Grant applications and the EPSRC

I recently attended a workshop on the grant application procedure ran by the Engineering and Sciences Research Council (EPSRC). The EPSRC is one of several UK research councils and is responsible for funding research across engineering, science, and mathematics through a number of grant and fellowship schemes. I went to the workshop with many questions, and misconceptions, about the grant review process and how funds are allocated. I’m happy to say that I learned a lot, and most of my questions were answered.

The grant writing process is a bit of a mystery and I suspect that this is also true for many other early career academics. I hope that a better understanding of the review process for grant proposals will make it easier when I do eventually apply for a grant. I thought it wise to share what I learned from the workshop. Obviously this is specific to mathematics, but the procedure in other subjects is presumably similar.

Disclaimer: I do not claim to be an expert on grant proposal writing, and I do not represent the EPSRC in any way. I hope that this article is useful to people and that the information contained within is accurate. Please let me know if there are any errors so that they may be corrected.


Once a grant proposal has been submitted, the proposal is first passed to one of a number of portfolio managers, each covering one or more subject areas within mathematics. They will find three reviewers, who will read and comment on the proposal. Two of these reviewers will be found by the portfolio manager from the EPSRC college of reviewers. The third reviewer is chosen will be one of three reviewers suggested by the applicant. (Assuming that these suggestions are appropriate and able to provide a review.)

The reviewers will score the proposal and make comments to be passed back to the applicant. If the reviews are supportive of the proposal, it will be passed to the next stage; an unsupported proposal will be rejected. If the proposal progresses to the next stage, the reviews of the proposal will be passed back to the applicant, and they will have the opportunity to respond to some of the points raised by the reviewers. It is important to note that this response will not bee seen by the reviewers!

The response by the applicant should address any criticisms and concerns, and should be reasonably self-contained. The reviews and the applicants response will be the main points considered in the next stage of the application procedure, which is a panel.

The grant review panel meets several times per year to consider proposals and decide which have sufficient merit to be funded. The panel consists of a number of academics, around 15 I believe, who sit at a table and discuss each proposal, its reviews, and the applicant’s response to the criticism. The proposals are ranked, and a number of proposals from the top of this list are chosen to be funded. The number will depend on the value of each proposal and the funds available.


At present, the EPSRC offer a number of grant and fellowship schemes. For most, especially those in established positions who have received grants in the past, the standard grant scheme will be most appropriate. This scheme covers any proposals that fall within the EPSRC remit with no restrictions placed on the length or value of the proposal.

For early career academics who have not yet submitted a grant proposal, there is also the “new investigator award“, which is only available for those who have not yet been the recipient of a significant grant (over the value of £100k). There are no restrictions on when an proposal can be submitted to this scheme – this is a recent change to allow more flexibility for those who have taken career breaks. Note that the applicant is expected to hold a permanent academic post in order to apply for this scheme.

In addition to these grant schemes are three fellowship schemes, which aim to pay for the applicants time to further their research and typically last three to five years. Unlike other awards a fellowship is a personal award, which means that the funding is tied to the investigator and not a specific institution. There are limitations placed on the subject of a fellowship: it must align with one of the EPSRC priority areas. At present, the areas “intradisciplinary research” and “new connections from mathematical sciences” cover a large number of possibilities.

There are three levels of fellowships available: postdoctoral; early career; established career. These levels represent the different career stages to which they are available, although it is left to the applicant to apply for the scheme that they believe is most appropriate. The EPSRC provides person specifications that describe typical applicants at each stage. Postdoctoral fellowships have a shorter duration but offer the greatest flexibility in subject area, whilst established career fellowships have the longest duration but are more restrictive on subject area.

It seems that there is a large amount of flexibility in the fellowship schemes. However, I feel that fellowships are still extremely competitive and will likely require a large investment of time, with the knowledge that the proposal might not be funded. The standard grant schemes may be less competitive but also seem to be intended for people who already hold (permanent) lectureship positions. (Even if this is not strictly the case, it would be troublesome to apply and receive a grant on a temporary contract.)


