Project description
Asymptotic spectra to expand our understanding of computer science
Throughout computer science, mathematics, and physics, one question keeps being raised: What is the cost of a task performed multiple times? It forms the core of many challenging problems. The capset problem in additive combinatorics, fast matrix multiplication in algebraic complexity theory, and other similar issues have, despite significant effort, seen few structured approaches that avoid known barriers. The recent theory of asymptotic spectrum duality is key in this struggle. The ERC-funded SPECTRA project aims to develop an approach using asymptotic spectrum duality theory and apply it to direct-sum problems. The project will lead to new insights and fast matrix multiplication algorithms. It will also circumvent current barriers and expand our understanding.
Objective
What is the cost of a task if we have to perform it many times? This fundamental question appears throughout computer science (direct-sum problems), mathematics, and physics. Challenging, protagonistic problems of this kind, that play a central role in this proposal, are fast matrix multiplication in algebraic complexity theory, Shannon capacity in graph theory, efficient asymptotic entanglement transformations in quantum information, and the cap set problem in additive combinatorics. Despite tremendous effort, structured approaches avoiding known barriers have been lacking.
Recent work by the PI has built the theory of asymptotic spectrum duality, which Strassen originally introduced to study matrix multiplication, into a powerful theory for direct-sum problems in various areas—from algebraic complexity, to discrete mathematics, quantum information and computational complexity—characterizing such problems in terms of an “asymptotic spectrum”. This approach opens a wealth of unexplored routes towards solving direct-sum problems via methods from algebra, analysis, combinatorics, and optimization.
This proposal develops the asymptotic spectrum approach and synergetic applications to direct-sum problems: their general structure theory, methods for specific problems (matrix multiplication, Shannon capacity, and beyond), and interactions among them. Key objectives are: (1) to construct, through topological properties of asymptotic spectra, entirely new kinds of fast matrix multiplication algorithms and circumvent barriers of existing methods; (2) determine the Shannon capacity and its properties through a new approximation approach induced by asymptotic spectrum distance and structured (orbit) packings; (3) determine the structure (topological, geometric, computational) of asymptotic properties of quantum entanglement (tensors); and (4) develop the structural theory and broad applications of asymptotic spectra and interdisciplinary methods for direct-sum problems.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics algebra
- natural sciences mathematics pure mathematics discrete mathematics graph theory
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
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.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
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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
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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-ERC - HORIZON ERC Grants
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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) ERC-2025-STG
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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.
1012WX Amsterdam
Netherlands
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