Publications

This work is set in the broader context of string theory and the AdS/CFT correspondence; in this field geometry can be used to build and study quantum field theories. In this framework, 4D superconformal quiver gauge field theories arises from Calabi–Yau singularities. The combinatorial properties of the associated toric diagram encodes important physical information such as the superconformal central charge, which, for example, tells us about the effective number of degrees of freedom in the theory. The work produces a new geometric reformulation of the Butti-Zaffaroni construction which is relevant computationally: the time needed to compute a single trial R-charge drops considerably from 0.008376 seconds to 0.001536 seconds, meaning the new method uses only about 18% of the original time, or in other words gives a speed-up of roughly 80%.

This work is set in the context of structure transitions in quantum gravity and infrared duality in geometrical engineered field theories from string theory constructions. The work studies what happens when an orientifold projection is introduced. In simple terms, this operation acts like a mirror transformation in string theory: it changes the geometry and modifies the quantum field theory associated with it. In some cases, this transformation does not simply reduce the original theory, but appears to drive it toward a new theory at low energies. The main result is an algebro-geometrical interpretation of orientifolds: they can be seen as maps between different Calabi–Yau geometries. This provides a geometric explanation for certain infrared dualities, where two apparently different theories become equivalent at low energy by renormalization flow.

This work is set in the context of general relativity, gravisolitons and the search for new structures in quantum gravity. Gravisolitons, are exact solutions of Einstein’s equations. Some familiar objects, including black-hole-like solutions are part this broader family.  The paper focuses on a particular class called axialgravisolitons, which have axial symmetry. The main goal is to understand how these spacetimes are at their infinite distance corners. This is important because, in gravity, the behavior of spacetime at large distances reveals hidden symmetries carrying deep physical information. The original result is the construction of a systematic asymptotic expansion for axialgravisolitons and using this expansion, the work identifies the leading asymptotic symmetries and connects them to the corner symmetry proposal, an approach where boundary-like regions of spacetime play a fundamental role in quantum gravity.

This work is set in the context of exotic gauge theories, duality and the infrared structure of the theory. The paper focuses on p-form gauge theories, a generalization of electromagnetism that naturally appears in string theory, supergravity, holography and theories with extended objects such as branes. The central idea is to understand how the asymptotic charges of a p-form theory behave under Hodge-Young duality. Just as electric and magnetic fields are related in ordinary electromagnetism, a p-form gauge field can have a dual description in terms of another form field. The paper shows the construction of a general duality map between asymptotic charges, together with an existence and uniqueness theorem showing that this map is well-defined under suitable topological conditions. The work also connects these asymptotic charges to higher-form symmetries, suggesting that the charges measured at infinity may encode information about extended symmetries in the bulk theory. In a broader perspective, the paper contributes to the study of celestial holography, where physics at infinity is organized as a kind of conformal field theory on the celestial sphere. The appearance of Möbius transformations in the duality of charges suggests a new way to think about celestial CFTs like equivariant principal bundles.

This work, in collaboration with Matteo Romoli, is set in the context of higher-order asymptotic symmetries. The paper focuses on p-form fields in the special dimension D=p+2, where these theories are naturally dual to a scalar field.  The main idea is to study not only the usual asymptotic symmetries, but a whole tower of higher-order symmetries. These symmetries are associated with charges that grow with higher powers of the radial distance before being properly renormalized. To make sense of them, the work uses symplectic renormalization, a procedure that removes divergent terms while preserving the physically meaningful finite charges.  The original result is the identification of N+1 asymptotic charges for a p-form gauge field, each controlled by a function on the angular sphere. Thanks to the Hodge decomposition, these charges take a universal form, essentially independent of the degree of the form field, and are manifestly connected to the dual scalar description. The charge algebra is mostly abelian, with the possibility of central extensions linked to electric/magnetic sectors and renormalization ambiguities.

This work is set in the context of duality in gravity and mixed symmetry tensors. In ordinary gravity, the BMS algebra describes the symmetries that survive at null infinity, extending the usual spacetime symmetries through angle-dependent translations. This paper asks what happens to this picture when gravity is described not by the usual metric field (the graviton), but by its dual formulation in five dimensions.  The central object is the Curtright field, a mixed-symmetry tensor that, in D=5, is the “dual graviton”; thus providing an alternative description of gravity useful for understanding quantum gravity. Although it describes the same physical degrees of freedom as the graviton on shell, its gauge structure is much richer: instead of the familiar metric symmetry, it involves several gauge parameters and gauge-for-gauge redundancies. The original result is the construction of the asymptotic charges of the Curtright field at future null infinity in arbitrary dimension. In five dimensions, these charges split into three sectors: a scalar sector, analogous to supertranslations; a vector sector, related to rotations on the celestial three-sphere; and a transverse-traceless tensor sector, which behaves like a higher-spin extension of the supertranslation part. The resulting algebra closes as a Curtright version of a BMS-like algebra, enriched by this additional tensorial sector.

This work, in collaboration with Domenico Monaco and Gabriele Peluso, is set in the context of topological phases of matter, especially one-dimensional quantum chains. A central object is the Zak phase, a geometric phase acquired by Bloch states along a one-dimensional momentum cycle, widely used as a marker of topology in insulating chains.  The paper investigates how reliable the Zak phase really is across all one-dimensional Altland–Zirnbauer–Cartan symmetry classes, namely the standard symmetry classes used to organize topological insulators and superconductors in the so-called “topological periodic table”. The main idea is to construct Bloch bases adapted to the symmetries of the system and then extract from the Zak phase a Z2​-valued invariant. This gives a unified way to understand when the Zak phase detects some topological information.  The original result is also a limitation result: the Zak phase does not always capture the full topology of the system. In classes with quaternionic structures, associated with anti-unitary symmetries squaring to minus the identity, the invariant obtained from the Zak phase necessarily vanishes. In other cases, such as generalized Kitaev chains, the Zak phase detects only partial information, for example the parity of a richer integer invariant.

This work studies a specific system of partial differential equations, where a scalar function and a one-form are coupled through the Laplace–Beltrami operator, the divergence and the gradient. The motivation comes from theoretical physics: similar equations appear when studying gauge parameters, gauge-for-gauge structures and asymptotic symmetries in exotic gauge theories. The paper focuses on manifolds with constant sectional curvature, especially positive-curvature space forms. These spaces include spheres and their quotients, such as lens spaces, which also appear in string theory, holography and extensions of the AdS/CFT framework. The main strategy is to reduce the original coupled second-order PDE system to a single scalar fourth-order differential equation. This reduction makes it possible to identify an explicit exceptional set of parameters, determined by the laplacian spectrum, where non-trivial solutions may appear. Away from this resonant set, the operator has trivial kernel, which forces the whole original system to collapse to the trivial solution. The central result is a trivialization theorem: on positive-curvature space forms, and outside the excluded resonant parameter set, the only smooth solution is the trivial one. This is first proven on the sphere using spectral and energy arguments and then extended to all positive-curvature space forms through the Killing–Hopf theorem. The relevance of the result is that it provides a clean mathematical criterion for when certain gauge modes or asymptotic sectors cannot exist. In physical terms, it helps clarify when residual gauge parameters or asymptotic charges in higher-form and mixed-symmetry theories are forced to vanish, and when non-trivial structures may require special parameter values, weaker boundary conditions, or additional global/topological ingredients.