Leonardo Santilli is a PhD student in Mathematics at Group of Mathematical Physics, University of Lisbon, since spring 2018. He works under the supervision of Miguel Tierz.
After graduating at La Sapienza University in 2015, he obtained a Master in Theoretical Physics and a Master in Mathematics at the University of Valencia.
He works on Random Matrix Theory and its applications to gauge theories. On the physical side, his focus is on solvable quantum field theories, especially low-dimensional and/or supersymmetric ones. On the mathematical side, he is devoted to the study of unitary, discrete and q-deformed random matrix ensembles and their large N limits. In addition, he is interested in connections between matrix models and algebraic varieties in the framework of supersymmetric field theories. His research achievements include:

• Analysis of the TT-bar deformation of two-dimensional gauge theories (joint work with R.J. Szabo and M. Tierz);
• Exact results in supersymmetric three-dimensional gauge theories and characterization of their phase structure (with M. Tierz);
• Correspondence between crystal bases and three-dimensional N=4 Coulomb branches (with M. Tierz);
• Analysis of the phase diagram of five-dimensional supersymmetric gauge theories;
• Cohomological supersymmetric localization in five dimensions (with R.J. Szabo and M. Tierz).
• Asymptotic behaviour of unitary matrix models and applications to gauge theories and spin chains (with M. Tierz);