It seems that the EPSRC have made a number of positive steps recently to provide what support they can to academics on “non-standard” career paths; in particular, those who have taken career breaks or breaks from research. This is important for those who intend to start families early in their careers. It also seems that they value input from early career researchers through their early career forum, of which I was not aware before the workshop. They also seem to encourage the participation of early career researchers in the review and panel processes.

The napkin ring problem

I heard an interesting thought experiment on a podcast some time ago, but I am not sure of the origins of the problem. This problem is the napkin ring problem. Despite hearing this problem some time ago I have only just found time to convince myself that it is true, surprising as it is. I thought I would share the solution since it is a lovely application of multiple integrations. The problem is as follows:

Take a tennis ball and drill a cylindrical hole exactly through the centre of the ball so a to leave a ring around the circumference whose height is 2cm. (This ring would resemble a napkin ring.) Now take a much larger ball, say the Earth (if this were a perfect sphere), and perform the same task, leaving a ring around the equator of height 2cm. Then these two rings will have precisely the same volume.

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Off on a tangent

I’ve recently become somewhat interested in smooth manifolds and surfaces as a result of preparation for various interviews, amongst other reasons. The concept of a surface is very intuitive, and is a concept that a student of mathematics is likely to encounter very early in their mathematical careers, though a reasonable definition of a surface takes more effort. The result of this formalisation is a remarkably elegant theory, which eventually leads to ideas of smooth manifolds – arguably one of the best sounding mathematical objects – and generalised calculus.

It took quite some time before I had a “big picture” of what a surface is, and how this fits into the grander theory. Undoubtedly I am missing some of the major pieces to this puzzle, but it does show some of the elegance of the theory (at least for me). 

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The ArXiv and me (Part 1)

The ArXiv is a popular pre-print article server for physics, mathematics, and computer science (and other subjects) hosted by Cornell University. It is a fairly common practice for academics to upload a preliminary version of their articles (or other works) to the ArXiv to make them publicly available before they are formally published in a journal. (The process of publication is often lengthy, and many consider it best to make the article available in advance, even though it probably has not yet been peer-reviewed.)

At present, there are around 1.4 million articles hosted on the ArXiv, and more are added every day. (Should you wish to see a visual representation of the articles on the ArXiv, which I assume you do, you should visit paperscape.) In the sub-topics that I watch, there are (approximately) between 4-10 new papers added per day, and these topics are not amongst the most active on the ArXiv. The problem then is to filter the daily uploads to find the papers that are likely to be of interest for me. Luckily, about the same time that I started to think of an automated solution to this problem, I discovered that the ArXiv has some tools that can help with this problem.

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The Zombie Apocalypse

Zombies are a staple of modern popular culture, and appear in a variety of forms, including the traditional slow-moving, unintelligent zombie hordes and less common fast-moving – and perhaps intelligent – zombies. The common theme in media featuring zombies is the the zombie infection, which may affect either the living or the deceased, or both. It is generally agreed that this infection is passed from zombie to non-zombie by means of a scratch or bite, and infection always leads to a transformation into a zombie. (In some more modern interpretations, this transformation may be reversible.)

The spread of the zombie infection is an interesting problem to model mathematically. There are many factors to consider: the chances of a non-zombie becoming infected in an interaction with a zombie; the rate at which interactions between non-zombies and zombies occur; the spread the zombie horde from place to place; and the “critical mass” of the zombie horde at which point there is insufficient food for all zombies. We can model parts of this problem in isolation, with some simplifying assumptions.

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Abstract Python

The use of computers in mathematics for long and complex calculations has allowed us to use mathematical tools to model the real world in detail that would have been unimaginable in past decades. In recent years, computational mathematical tools have been used for a huge variety of tasks, from detecting gravitational waves to contactless payment. All of these tasks are computational problems, usually involving very long or complex calculations, but the link between mathematics and computer science is much deeper than as a tool for solving computational problems.

Mathematics and computers share the same basic language, the language of logic, but they also share a philosophy. In object orientated programming, objects are created according to a template called a class. A class outlines the properties and operations that can be performed on the corresponding objects, and can inherit properties from parent classes. This allows the programmer to ensure objects that are similar in some way to share a common collection of properties and operations. This process of abstraction is very powerful and flexible, and is precisely the same as the process of abstraction that has been employed by mathematicians. Continue reading “Abstract Python”