EPSRC Reference: 
EP/V009044/1 
Title: 
Graph theory in higher dimensions 
Principal Investigator: 
Georgakopoulos, Dr A 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
University of Warwick 
Scheme: 
Standard Research 
Starts: 
01 July 2021 
Ends: 
30 June 2024 
Value (£): 
377,948

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 
Graph theory is a modern and highly active branch of mathematics with an increasingly important impact on other areas, including computer science, geometry, number theory, topology, probability, and statistical mechanics.
A mainstream trend in graph theory aims at generalising results from graphs to hypergraphs. Such gen eralisations tend to be much harder than their graph analogues, or even provably impossible, and so despite the careerlong efforts and deep machinery of generations of graph theorists, we will never be able to extend all of graph theory to hypergraphs. But it is definitely worth doing so for those statements likely to have an impact on other disciplines.
This proposal takes this viewpoint as a starting point. It departs from the mainstream in two ways. Firstly, the generalisations we seek are driven by concrete applications to other areas of mathematics highlighted by the objectives set below. Secondly, rather than a purely combinatorial approach to graphs and hypergraphs, we take a topological viewpoint: when graphs are viewed as 1dimensional simplicial complexes, natural topological extensions of definitions and theorems to higherdimensional cellcomplexes the alter ego of hypergraphs suggest themselves.
One of the ambitions of this project is to advance the development of a unified theory of lowdimensional topological combinatorics that parallels the growth of graph theory into a discipline and has a longlasting impact on other disciplines. To avoid the risk of getting lost in abstract theory building, concrete objectives are set out below to ensure that the theory grows into the right directions and bears fruit within the timeframe of the project. Planarity, and its higherdimensional analogues, plays an important role throughout providing some common ground for the various objectives. These objectives are both important and timely, being strongly related to seminal recent advances.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


Sectors submitted by the Researcher 
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Project URL: 

Further Information: 

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