I am presently working on a mathematical physics project — to construct 4d quantum Yang‑Mills theory using the machinery of 2d CFT and integrable 2d QFT
My other projects are described on the research page.
The most recent was an ill-fated attempt at fundamental cosmology. The cosmology is a very nice, highly symmetric classical universe that has dark matter as a coherent Standard Model effect. Sadly, the classical cosmology is unstable to local fluctuations. I can't find a mechanism to suppress the instability.
Before that was another unsuccessful physics project — to encode all of spacetime physics in two dimensional quantum field theory. It started when I was a grad student at Berkeley. I derived Einstein's equation for a Riemannian metric as the renormalization group fixed point equation in 2d quantum field theory. This idea merged into string theory in the early 1980s. Eventually I came up with a 2d field theory mechanism that constructs the quantum string ground state. Sadly, I haven't been able to see how this mechanism can solve the basic problem of string theory — selecting our universe from the multitude of classical string ground states. It still seems to me that mine is the only coherent construction of the quantum string ground state, but unless it can be found to produce the real world, it isn't of any use for physics.
I still have hopes for my ideas about large scale quantum computing. Asymptotically large scale quantum computers must be one dimensional physical systems near a critical point. The fundamental physical design principles should be based on entropy flow in near-critical quantum circuits. I don't have a way to tell when the asymptotic regime starts, but I suspect sooner rather than later.
Over the years I've written a few short essays expressing my idea about doing fundamental theoretical physics.