# Research Interests

• Random matrix theory and Gauge theory

• Solvable and integrable statistical mechanics models

• Orthogonal polynomials, Toeplitz+Hankel determinants, combinatorics.

• Open quantum systems and its applications

• Solvable and integrable statistical mechanics models

• Orthogonal polynomials, Toeplitz+Hankel determinants, combinatorics.

• Open quantum systems and its applications

*(more recenly)*Citations to my work can be found at Inspire database. Citations

not from hep-th papers can be found at Google Scholar. If interested

in a PhD position, please do not hesitate to contact me and see also

the National PhD Call.

# Brief Research description

I have been mainly working on matrix model descriptions of gauge theories, including Chern-Simons theory, supersymmetric gauge theories and 2d Yang-Mills theory (and its q-deformation and refinements). Chern-Simons theory in particular, is a purely topological three dimensional quantum field theory with a gauge symmetry. It has been relevant in topology, as it provided a physical way to obtain novel 3d topological invariants. In physics, Chern-Simons theory appears in the study of topological strings and also in condensed matter physics applications, such as the fractional quantum Hall effect.

We are currently studying, in different works and using matrix models, connections between Chern-Simons theory and spin chains, Wilson loops in N=4 susy gauge theory and quantum phase transitions in gauge theories. I am also interested and currently working on the SYK model.

The models of random matrix theory that appear in the gauge theories above mentioned are often very rich from a mathematical point of view, and the methods to understand them involve a multitude of connections to problems in algebraic combinatorics, representation theory, operator theory (Fredholm and Toeplitz/Hankel determinants and minors) and the theory of special functions. On these topics, I am supervising the PhD thesis of David García-García.

Ideas and results from statistical mechanics have also been useful to establish connections between gauge theories, such as Chern-Simons theory or supersymmetric gauge theories, with non-intersecting Brownian motion and integrable and solvable models such as six-vertex models, spin chains and Coulomb gases. I also have started working on matrix models and noncommutative field theory, together with PhD student, Leonardo Santilli.

More recently, I have started working on open quantum systems, looking also into some of its applications, such as photosynthetic light harvesting. For this, it seems interesting to focus on realistic, experimentally-driven, spectral bath functions. In addition, I also started working on exact solutions of some models of disordered systems (such as organic semiconductors) and of relaxation processes.

## Contact Data

Departamento de Matemática, Grupo de Física Matemática, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edificio C6

1749-016 Lisboa, Portugal.

**Tel. **+351 217500267**Fax **
**Email **