Lev Borisov's research is in the general area of algebraic geometry, with particular focus on mirror symmetry and other byproducts of string theory. He is also interested in the theory of modular forms, in particular the geometry of the modular curves X_1(n). Lev Borisov has recently worked on elliptic genera, vertex algebras, toric varieties and their hypersurfaces, modular forms. He is also engaged in miscellaneous projects related to stacks and derived categories.