# Research

I became a theoretical physicist to learn what the world is. While that sounds general and rather qualitative, my research almost always requires concrete & fairly technical calculations, because without precise results it’s very difficult to avoid fooling yourself, and others. Genuinely new ideas should lead to new equations.

I prefer to work on problems that are precise enough that it’s clear whether we’ve made progress, but vague enough that we currently lack both the tools and the vision to anticipate the solution.

Some questions that interest me, in order of decreasing vagueness:

- Cosmologically speaking, what was the origin, and what will be the eventual fate of the universe? What kind of theory describes cosmology – what are the well-defined observables in this manifestation of quantum gravity? How does it fit with the idea that many of the parameters governing the laws of physics in our world, such as the cosmological constant and the Higgs mass, may take special values due to anthropic selection in a multiverse?
- How can we resolve the paradox of black hole evaporation, which pits quantum mechanical consistency against the equivalence principle of general relativity, ie locality and effective field theory? More specifically, in the context of AdS/CFT, is there a well-defined construction of local observables near and across the horizon of an AdS black hole?
- What is the ‘space’ of unitary Conformal Field Theories? Are local AdS effective field theories (such as our world, transplanted to an AdS box) generic, somewhat special, rare, non-existent? Can we make more precise predictions concerning “strongly coupled”, ie generic, quantum field theories?
- How can we understand AdS locality and black hole thermodynamics from the point of view of CFT? Can we both observe and resolve information loss in some parametric limit of CFT?
- How can we exploit the deep connections between condensed matter systems and the quantum field theories that appear in high-energy physics? What explains the universal features of strange metallic phases?
- What is dark matter? What was the mechanism of cosmological inflation?
- Are there interesting new particles and forces waiting to be discovered at the LHC and other experiments? Will they provide clues concerning dark matter, baryogenesis, grand unification, and naturalness?

Early in my career, I mostly focused on the last two questions, but more recently I’ve been working on those in the middle of this list. This work has largely been based on the CFT bootstrap, which uses the fundamental principles of quantum mechanics, conformal symmetry, and crossing symmetry to constrain or determine CFT correlators. In the past two years my research has focused on harnessing the power of Virasoro symmetry in 2d CFTs to understand quantum gravity in 2+1 dimensional AdS.

For more information, scan the titles and abstracts of my recent publications. For additional resources and related topics, see the Simons Collaboration on the Nonperturbative Bootstrap.

Since early 2018 I have been spending some of my time learning about and conducting research on Machine Learning. Contemporary ML research has much in common with statistical physics and physics-style phenomenological analysis and model building. So I’d like to help to develop a more thorough scientific understanding of these very new and powerful systems. I believe that such an understanding will also be relevant for ensuring their ethical use — which is a very important problem!