Random Matrix Theory provides us with a useful toolkit to explore the net of relationships between physics, geometry and integrable systems. By definition, random matrix theory studies matrix-valued random variables. Its origins in mathematical physics date back to the seminal work by Nobel laureate Eugene Wigner, in the context of nuclear physics. The subject has grown to become a very significant tool in physics, with a varied number of applications spanning from condensed matter physics to quantum gravity and in gauge and string theory.
Our research lines are devoted to application of Random Matrix Theory to an in-depth mathematical investigation of low-dimensional topological and supersymmetric gauge theories, and the analysis of their exactly solvable structure. Indeed, our research goals are mostly achieved by exploiting and developing the matrix model formulation of quantum field theories. By matrix model formulation one refers to the situation where the observables of the gauge theory in question admit an integral representation over the eigenvalues of a random matrix ensemble. This approach, put forward by Pestun in 2007, and partially based on seminal mathematical results in the 1980s, such as the Duistermaat-Heckman theorem, has been enormously influential, leading to a new world of possibilities in the analysis of supersymmetric gauge theories in curved manifolds.