Project description
Ensuring electric vehicles keep humming in extreme cold
The seven Millennium Prize Problems play a crucial role in exploring fundamental questions in mathematics and related fields. The P vs NP problem is essential for understanding complexity theory. In contrast, the graph isomorphism problem (GI) and other challenges in computational group theory, which are neither in P nor NP, offer promising paths for advancement. With the support of the Marie Skłodowska-Curie Actions programme, the AlFiGs project will study the NORM problem by utilising GI to develop more accurate and efficient practical algorithms and sharpen complexity bounds. Further, by taking advantage of their findings and the novel algorithms they enable, the discovery of key insights into computational group theory will be possible.
Objective
P vs NP, one of the seven Millennium Mathematics Problems, drives fundamental questions in complexity theory. The graph isomorphism problem (GI) and related challenges in computational group theory occupy a fascinating position in this landscape—potentially neither in P nor NP-complete—making them fascinating test cases for understanding computational hardness. Babai's breakthrough quasipolynomial algorithm for GI uses advanced group theory, demonstrating how group-theoretic approaches can revolutionise computational complexity.
This project targets the NORM problem: given subgroups G and H of a fixed symmetric group, construct the normaliser of G in H. Both GI and NORM are related to a family of polynomially equivalent group theory problems, the Luks class. GI reduces to this class, and all problems in the Luks class reduce to NORM, positioning it at the apex of the hierarchy. I will prove sharper complexity bounds and develop efficient practical algorithms using an innovative approach that utilises deep structural properties of finite groups.
Current general bounds for NORM show simply exponential complexity. Recent advances have achieved quasipolynomial-time solutions for primitive groups, but vast gaps remain for general permutation groups. I will fill these gaps by combining, in an innovative way, my expertise in generation and crown theory with my supervisor's computational algebra expertise. I will develop polynomial algorithms for primitive groups (WP1) and quasipolynomial ones for the general case (WP2), and release optimised algorithms in GAP/MAGMA (WP3).
AlFiGs will innovately apply structural group theory to computational problems, while building new algebraic tools, and delivering immediate benefits to researchers through open-source implementations that accelerate progress in computational group theory and in its endless applications.
This will make me a competitive independent researcher, who can aspire to become an expert in the field.
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.
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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.1.2 - Marie Skłodowska-Curie Actions (MSCA)
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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
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-2025-PF
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KY16 9AJ ST ANDREWS
United Kingdom
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