EPSRC Reference: 
EP/L018896/1 
Title: 
Geometry and Conformal Invariance of Random Structures 
Principal Investigator: 
Berestycki, Professor N 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Pure Maths and Mathematical Statistics 
Organisation: 
University of Cambridge 
Scheme: 
EPSRC Fellowship 
Starts: 
01 October 2014 
Ends: 
30 September 2020 
Value (£): 
1,044,626

EPSRC Research Topic Classifications: 
Algebra & Geometry 
Mathematical Analysis 
Statistics & Appl. Probability 


EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
The interface between probability, geometry and analysis is enjoying an intensely creative phase where new geometric aspects of random structures are discovered. The random structures considered are ultimately of interest as models in physics, or biology or computer science but are motivated at least as much by the possibility that they are fundamental, universal mathematical objects.
A key example is the emerging theory of random planar geometry, which is the primary concern of this project. What does a typical, random surface look like? And what is, in fact, the 'right' notion of a random surface?
In this project, we aim to unify two distinct approaches to this question (discrete and continuous) and try to show that they form two sides of one same coin. Along the way, this would show that certain natural discrete notions of random surfaces gain a fundamental new set of symmetries (known as conformal invariance) in the scaling limit, i.e., when viewed from far away. This would identify a canonical model of random geometry, known as Liouville random geometry.
Liouville random geometry is believed to be fairly counterintuitive. Its 'topological' and 'metric' dimensions do not coincide; in order to travel from A to B you must first travel towards C, etc. Hence another main goal of this project is to develop new techniques to better understand the properties of this geometry.

Key Findings 
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk

Potential use in nonacademic contexts 
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk

Impacts 
Description 
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk 
Summary 

Date Materialised 


Sectors submitted by the Researcher 
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk

Project URL: 

Further Information: 

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