My main current interests are in theoretical quantum information theory and quantum complexity theory. I am particularly interested in non-local games and the power of entanglement. I am helping organizing a seminar on this topic at the University of Copenhagen, more information here.
Work in collaboration with Eric Culf and Hamoon Mousavi. You can find the paper here.
Abstract: We study operator - or noncommutative - variants of constraint satisfaction problems (CSPs). These higher-dimensional variants are a core topic of investigation in quantum information, where they arise as nonlocal games and entangled multiprover interactive proof systems (MIP*). The idea of higher-dimensional relaxations of CSPs is also important in the classical literature. For example since the celebrated work of Goemans and Williamson on Max-Cut, higher dimensional vector relaxations have been central in the design of approximation algorithms for classical CSPs. We introduce a framework for designing approximation algorithms for noncommutative CSPs. Prior to this work Max-2-Lin(k) was the only family of noncommutative CSPs known to be efficiently solvable. This work is the first to establish approximation ratios for a broader class of noncommutative CSPs. In the study of classical CSPs, k-ary decision variables are often represented by k-th roots of unity, which generalise to the noncommutative setting as order-k unitary operators. In our framework, using representation theory, we develop a way of constructing unitary solutions from SDP relaxations, extending the pioneering work of Tsirelson on XOR games. Then, we introduce a novel rounding scheme to transform these solutions to order-k unitaries. Our main technical innovation here is a theorem guaranteeing that, for any set of unitary operators, there exists a set of order-k unitaries that closely mimics it. As an integral part of the rounding scheme, we prove a random matrix theory result that characterises the distribution of the relative angles between eigenvalues of random unitaries using tools from free probability.
Work in collaboration with Marco Meineri and Joao Penedones. You can find the paper here.
Abstract: We study correlation functions of the bulk stress tensor and boundary operators in Quantum Field Theories (QFT) in Anti-de Sitter (AdS) space. In particular, we derive new sum rules from the two-point function of the stress tensor and its three-point function with two boundary operators. In AdS2, this leads to a bootstrap setup that involves the central charge of the UV limit of the bulk QFT and may allows us to follow a Renormalization Group (RG) flow non-perturbatively by continuously varying the AdS radius. Along the way, we establish the convergence properties of the newly discovered local block decomposition of the three-point function.
You can read more about the ideas of the conformal bootstrap on the bootstrap collaboration website.
Here are the thesis I have written during my Bachelor and my Master's which might be helpful to someone.
This is my Master's thesis which I have written under the supervision of Philip Candelas and Chris Beem. It is a review of the seminal paper arXiv:hep-th/9601029 by Andrew Strominger and Cumrun Vafa who derived microscopically the entropy of an extremal black hole in type IIB string theory in five non-compact dimensions.
You can read it by clicking on the following link: MScThesis.pdf
This is my Bachelor's thesis which I have written under the the supervision of Giovanni Felder and Gabriele Rembado. It is a review of geometric quantisation which consists in constructing a Hilbert space out of sections of a line bundle. A thorough background in differential geometry is also given. The simple example of the n-dimensional harmonic oscillator is worked out explicitly.
You can read it by clicking on the following link: BScThesis.pdf