| EPSRC Reference: |
EP/L018896/1 |
| Title: |
Geometry and Conformal Invariance of Random Structures |
| Principal Investigator: |
Berestycki, Professor N |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| 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
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Analysis |
| Statistics & Appl. Probability |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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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 counter-intuitive. 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.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.cam.ac.uk |