Quadratic transformations for the third and fifth Painlevé equations.
Quantum Painlevé equations: from continuous to discrete.
Quasialgebraic functions
We introduce and discuss a new class of (multivalued analytic) transcendental functions which still share with algebraic functions the property that the number of their isolated zeros can be explicitly counted. On the other hand, this class is sufficiently rich to include all periods (integral of rational forms over algebraic cycles).
Quiver varieties with multiplicities, Weyl groups of non-symmetric Kac-Moody algebras, and Painlevé equations.