research

 

The general aim of my research is to understand the fundamental structure of spacetime. Yikes! This is very, very ambitious and requires more insight than not only one human but an entire generation of researchers can possibly have. Yet science has always been a civilizational project, and that's what all problems thus far have been like. It's not unlike ants digging a long tunnel, but this one does seem to go on a bit longer than most.

I'm currently very interested in formulations of quantum field theory, like AQFT and (pre)factorization algebras. All of this tends to involve a very simple notion of putting one thing on top of another. And often, we want to describe something locally and then glue it together into one big thing... this leads one to descent theory, a mathematical subject due to the great(est?) 20th century mathematician Grothendieck.

And these are all very simple problems, at heart. As I said, putting one thing on top of another (matter on top of space). What exactly is this matter, what is space, how it interacts and how you can do all of the above coherently - this is the main issue.

So, I have this deep conviction that all of Nature can be described in a few simple ideas. And history teaches us that things get unified once we learn how to speak its language. Most of this language can, at least this far, be described using (higher) category theory, which is another interest of mine .

Some other more down-to-Earth things I'm interested in regarding QFT are Epstein-Glaser (re)normalization, resurgence theory. On the maths side I'm really looking into deformation theory on the path of Kontsevich.

A while ago, my own intellectual mandibles (forget not the ants!) were happily chipping away at more specialized subjects: noncommutative geometry and quantum groups. I was also looking into why some classical, nontrivially constrained systems describing a relativistic spinning top (which is a picturesque model for electron spin) yield spacetime noncommutativity when quantized. Honestly, it might even be expected from basic, introductory NRQM that it might not be that simple to treat spin as an "arrow". The matter is of course more subtle, since a gauge symmetry eliminates both the spin vector and its conjugate momenta as observables and leaves their antisymmetrized product as an observable, which to first order also corresponds to the generator of Lorentz symmetries. It really makes my head spin, at least.

On the other hand, there is the problem of putting spacetime noncommutativity in by hand, which becomes relevant at high energy scales. Well, by itself it's no problem, but the consequences need to be worked out. One immediate result is a Hopf algebroid structure on the algebra of functions, which carries a lot of information about spacetime. Well, the phase space is actually a twisted Hopf algebroid, the twist itself being a special operator which determines everything from multipication to addition of momenta to particle statistics. To keep myself from rambling, I will just say that there are a lot of interesting physical and mathematical problems - the two are really "forced" to hold hands in this particular image of spacetime!

Some of my other interests are jazz (I play sax, guitar and a bit of piano), philosophy, weightlifting, and late night conversations.