Homogeneous structures and their automorphism groups

Lead Research Organisation: Imperial College London
Department Name: Dept of 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.

Publications

10 25 50

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509486/1 01/10/2016 30/09/2021
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