Keywords: Supergravity, Supersymmetric Quantum Field Theories, Holography, Equivariant Localization.

In my research I study supergravity and holography using tools from differential and algebraic geometry, with a particular focus on localization techniques.

On the supergravity side, equivariant localization can be used to infer the existence of solutions with a given topology and to compute some of their key properties without the need to actually solve the equations. The observables that can be computed this way are relevant for the AdS/CFT holography, which provides a bridge between supergravity and quantum field theories defined on the conformal boundary of the spacetime.

On the quantum field theory side, localization allows to compute supersymmetric partition functions which give valuable insight into the non-perturbative regime of gauge theories. These partition functions are crucial for discovering and testing various dualities, and in the context of holography they can provide a microscopical explanation for the entropy of AdS black holes and more. Recently, the importance of geometries with orbifold singularities has been recognized, leading to many new interesting prospects for research.

• Math. Dept.