Details of Grant 

EPSRC Reference:	EP/N027531/1
Title:	Differentiability and Small sets
Principal Investigator:	Maleva, Dr O
Other Investigators:
Researcher Co-Investigators:
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:	Panel Date Panel Name Outcome 02 Mar 2016 EPSRC Mathematics Prioritisation Panel Meeting March 2016 Announced
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 well-known 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.
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Organisation Website:	http://www.bham.ac.uk