My current research interests lie at the junction between different areas of Pure Mathematics and Mathematical Physics: Algebraic Topology, Homological Algebra and Deformation Theory, Noncommutative Geometry and Conformal Field Theory.

The projects I am presently working on aim to apply ideas and methods of quantum field theory (Feynman path integrals) to classical problems of algebra and geometry, such as the study of moduli spaces. I am also interested in algebraic topology, rational homotopy theory and deformation theory.

Graph Cohomology
Higher structures and noncommutative geometry
Deformation theory of geometric and algebraic structures
Operads and Topological Field Theories

http://www.maths.lancs.ac.uk/~lazarev/