About Me:

I completed my PhD under the supervision of Prof. Charlie Elliott and Dr. Björn Stinner. I may now be found at the University of Koblenz. My new webpage is here. This webpage will no longer be kept up to date.

My office is B3.04 in the Zeeman Building and if you wish to contact me, my email is P.J.Herbert<at>warwick.ac.uk. My interests lie in PDE and their applications, especially biological applications. I am also particularly interested in numerical analysis in non-standard settings.

Background:

I graduated from Warwick in 2016 with an MMath, I did my project under the supervision of Prof. James Robinson discussing the stationary Navier-Stokes equations.

For my MASDOC MSc project I studied the shape of biomembranes with embedded proteins using a linearisation Cahnam-Helfrich energy for both the sphere and in the case of a plane, extending the work of A Variational Approach to Particles in Lipid Membranes using the tools of Small deformations of Helfrich energy minimising surfaces with applications to biomembranes.

Current research:

My current research is around the topic of point particles embedded in these biological membranes along with a so called second order splitting method. Details of the second order splitting can be found in the paper of Elliott, Fritz and Hobbs Second order splitting for a class of fourth order equations. We are also studying the 'forcing' applied to embedded groups of point particles by the membrane.

For the period of June and half of July 2019 I visited Carsten Gräser and Ralf Kornhuber at FU Berlin under the Research Alumni Program.

Publications:

Second order splitting of a class of fourth order PDE with point constraints (with C. M. Elliott), in Mathematics of Computation.

Small deformations to spherical biomembranes (with C. M. Elliott and L. Hatcher), to appear in Advanced Studies in Pure Mathematics, Volume 85.

Teaching:

2015/16:

- Supervisions for first year maths students

2016/17:

- Supervisions for first year non-maths students

2017/18:

- Term 1: Supervisions for second year maths students, TA for MA250 Introduction to PDE

- Term 2: Supervisions for second year maths students, TA for MA3B8 Complex Analysis

2018/2019:

- Term 1: Supervisions for second year maths students, TA for MA3G7 Functional Analysis I and C++ part of MA913 Scientific Computing

- Term 2: Supervisions for second year maths students, TA for MA3H0 Numerical Analysis and PDE's

2019/2020:

- Term 1: Supervisions for first year math students, TA for MA4A2 Advanced PDEs

Talks Given:

June 2017: Mathematics of Batteries, at the MASDOC retreat, with Letizia Angeli and Quirin Vogel

October 2017: Particles in Biomembranes, at the Warwick Post Graduate Seminar

December 2017: Particles in Biomembranes, at WIMP Autumn meeting (Warwick)

April 2018: Particles in Biomembranes, at CDT Joint Colloquium (Oxford)

April 2018: Particles in Biomembranes, at the MASDOC 2018 retreat

October 2018: An introduction to surface PDEs and surface finite elements, at the Warwick Post Graduate Seminar

April 2019: Biological membranes with deformations induced by point particles, at BAMC 2019

May 2019: Biological membranes with deformations induced by point particles, at the MASDOC 2019 retreat

July 2019: A quadratic energy for a near tube biological membrane, FU Berlin Numerical Analysis of PDE biweekly meeting.

Non Research Activities

I am the Chair of the maths SGSLC (2018/2019,2019/2020) and chair of MASDOC SSLC. I was Secretary (2017/2018,2018/2019) for the MASDOC SSLC. I helped to organise the MASDOC 2019 retreat.