Related papers: Real analytic counterexample to the freeness conje…

We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.

For a quasi-free module over a function algebra $A(\Omega)$, we define an analogue of the Berezin transform and relate this to the quotient of the C*-algebra it generates modulo the commutator ideal.

We provide a broad class of counterexamples to a conjecture of L. de Branges concerning the superfluity of the continuity property in the axiomatic description of de Branges spaces.

We develop a numerical approach for computing the additive, multiplicative and compressive convolution operations from free probability theory. We utilize the regularity properties of free convolution to identify (pairs of) `admissible'…

We provide a counter-example to Hutchinson's original proof of $C^{1,\alpha}$ representation of curvature $m$-varifolds with $L^q$-integrable second fundamental form and $q>m$ in [6]. We also provide an alternative proof of the same result…

We give an example of iteration of length omega of (<kappa)-complete kappa^+-cc forcing notions with the limit collapsing kappa^+. The construction is decoded from the proof of Shelah [Proper and Improper Forcing, Appendix, Theorem 3.6(1)].

Scarparo has constructed counterexamples to Matui's HK-conjecture. These counterexample and other known counterexamples are essentially principal but not principal. In the present paper, a counterexample to the HK-conjecture that is…

We prove that the intersection of a Hirsch polytope and a cube may be a non-Hirsch polytope.

The present paper is exclusively devoted to counterexamples about commutators and self commutators of unbounded operators on a Hilbert space. As a bonus, we provide a simpler counterexample than McIntosh's famous example obtained some while…

We study the reverse mathematics of pigeonhole principles for finite powers of the ordinal $\omega$. Four natural formulations are presented and their relative strengths are compared. In the analysis of the pigeonhole principle for…

We give a generalization of Beurling's theorem for the Clifford-Fourier transform. Then, analogues of Hardy, Cowling-Price and Gelfand-Shilov theorems are obtained in Clifford analysis.

We extend the free difference quotient coalgebra approach to analytic subordination to the case of a free compression in free probability.

We give a counterexample to the PIA (precise inversion of adjunction) conjecture for minimal log discrepancies. We also give a counterexample to the LSC conjecture for families.

A conjecture of Woods from 1972 is disproved.

We provide a simple explicit counterexample to a group completion conjecture for simplicial monoids attributed to JC Moore.

We prove Landen's transformation by a direct elementary transformation of infinite series

The bounded orbit conjecture says that every homeomorphism on the plane with each of its orbits being bounded must have a fixed point. Brouwer's translation theorem asserts that the conjecture is true for orientation preserving…

In a first (theoretical) part of this paper, we prove a number of constraints on hypothetical counterexamples to the Casas-Alvero conjecture, building on ideas of Graf von Bothmer, Labs, Schicho and van de Woestijne that were recently…

In this lecture we prove a converse to Cartan's Theorem B for real analytic sets, due to Fernando and Ghiloni [arXiv:2506.18347].

It is proved that any free Moufang loop can be embedded in a loop of invertible elements of some alternative algebra.