My interests:
En escrime, ce qui est simple est inspiration.
Ce qui est complexe est technique.
---- Arturo Pérez-Reverte: Maître d'escrime

Knot and link invariants (Misha Polyak is my mentor)

Cluster algebras and varieties: References

Algebraic structures up-to homotopy: L-infinity, A-infinity etc

Deformation & Quantization
Deformation Quantization
Formality theorems
Operads and PROPs
Lie Algebroids
Hopf Algebras
Lie bialgebras and Lie quasibialgebras
Batalin-Vilkovisky structures