EPSRC Reference: 
EP/P026729/1 
Title: 
Dynamic models of random simplicial complexes 
Principal Investigator: 
Fountoulakis, Dr N 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
School of Mathematics 
Organisation: 
University of Birmingham 
Scheme: 
Standard Research 
Starts: 
03 December 2017 
Ends: 
02 December 2020 
Value (£): 
269,286

EPSRC Research Topic Classifications: 
Algebra & Geometry 
Logic & Combinatorics 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
Networks have recently become a central notion in a variety of scientific disciplines such as computer science, data science, biology and economics. Their importance increased in the last decade as the development of the Internet and the mobile networks have had a significant impact on society and various sectors of the economy. This makes it important to develop an appropriate mathematical framework to understand their formation and evolution. In particular, it turns out that an intrinsic characteristic of network evolution is randomness. In fact, large networks involve randomess both in their formation and their evolution. One of the main challenges is to gain insight into how randomness actually gives rise to structure and selforganisation.
The most common representation of networks is through graphs, where the interaction between individuals is represented by an edge that joins the corresponding nodes. However, in reality interactions are far more complex and, in fact, involve a multitude of individuals. In this project, we will use the mathematical framework of random discrete topological spaces to develop a systematic theory of the evolution of networks whose growth is characterised by multidimensional interactions. Such spaces have also been used in an entirely different context, as part of the development of the theory of quantum gravity. There, they were used as an expression of the granular structure of spacetime, in an attempt to unify general relativity with quantum mechanics.
In our project, we will consider even more general models which allow for dynamically growing structures. The objectives focus on the study of largescale properties of these objects, based on tools and notions from combinatorics, probability theory and topology. Furthermore, we will explore how these features are linked to dynamics on these spaces, such as random walks and their mixing time. We will also determine the key combinatorial characteristics of these networks and investigate the emergence of globalscale phenomena in them. In particular, we will be aiming to determine those conditions on the growth mechanism which ensure the emergence of powerlaw degree distributions in the network as well as its smallworld properties. Furthermore, we will aim to discover those conditions that characterise the emergence of condensation phenomena in these networks. Such phenomena are also relevant in statistical physics. In this context, they are linked to the emergence of irregularities in the distribution of the degrees and the existence of extremely highly connected nodes.

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Further Information: 

Organisation Website: 
http://www.bham.ac.uk 