Research interests
I study algebraic structures arising in geometry and theoretical physics. A lot of my past work concerned Courant algebroids, a kind of higher (string-theoretic) analogue of Poisson structures familiar in particle mechanics. I have applied the theory of supermanifolds to obtain a streamlined description of these and other structures as various kinds of differential graded manifolds. More recently, I became interested in applying homotopy-theoretic and and higher categorical methods to problems in geometry, specifically in the homotopy theory of differential graded manifolds and higher differentiable stacks, derived differential geometry and higher Lie theory. I am currently involved in two projects. In one of them, together with Dave Carchedi, we are developing differential graded models for derived differential geometry; in the other, jointly with Paul Bressler, we are investigating the precise relation between Courant algebroids and Poisson structures on loop spaces (vertex Poisson algebras).