EPSRC Reference: 
EP/W026554/1 
Title: 
Dynamics on CalabiYau and abelian varieties 
Principal Investigator: 
Prendergast, Dr A 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematical Sciences 
Organisation: 
Loughborough University 
Scheme: 
Standard Research  NR1 
Starts: 
01 October 2022 
Ends: 
30 June 2023 
Value (£): 
80,635

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
This exploratory project will study symmetries of geometric objects called algebraic varieties. These are shapes defined by algebraic equations: the simplest example is the circle of radius 1, which is the set of solutions of the equation x^2+y^2=1. A symmetry is a function or rule that sends each point on the variety to another point on the variety, in a reversible way: for example, rotating a circle around its centre by some chosen angle.
In our project, we will study algebraic varieties with more dimensions, and our goal is to get a better understanding the properties of symmetries on these varieties. In particular, we would like to understand the entropy of the symmetries. Entropy is a measure of the complexity of a symmetry; higher entropy means that the symmetry is more complicated, with nearby points on the variety moving apart more quickly as the symmetry is applied again and again.
We will study this problem for two different kinds of algebraic varieties, called CalabiYau varieties and abelian varieties. These kinds of varieties are of interest in geometry, number theory and theoretical physics. In this context there are many interesting symmetries that we can study and numerous theoretical tools that we can use to calculate entropy. By studying our problem in this context, we hope to gain a better understanding of the possibilities for entropy of symmetries.

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.lboro.ac.uk 