General research interests:
- Quantum gravity
- Quantum field theory and renormalization
- Interplay between quantum foundations, quantum information and quantum gravity
- Interplay between mathematical physics and combinatorics
My main research interests lie at the crossroad of quantum gravity and quantum field theory, with a particular emphasis on Group Field Theory (GFT) and Tensor Models (TM). These closely related approaches to quantum gravity can most easily be understood as generalizations of Matrix Models to space-time dimensions d>2. They are statistical / quantum theories of tensor-like objects, whose Feynman diagrams can be canonically associated with discrete geometries. Henceforth, these models can be understood as theories of random / quantum geometries and can be taken advantage of to investigate the quantum dynamics of space-time. Furthermore, the GFT formalism can be viewed as a tentative completion of non-perturbative approaches to quantum gravity such as Loop Quantum Gravity and Spin Foam models. It provides additional technical and conceptual tools which may help understand their dynamics. In the past years, I have myself been focused on how to generalize standard renormalization group methods to GFT, and how to use them to extract the effective large scale dynamics of Spin Foam models.
More recently, I got interested in a newly discovered connection between tensor models and so-called Sachdev-Ye-Kitaev (SYK) models. The latter are quantum-mechanical models (or QFTs in 0+1 dimensions) which describe many-body systems of fermions with random and all-to-all interactions. They have been shown to develop an emergent conformal symmetry in the strongly coupled regime, and have therefore been proposed as simple models of AdS/CFT in 1+1 space-time dimensions. Interestingly, the main reason why SYK models are solvable (in the large N limit) is because they are dominated by the same simple Feynman diagrams as tensor models (and GFTs), the so-called melonic graphs. This has led to exciting new applications of tensor models to the gauge/gravity duality.
Finally, I am fascinated by recent developments at the interface between quantum gravity and quantum information, which I am also working on whenever I find the time to.