The q-deformed Knizhnik-Zamolodchikov-Bernard heat equation
  We introduce a q-deformation of the genus one sl_2 Knizhnik-Zamolodchikov-Bernard heat equation. We show that this equation for the dependence on the moduli of elliptic curves is compatible with the qKZB equations, which give the dependence on the marked points. 
Giovanni Felder (ETH Zurich) and Alexander Varchenko (UNC Chapel Hill)