- 1. Perturbation theory and asymptotic analysis of N=non-perturbative phenomena in AdS/CFT
- 2. Exponential Asymptotics and resurgence in non-linear ODEs and discrete equations
- 3. Exact quantisation methods for field theoretic observables
- 4. Integrability in AdS/CFT, semi-classical strings and correlation functions
1. Perturbation theory and asymptotic analysis of non-perturbative phenomena in physics and applied mathematics
My main interests are currently focused on the study of asymptotics in non-linear ODEs, random matrix models and gauge theories, via the development of the mathematical framework of resurgence.
One of my short term goals is to fully understand the resurgent behaviour and Stokes phenomena for problems with a multi-dimensional phase space. More concretely, I am interested in the applications of resurgence to pattern formation and time-evolution in certain PDEs, the large-N expansions of free energies in matrix models and large proper-time expansion of Yang-Mills plasma and the prediction of the dual quasinormal modes.
I am also interested in the study of asymptotic solutions to non-linear ODEs and discrete equations, such as the Painlevé equations, and how to use summation procedures and resurgence to retrieve global analytic information of these solutions.
2. Integrability in AdS/CFT, semi-classical strings and correlation functions
Another main area of research interest is the integrability properties of sigma-models, and the semi-classical analysis of string solutions. My most recent work focused on the problem of having adding contributions of massless modes to semi-classical integrability-based calculations, and how these related to massless TBA equations. I am also interested in the uses of integrability in the calculation of correlation functions.
The two research areas often overlap, as resurgence has shown great applicability to observables with associated asymptotic expansions calculated via integrability. A particular interest is on the applications of resurgence to TBA equations.