Keywords: Supergravity and Supersymmetric Quantum Field Theory, Holography, Equivariant Localization, Differential Geometry.

My research interests revolve around supergravity, holography, and quantum field theories, in particular in situations characterised by  supersymmetry. The common thread behind these topics is the underlying mathematical structures and the mutual connections, often underpinned by physically motivated relationships, known as dualities, between different theories. My research pursues the discovery of new relationships, with the twofold goal of improving our understanding of fundamental physical theories and of uncovering original results, with independent mathematical interest. In more details, the following are my main research areas.

Supergravity 

Supergravity is an extension of General Relativity which incorporates a local version of supersymmetry. A hallmark of supergravity is that it is directly related to string theory, which is an intrinsically quantum theory of gravity. In my research I have been exploring the “landscape” of solutions to supergravity theories in various space-time dimension. In particular, I developed a systematic approach to the study of supersymmetric solutions, employing group-theoretic methods based on the mathematical framework of group structures. 

Holography

It is a conjectural duality proposed by Maldacena 25 years ago, relating gravitational theories to quantum field theories. It is by far the deepest conceptual breakthrough occurred in fundamental theoretical physics in recent decades, which has revolutionised the way to think about gravity and quantum field theory. Hinging on this duality, also known as AdS/CFT correspondence or gauge/gravity duality, a cornucopia of applications have been proposed, offering new viewpoints on a variety of physical systems, including elementary particles, nuclear physics, condensed matter, hydrodynamics, quantum information, just to name a few. I have discovered several new instances of holographic dual systems displaying previously unseen features. 

Quantum field theories 

Although quantum field theories were originally motivated as a powerful predictive framework describing fundamental physical interactions, they have ramified into areas that have deeply influenced research in mathematical physics and pure mathematics in the past thirty years. For example, topological field theories and supersymmetric field theories led to numerous results in pure mathematics — the groundbreaking results of Witten being perhaps the most emblematic example. In recent years, there have been significant progress in different directions, including (quantum) integrability and localization techniques, which led to astonishing exact results. I have contributed to research in this area by studying supersymmetric quantum field theories in non-trivial backgrounds and evaluating various generating functionals using the technique of supersymmetric localization, that is a functional extension of the idea of equivariant localization, developed by Vergne and others. 

Microscopic structure of black holes

Black holes are mysterious celestial bodies whose existence was originally predicted by General Relativity and spectacularly confirmed very recently by astrophysical observations. In the ‘70s it has been understood (Hawking and Bekenstein) that black holes behave as thermodynamical systems. However, from a theoretical point of view this poses a great challenge as their fundamental structure is intimately related to quantum dynamics, thus ultimately hinging on the quantum nature of gravity. In recent years important work has revealed that black holes arising in string theory, and hence realised in supergravity, can be understood microscopically, in terms of quantum states that can be identified in detail. I am currently pursuing vigorously research aimed at broadening the spectra of examples where such a detailed microscopic description of black holes is applicable, including black holes with singular event horizons, which I have discovered. 

Geometry 

String theory and supergravity served as motivation for developments in different areas of geometry. Prompted by the idea of “compactifications” of string theory, motivated by phenomenological ambitions, older examples include the study of Calabi-Yau and other special-holonomy manifolds. Another ubiquitous area of geometry motivated by physics is the study of Dirac-like operators, including (equivariant) index theorems. The advent of the “compactifications with fluxes” in the early 2000s has substantially broadened the types of geometries of interest, extending special holonomy manifolds to manifolds admitting non-integrable G-structures. These include the famous Strominger-Hull system, and many more. In the context of the AdS/CFT correspondence, relevant geometries include Sasaki-Einstein and various generalisations, to which I have given fundamental contributions. My current research aims at obtaining a unified view on the different geometries arising in the context of the AdS/CFT correspondence, all of which should be characterised by a broad class of extremal problems, akin volume extremization in Sasakian geometry. 

• Math. Dept.