Research interests
 

Most of my research is concerned with using algebraic topology and homotopical algebra to study geometric spaces and algebraic structures.

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- Unstable homotopy theory of topological spaces, rational and p-adic homotopy theory.

- Topology and geometry of free loop spaces, string topology.
- Multiplicative and higher categorical structures in homotopical algebra, cohomological  operations, operads.
- Poincaré-Verdier duality, intersection cohomology, topology of singular spaces.
- Topology of complex algebraic varieties, mixed Hodge theory, formality.