I am broadly interested in applying combinatorics, representation theory, and algebraic geometry to problems in complexity theory.

Some projects I have been thinking about recently:

• Betti tables and GL(V)-module structure of resolutions of varieties of binary forms

• Tensor complexity of GL(V)-invariant tensors, paticularly border apolarity and geometric rank

• Vacillating tableaux and partition algebras

• Construction and complexity of tensors invariant under the symmetric group

Border rank bounds for GL(V)-invariant tensors arising from matrices of constant rank. Submitted.