Dmytro Shklyarov worked on the subject of quantum groups with late L. Vaksman n Ukraine. After that he got Ph. D. in mathematics from Kansas State University where he studied noncommutative algebraic geometry under Yan Soibelman. He is now a postdoc in Augbusrg, Germany.
Hirzebruch-Riemann-Roch theorem for differential graded algebras, PhD Thesis, Kansas State University (2009). Available at <http://krex.k-state.edu/dspace/handle/2097/1381>, with preprint version Hirzebruch-Riemann-Roch theorem for DG algebras, arxiv/0710.1937
2-Representations and Equivariant 2D Topological Field Theories, arxiv/0812.4482
Non-commutative Hodge structures: Towards matching categorical and geometric examples, arxiv/1107.3156