Areas of research: Algebraic Topology, Algebraic Geometry, Mathematical Physics, Higher Stuctures.
In particular:
- Feynman Categories
- String Topology and Related Operations such as Deligne Conjectures
- Hopf Algebras
- Quantum Cohomology and Mirror Symmetry
- Stringy Phenomena for Stacks/Orbifolds
- Geometry of Moduli and Teichmueller Spaces
- Noncommutative Geometry
- Nano Wire Networks
- Topological Insulators
- 2+1 dim TQFT and its Extensions