EPSRC Reference: 
EP/N027531/1 
Title: 
Differentiability and Small sets 
Principal Investigator: 
Maleva, Dr O 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
School of Mathematics 
Organisation: 
University of Birmingham 
Scheme: 
Standard Research 
Starts: 
01 July 2016 
Ends: 
30 June 2019 
Value (£): 
254,111

EPSRC Research Topic Classifications: 
Algebra & Geometry 
Mathematical Analysis 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
An ever increasing number of mathematical models, including those behind some cutting edge technology used in drones and driverless cars, use functions which are not differentiable, yet satisfy constraints on how fast they change. A distinguished class of such functions are known as Lipschitz functions. Points where a Lipschitz function fails to behave as an ordinary, differentiable function, form an exceptional "small set" whose nature, though elusive, holds a key to crucial properties of the whole class of Lipschitz functions on a given space. In recent years, these exceptional sets have begun to be extensively studied, but many fundamental questions remain open. The proposed project aims to attack such questions, especially those that concern their geometric properties. For example, a small set may have dimension which is not an integer, which is a common feature of fractals. And indeed, one of the direcions in the proposed research is to capitalize on the most recent advances concerning fractal sets and possibly ergodic theory, and instead of relying on the wellknown Hausdorff dimension, find the minimal possible dimension functions which gauge the size of the set in a precise way. The research will also lay the foundations of the geometric theory of curve porous sets, expected to be the "correct" class of small sets for Lipschitz functions of two or more variables, and obtain precise results on typical differentiability type of Lipschitz functions on a null set in a Euclidean space.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


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Project URL: 

Further Information: 

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