My main current interests are in 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 Hamoon Mousavi. ITCS 2025. arXiv.
Abstract: After the NP-hardness of computational problems such as 3SAT and MaxCut was established, a natural next step was to explore whether these problems remain hard to approximate. While the quantum extensions of some of these problems are known to be hard-indeed undecidable-their inapproximability remains largely unresolved. In this work, we introduce definitions for the quantum extensions of Label-Cover and Unique-Label-Cover. We show that these problems play a similarly crucial role in studying the inapproximability of quantum constraint satisfaction problems as they do in the classical setting.
Work in collaboration with Eric Culf and Hamoon Mousavi. FOCS 2024. arXiv.
Abstract: Noncommutative constraint satisfaction problems (NC-CSPs) are higher-dimensional operator extensions of classical CSPs. Despite their significance in quantum information, their approximability remains largely unexplored. A notable example of a noncommutative CSP that is not solvable in polynomial time is NC-Max-3-Cut. We present a 0.864-approximation algorithm for this problem. Our approach extends to a broader class of both classical and noncommutative CSPs. We introduce three key concepts: approximate isometry, relative distribution, and *-anticommutation, which may be of independent interest.
Work in collaboration with Marco Meineri and Joao Penedones. JHEP. arXiv.
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