**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);

- Santilli, Leonardo, and Tierz, Miguel. "Crystal bases and three-dimensional N=4 Coulomb branches." [2111.05206].
- Santilli, Leonardo. "Phases of five-dimensional supersymmetric gauge theories." Journal of High Energy Physics 2021.088 (2021): 1-63 [2103.14049].
- Santilli, Leonardo, Szabo, Richard J. and Tierz, Miguel. "$T\overline {T} $-deformation of q-Yang-Mills theory." Journal of High Energy Physics 2020.11 (2020): 1-46, [2009.00657].
- Santilli, Leonardo, and Tierz, Miguel. "Exact equivalences and phase discrepancies between random matrix ensembles.” Journal of Statistical Mechanics: Theory and Experiment 8 (2020): 083107, [2003.10475].
- Santilli, Leonardo, and Tierz, Miguel. "Phase transitions and Wilson loops in antisymmetric representations in Chern–Simons-matter theory." Journal of Physics A: Mathematical and Theoretical 52.38 (2019): 385401, [1808.02855].