Differential Geometry, Topology, and Mathematical Physics.
Earlier "best results": (1) de Rham theory for supermanifolds, discovery of new "variational" differential and links with Gelfand's general hypergeometric equations and integral geometry; (2) higher derived brackets, with applications to graded manifolds, homological vector fields, and BatalinVilkovisky geometry; (3) universal recurrence relations for super exterior powers, new formula for Berezinian as ratio of polynomial invariants, and applications to BuchstaberRees theory of nhomomorphisms (joint with H. Khudaverdian); My work also concerned quantization and AtiyahSinger index theorem, quantum groups, and generalizations of characteristic classes. Current interests: analytic formulas for volumes of classical supermanifolds, microformal geometry and homotopy algebras, and super Darboux transformations. 
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Last modified: 8 (15) October 2017. Ted Voronov