Considerate la vostra semenza: fatti non foste a viver come bruti, ma per seguir virtute e canoscenza. (Dante Alighieri)

Research

My research is mostly focused on the use of Riemann-Hilbert techniques to study physically meaningful quantities arising in the field of Random Matrix Theory or Integrable PDEs. In both fields, it is possible to analyze their asymptotic behaviour in certain limit or critical regime.
Furthermore, in the Random Matrix field, gap probabilities of eigenvalues (determinantal poit processes) can be throughly described in terms of differential equations and integrable Hamiltonian systems, coming from the Riemann-Hilbert problem associated to them.

Research Interests

Riemann-Hilbert problems. Random matrices, Integrable Systems, Analysis of non-linear (possibly integrable) PDEs.


Research group seminars

We are starting a research group on Random Matrix Theory and Analysis of nonlinear PDEs at CSU!
Here are some notes to get an idea of what we’re dealing with:

  • Determinantal Point Processes, notes from the lecture given at the Inverse Problem seminar series on February 2017.
  • Random Matrices, notes from the lecture given at the Inverse Problem seminar series on February 2017.




  • Variational formulation of a PDE, notes from the lecture given at the PDELab seminar in October 2017.


  • For more information, check prof. McLaughlin webpage.