We establish a link between the new theory of-deformed rational numbers and the classical
Burau representation of the braid group. We apply this link to the open problem of …

We study analytic properties of``$ q $-deformed real numbers'', a notion recently introduced
by two of us. A $ q $-deformed positive real number is a power series with integer …

In this paper, we construct a compactification of the space of Bridgeland stability conditions
on a smooth projective curve, as an analogue of Thurston compactifications in Teichm\" uller …

The left and right $ q $-deformed rational numbers were introduced by Bapat, Becker and
Licata via regular continued fractions, and they gave a homological interpretation for left and …

This paper is an attempt to apply the tools of supergeometry to arithmetic. Supergeometric
objects are defined over supercommutative rings of coefficients. We consider an integral ring …

Abstract q-deformed real numbers are power series with integer coefficients. We study
Stieltjes and Jacobi type continued fraction expansions of q-deformed real numbers and find …

The recent notion of $ q $-deformed irrational numbers is characterized by the invariance
with respect to the action of the modular group $\PSL (2,\Z) $, or equivalently under the …

We describe new $ q $-deformations of the 3-dimensional Heisenberg algebra, the simple
Lie algebra $\mathfrak {sl} _2 $ and the Witt algebra. They are constructed through a …

We give enumerative interpretations of the polynomials arising as numerators and
denominators of the $ q $-deformed rational numbers introduced by Morier-Genoud and …

where q is a parameter, is commonly considered as a “quantum”, or a q-analogue of a
(positive) integer n. The expression goes back to Euler («1760) who used it in the context of …