Katie Gittins

Currently, I am an Assistant Professor in Analysis at the Department of Mathematical Sciences, Durham University, U.K. For further information, you can find my CV here.

From August 2018 to August 2020 I was a maitre-assistante at the Université de Neuchâtel, Switzerland.

I was a Postdoctoral Fellow at the Max Planck Institute for Mathematics in Bonn, Germany, from October 2017 until July 2018. 

I spent one year as a post-doctorante working with Prof. Bruno Colbois at the Université de Neuchâtel, Switzerland.

I completed my PhD at the University of Bristol, U.K., in September 2016 under the supervision of Prof. Michiel van den Berg.

Research Interests

I am fascinated by problems which lie on the interface between Analysis and Geometry and typically involve Partial Differential Equations.

For example,

• The heat flow on certain sets in Euclidean space. Take an open set in Euclidean space and suppose it has initial temperature 1, while its complement has initial temperature 0. I explore the interplay between the geometry of this set and the amount of heat which is left inside it at a given time.

• Optimisation of the eigenvalues of the Laplacian (with boundary conditions) among collections of open sets in Euclidean space. The sets in these collections satisfy some geometric constraints, such as prescribed measure or prescribed perimeter. I am particularly interested in the asymptotic behaviour of a sequence of such optimal sets.

• The Courant-sharp eigenvalues of the Laplacian with Dirichlet, Neumann or Robin boundary conditions on open sets in Euclidean space. How many are there and how does this number depend upon the geometry of the set? 

For further information, please see the "Papers and Preprints" tab.

Durham University Maths First-Generation Scholars Group

Jointly with Tyler Helmuth, I am running the Maths First-Generation Scholars Group which forms part of Durham University's First-Generation Scholars’ network. If you are a member of Durham University who would like to participate in this group, then please feel free to contact me by email.