Research

Algebra, Differential Geometry, Topology, and Mathematical Physics

Much of what I do is related with supermanifolds and their applications. Among topics I have worked on are: integration on supermanifolds, geometry of brackets (even and odd Poisson structures, Lie algebroids and their generalizations, homotopy algebras, etc.), quantization and Atiyah-Singer index theorem, super Darboux transformations, and superanalog of cluster algebras.

So far, my most influential work has been on "higher derived brackets", and after it, the works on super de Rham theory. As a single recent achievement I value most, I can name the idea of "microformal geometry", in which ordinary maps of (super)manifolds are generalized to "thick morphisms" [a notion I introduced] that induce non-linear, in general, pullbacks of functions. These non-linear pullbacks can be characterized algebraically as "non-linear ring homomorphisms", that is, such non-linear, in general, maps of algebras that their differentials at every point are ring homomorphisms. (This construction is motivated by application to homotopy analogs of Poisson brackets and seems to give the correct notion of P-infinity and S-infinity morphisms.)

Publications

Meetings and activities:

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http://personalpages.manchester.ac.uk/staff/theodore.voronov

Last modified: 21 August (3 September) 2026. Ted Voronov