Project description
Decoding symbolic systems using quantum theories
Symbolic dynamics is a key area in mathematics, closely linked to coding theory, information theory and operator algebras. Since the 1970s, a major challenge has been to classify symbolic dynamical systems to better understand their intricate properties. Funded by the Marie Skłodowska-Curie Actions programme, the SDQI project aims to classify symbolic systems and their symmetries using recent advances in graph theory, quantum information and quantum groups. The research team will introduce the Conjugacy Game to define quantum conjugacies and quantum automorphisms for symmetries, marking the first interaction between quantum information, quantum groups and symbolic dynamics.
Objective
This project in pure mathematics aims to solve problems in symbolic dynamics (a mature branch of dynamics with important connections to coding theory, information theory, and operator algebras) using tools from the modern theories of quantum information and quantum groups. The central challenge dating back to at least the 1970s is to classify symbolic dynamical systems. My proposal pioneers a highly interdisciplinary and novel approach using the uniquely quantum phenomena of ‘entanglement’ and ‘noncommutativity’ as they appear in quantum information/quantum groups. The main objective is therefore to establish a fruitful connection between symbolic dynamics, quantum information theory and quantum groups to the benefit of all three communities.
The proposal is based around two central open problems: how do we classify symbolic systems, and what are the symmetries of symbolic systems? A novel approach to these problems builds on the recent advances made in part by the supervisor that connect graph theory with quantum information/quantum groups. I introduce a new nonlocal game (the Conjugacy Game) that will define ‘quantum conjugacies’, and a notion of quantum automorphism that will define ‘quantum symmetries’ of symbolic systems. This marks the first interaction between quantum information/quantum groups and symbolic dynamics. The ideas are therefore very timely, will have high impact, and set a precedent for future uses of quantum mathematics in other domains and specifically other classes of dynamics (e.g. multidimensional subshifts and algebraic actions).
The fellowship will strengthen my academic career via the opportunity to learn new tools in quantum mathematics and apply them to solve important problems in dynamics. It will also allow me to establish new collaborations with leading experts in dynamics and quantum information/quantum groups that will play a key role in my goal of obtaining a permanent academic job and an investigator grant to build a research g
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Keywords
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2023-PF-01
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
1165 KOBENHAVN
Denmark
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.