Talks

Quantum field theories play an important role in many condensed matter systems for their description at low energies and long length scales. In 1+1 dimensional critical systems the energy spectrum and the spectrum of scaling dimensions are intimately related in the presence of conformal symmetry. In higher space-time dimensions this relation is more subtle and not well explored numerically. In this talk we motivate and review our recent effort to characterize 2+1 dimensional quantum field theories using computational techniques 2+targetting the energy spectrum on a spatial torus. We discuss several examples ranging from the O(N) Wilson Fisher theories and Gross-Neveu-Yukawa theories to deconfinement- confinement transitions in the context of topological ordered systems. We advocate a phenomenological picture that provides insight into the operator content of the critical field theories.

Recently, Roland van der Veen and myself found that there are sequences of solvable Lie algebras "converging" to any given semi-simple Lie algebra (such as sl(2) or sl(3) or E8). Certain computations are much easier in solvable Lie algebras; in particular, using solvable approximations we can compute in polynomial time certain projections (originally discussed by Rozansky) of the knot invariants arising from the Chern-Simons-Witten topological quantum field theory. This provides us with the first strong knot invariants that are computable for truly large knots.  But sl(2) and sl(3) and similar algebras occur in physics (and in mathematics) in many other places, beyond the Chern-Simons-Witten theory. Do solvable approximations have further applications?

This is a repeat of a talk I gave in McGill University in February, 2017. A video recording, a handout, and some further links are at McGill-1702

How big can a star get? Why would a star only pretend to explode? Can you hide one star inside another?

Take a tour of some of the strangest stellar phenomena in the universe during this talk featuring Emily Levesque. From the biggest, brightest, and most volatile stars to the explosive fireworks of core-collapse supernovae and the fascinating physics of gravitational waves, "weird" stars serve as a common thread for exploring our universe's history, evolution, and extremes. Levesque will discuss the history of stellar astronomy, present-day observing techniques, and exciting new discoveries, and explore some of the most puzzling and bizarre objects being studied by astronomers today.

I'll ask whether the knowledge of a single eigenstate of a local lattice Hamiltonian is sufficient to uniquely determine the Hamiltonian. I’ll present evidence that the answer is yes for generic local Hamiltonians, given either the ground state or an excited state. In fact, knowing only the correlation functions of local observables with respect to the eigenstate appears generically sufficient to exactly recover both the eigenstate and the Hamiltonian, with efficient numerical algorithms. I may also comment on the extension of these ideas to the continuum, pose questions about the behavior of generic local spin systems, or discuss the question of what happens if you don't know a preferred factorization of the Hilbert space.