Assistant Professor of Physics Kate Brown presented “Jackson Pollock, Lightning Rods, Quantum Mechanics” at Harvard earlier this semester. Her talk was part of a seminar on “Widely Applied Mathematics.”
Brown focused on an idea proposed in the late 1990s by a group of physicists who claimed that Jackson Pollock’s drip paintings contained fractal patterns so distinctive they could be used to authenticate his work.
According to Brown, that idea was flawed. “From an applied math perspective, scalar-tensor theories of gravity are a difficult problem of coupled nonlinear partial differential equations,” she noted.
She showed that one class of scalar-tensor theories that is relevant to cosmology obeys an electrostatic analogy, and thus the field exhibits a shape enhancement at the ends of a pointed object, similar to the enhancement of the electric field at the end of a lightning rod.
She also presented a result from the realm of non-Hermitian quantum mechanics. “By introducing a non-Hermitian perturbation to the classic Hofstadter problem, we identify the imaginary counterpart to the famous Hofstadter butterfly: a cocoon from which the butterfly can ‘emerge’ in the Hermitian limit,” Brown said.