action of a countably infinite discrete amenable group on a nonempty compact Hausdorff zero-dimensional space has dynamical comparison, without assuming minimality, freeness, or metrizability. More precisely, strict inequalities under all invariant probability measures imply comparison in the clopen...

E. Glasner, Chun-Lin Liu · 4 citations · ⚡1
Preprint Sep 2026

Kontsevich-Zagier conjecture for Hensel-minimal fields with sections

We generalise Yin's motivic integration with section to the Hensel-minimal framework, with and without volume forms, building on Stout and Vermeulen's work on a Hrushovski-Kazhdan style motivic integral for $1$-h-minimal valued fields. In particular, we get a bijective motivic integral \emph{\`a la} Hrushovski-Kazhdan...

Xavier Pigé · 0 citations
Preprint Aug 2026

The conjugacy problem in cyclic extensions of one-ended hyperbolic groups

Let $G$ be a torsion-free one-ended hyperbolic group and let $\phi\in\operatorname{Aut} (G)$. We prove that the mapping torus, or suspension, $$ M:=G_{\phi}=G\rtimes_\phi \mathbb{Z} $$ has solvable conjugacy problem. This builds on the pioneering work of Pr\'eaux who solved the conjugacy problem for all (geometrisable)...

A. Martino · 0 citations

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