Academic Background

I am currently a fourth year MASDOC student at the university of Warwick, and am under the supervision of Charlie Elliott and Björn Stinner. Before that I completed my MMath also at the University of Warwick.

Research Interests

My primary area of research includes phase-field models and surface PDEs, particularly those with biological applications. Currently I am considering a model for certain shape and pattern formation observed on biological membranes known as lipid rafts. In particular I am considering the case when there is a coupling between the local curvature and local composition of the membrane. Some topics this work includes are gradient flows, a priori estimates (obtained by a Galerkin approximation) to prove existence and uniqueness results, formal asymptotic analysis, Gamma convergence and using Finite Element Software to conduct numerical simulations to explore the qualitative and quantitative behaviour for these problems.

Publications

• Elliott, C. M., & Hatcher, L. (2020). Domain formation via phase separation for spherical biomembranes with small deformations. European Journal of Applied Mathematics, 1-26. doi:10.1017/S0956792520000297
• Elliott, C. M., Hatcher, L., & Herbert, P. J. (2019). Small deformations of spherical biomembranes, in 11th
  Seasonal Institute "The role of metrics in the theory of partial differential equations", Mathematical Society
  of Japan, Tokyo,

Presentations

• Phase field models for small deformations of biomembranes arising as Helfrich energy equilibria, British Applied Mathematics Colloquium (BAMC), University of Bath, April 2019
• Sharp and diffuse interface problems relating to Canham-Helfrich equilibria, Interplay of Probability, Statistics and Analysis, University of Warwick, April 2019
• A Phase Field Model for Domain Formation for Small Displacements of a Spherical Biomembrane, UK Joint CDT Colloquium, University of Oxford, April 2018
• Lipid Rafts and Biomembranes, Warwick Postgraduate Seminar, University of Warwick, February 2018

Grants, Scholarships and Awards

• 1st prize in the 2019 British Applied Mathematics Colloquium (BAMC) Poster competition
• LMS Bursary to attend the 2019 British Applied Mathematics Colloquium
• Supported by the UK Engineering and Physical Sciences Research Council (EPSRC) Grant EP/H023364/1 within the MASDOC Centre for Doctoral Training

Conferences and Workshops attended

• LMS-CMI Research School on PDEs in Mathematical Biology: Modelling and Analysis, ICMS, Edinburgh, May 2019
• British Applied Mathematics Colloquium, University of Bath, April 2019
• Interplay of Probability, Statistics and Analysis, University of Warwick, April 2019
• Oberwolfach Workshop: Surface, Bulk, and Geometric Partial Differential Equations: Interfacial, stochastic, non-local and discrete structures, Oberwolfach, Germany, January 2019
• Joint CDT Colloquium: Analysis and PDEs, University of Oxford, April 2018

Teaching

I have recently been awarded Associate Fellow status of The Higher Education Academy in recognition of my engagement with pedagogic literature and compilation of a portfolio reflecting on my teaching experiences through the APP PGR course here at Warwick. A summary of my teaching experience can be found below.

2019/2020

Online Tutor for the Warwick Online Learning Certificate

Teaching assistant for MA250 Introduction to PDEs

Teaching assistant for MA258 Mathematical Analysis III

2018/2019

Teaching assistant for MA258 Mathematical Analysis III

Teaching Assistant for MA131 Analysis II

Supervisor for first year undergraduate students

2017/2018

Teaching Assistant for MA131 Analysis II

2015/2016

Supervisor for first year undergraduate students

Contact

My email address is L.Hatcher@warwick.ac.uk and my office is B3.04