Homogeneous structures and their automorphism groups
Lead Research Organisation:
Imperial College London
Department Name: Mathematics
Abstract
Infinite homogeneous structures arise as canonical 'limits' of certain classes of finite structures. There is a rich and surprising interplay between the combinatorics of the finite structures in the class and the automorphism group (that is, the symmetries) of the homogeneous structure obtained as its limit. The project will focus on various aspects of this interplay, such as subgroup structure of the automorphism group and actions of the automorphism group on various topological spaces. The project will involve a mixture of ideas from different parts of Mathematics, including combinatorics, group theory, topology and model theory. The research is aligned with the EPSRC research areas Logic and Combinatorics and Algebra within Mathematics.
People |
ORCID iD |
| David Evans (Primary Supervisor) | |
| Yibei Li (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509486/1 | 01/10/2016 | 31/03/2022 | |||
| 1834495 | Studentship | EP/N509486/1 | 01/10/2016 | 31/03/2020 | Yibei Li |
| Description | I have generalised an existing theorem in Model Theory. I then applied it to some mathematical structures and achieved some novel results about some algebraic properties of these structures. |
| Exploitation Route | The generalised theorem might be applied to some other mathematical structures. |
| Sectors | Other |
| Description | The automorphism groups of generalised metric spaces |
| Organisation | Charles University |
| Country | Czech Republic |
| Sector | Academic/University |
| PI Contribution | We worked on the automorphism groups side of the research and helped our collaborators understand how to apply some theorem in Model Theory to generalised metric spaces. |
| Collaborator Contribution | Our collaborators, Jan Hubicka and Matej Konecny, worked on generalised metric spaces and the application of some theorem in Model Theory on these metric spaces. |
| Impact | We produced a novel result about some algebraic property of the automorphism group of the generalised metric spaces. The preprint of the work has been put on arxiv and will be published. |
| Start Year | 2018 |
| Description | Imperial College Faculty of Natural Science research showcase |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | Local |
| Primary Audience | Postgraduate students |
| Results and Impact | I presented my poster about my current research to about 20 people at the event and had discussions with them. |
| Year(s) Of Engagement Activity | 2019 |
| URL | https://www.imperial.ac.uk/events/97093/faculty-of-natural-sciences-research-showcase-2019/ |
| Description | Imperial College PhD summer showcase |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | Local |
| Primary Audience | Postgraduate students |
| Results and Impact | I presented my poster about my current research to about 20 people at the event and had discussions with them. About 70 people attended the event. |
| Year(s) Of Engagement Activity | 2019 |
| Description | Imperial College President's PhD Scholars' Symposium |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | Local |
| Primary Audience | Postgraduate students |
| Results and Impact | I presented my researches to the postgraduate community at Imperial College, which sparked questions and discussions after the talk. About 80 people attended the event. |
| Year(s) Of Engagement Activity | 2019 |
| URL | https://www.imperial-scholar-symposium.co.uk/ |
| Description | STEM for Britain |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Public/other audiences |
| Results and Impact | STEM for Britain is a public engagement event organised by the UK parliament, where the participants make poster presentations to the general public as well as the parliament members to publicise the current researches in STEM. About 50 parliament members, 50 professors and 150 early-stage researchers attended. I presented my poster to about 20 people and had discussions with them about my research. |
| Year(s) Of Engagement Activity | 2019 |
| URL | http://www.setforbritain.org.uk/index.asp |