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We define monotone links on a torus, obtained as projections of curves in theplane whose coordinates are monotone increasing. Using the work ofMorton-Samuelson, to each monotone link we associate elements in the doubleaffine Hecke algebra and the elliptic Hall algebra. In the case of torus knots(when the curve is a straight line), we recover symmetric function operatorsappearing in the rational shuffle conjecture.  We show that the class of monotone links viewed as links in $\mathbb R^3$coincides with the class of Coxeter links, studied by Oblomkov-Rozansky in thesetting of the flag Hilbert scheme. When the curve satisfies a convexitycondition, we recover positroid links that we previously studied. In the convexcase, we conjecture that the associated symmetric functions are Schur positive,extending a recent conjecture of Blasiak-Haiman-Morse-Pun-Seelinger, and wespeculate on the relation to Khovanov-Rozansky homology.  Our constructions satisfy a skein recurrence where the base case consists ofpiecewise almost linear curves. We show that convex piecewise almost linearcurves give rise to algebraic links.

Monotone links in DAHA and EHA