The Quantization of the Generalized mKdV Equations for $\hat {\SL}_2$
  We construct quantum deformations of the integrals of motion of the generalized mKdV equations for $\hat {\SL}_2$. For this, we give the relevant vertex operator algebra and prove quantum Serre relations for vertex operators, it allows to construct a $q$-BGG resolution and to deform the classical integrals of motion in a commutativ family. 
Antoine Balan (Ecole Polytechnique)