InfGroups · Foundations for computing with infinite linear groups
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2016-05-01 → 2018-04-30
- EU contribution
- €183,455
- Participants
- 1
- Scheme
- MSCA-IF-EF-ST
Lines connect the coordinator with its partners.
Results in brief
Foundations for computing with infinite linear groups
This project is in a frontier area at the interface of algebra and computer science. The overall research objective is to build up a new domain of computational group theory: computing with finitely generated linear groups over infinite fields. To achieve that goal, the following problems were solved. We developed innovative methodology to compute in this class of groups, based on a computer realization of properties of linear algebraic groups. We applied the methodology to design algorithms for all major classes of finitely generated linear groups. Our results also justify decidability of related algorithmic problems; an achievement of interest in its own right. The algorithms have been implemented in the main computer algebra systems, and made available publicly. We have used this software to solve open problems in group theory and its applications by means of computer-aided experimentation. The project will contribute to the international competitiveness of the EU in fundamental science, specifically by strengthening its leadership in the development of major computer algebra systems.The project catalyzed collaboration between EU universities and academic institutions world-wide. This, together with dissemination activities of the project, contributed to EU plans to increase numbers of postdoctoral researchers by stimulating interest in STEM research.
Data: CORDIS, © European Union
Project objective
This project is in computational group theory (CGT), a novel domain of algebra at the interface with computer science. The main objective of the project is to build up a new area of CGT – computing with groups generated by a finite set of matrices over an infinite field. This entails: (i) development of a methodology to handle the main classes of finitely generated linear groups in a computer; (ii) justification of decidability and solution of fundamental algorithmic problems; and (iii) design of software for practical computation. In particular, we focus on practical algorithms for arithmetic groups, Zariski dense subgroups, and virtually solvable linear groups.The planned results will be the first of their kind. The project will impact group theory by replacing cumbersome methods with straightforward computation, allowing the solution of previously intractable problems. The project will impact other sciences and mathematics overall by providing a means for scientists to carry out effective mathematical experiments in areas where linear groups appear as a mathematical model of transformations.The planned research and related activities (such as the establishment of an international research team) will impact the career of the researcher by bringing her recognition as a leading expert in computational algebra and its applications. Training in computer science in the world-class environment provided by the host, and complementary training in IT skills provided by the industrial partner during secondment, will diversify competencies and career prospects of the researcher. The project is designed to make the host institution a world centre in this new area of computational algebra. The project's communication and public engagement strategy will promote mathematics as a profession for women, thereby impacting EU society by taking measures to redress gender imbalance in STEM.
Original text from CORDIS.
Participants
- THE UNIVERSITY COURT OF THE UNIVERSITY OF ST ANDREWS · ST ANDREWSCoordinatorUnited Kingdom
Links
Data: CORDIS, © European Union