Quantum field theories at strong coupling exhibit a much richer set of degrees of freedom than in the weak coupling limit. A striking example is the existence of two-dimensional, stringlike excitations in large classes of QFTs in 4,5, and 6 dimensions. A main focus of our research is to shed light on the properties of these extended degrees of freedom and use them to understand the non-perturbative behavior of quantum field theories.

Many aspects of quantum field theory and string theory are encoded by rich mathematical structures. Often the interplay with physics leads to a deeper insight into these mathematical structures and their relations among each other. An important aspect of our work is to develop new connections between enumerative and algebraic geometry, representation theory, and various generalizations of modular forms with the aid of string theory techniques.

Part of our research is devoted to developing formal aspects of string theory. Two recent developments in this direction are: the discovery of a hidden affine E₆ symmetry that underlies the pure spinor formulation of superstrings; and understanding the modular transformation properties of conformal blocks in two-dimensional conformal field theory.