Welcome. As this is my first post for this blog, an introduction is probably in order. I’m David, but most people call me DJ, and I am a second year graduate student at the University of Wisconsin – Madison. My research focuses on the intersection of commutative algebra, algebraic geometry, and number theory. Outside of mathematics I enjoy watching and playing sports (Go Blue!) as well as long walks on the beach. (Kidding I’d prefer to be playing volleyball on the beach.)
As Mathew mentioned in a previous blog post the National Science Foundation Graduate Research Fellowship Program (NSF-GRFP) is an amazing program that, “Recognizes and supports outstanding graduate students in NSF-supported science, technology, engineering, and mathematics disciplines who are pursuing research-based Master’s and doctoral degrees at accredited United States institutions.”  I have a bit of experience with the Graduate Research Fellowship (GRF) application, having applied to the NSF-GRFP twice, and am currently supported by the NSF-GRFP. Thus, since the deadline for this is fast approaching I figured I’d share a bit of advice regarding the application process. I should say that I am by no means an expert on the NSF-GRFP, and so all of this advice should be taken with a, possibly large, grain of salt.
Apply: It goes without saying that you will never win a GRF if you do not apply. So make sure you pay attention to deadlines and get all of your application materials in on time. Digressing a bit, I should also point out a few reasons you should consider applying for an NSF GRF:
- It provides an annual stipend of $34,000 for three years!!
- It covers your tuition for three years. This can be a huge benefit as it means that while on fellowship it may be easier for you to work outside of your home institute.
- It can provide you with additional funds to travel abroad for research purposes through the Graduate Research Opportunity Worldwide (GROW) program.
- Did I mention it you’d make $34,000 a year? Oh I did. Well it’s worth mentioning again.
Seek Advice: Applying for a grant is incredibly different from any other type of application. (Well at least for me it was). There are numerous unforeseen pitfalls throughout the application process. Having someone experienced in applying for grants helping you through the process can be invaluable. There is no way I would have been awarded a GRF without the advice, support, and guidance of numerous professors throughout the application process. (In fact I think the biggest difference between my first and second applications was the amount of advice I sought out.) So I would encourage everyone applying to find someone more experienced in applying for grants that you are comfortable turning to for advice. (Your letter writers are usually natural candidates for this role.)
Follow the Rules: Once again this might seem like a silly piece of advice, but the NSF is notoriously persnickety when it comes to following the rules. There is many a grad student whose application was entirely discarded because their margins were the incorrect size or their font was not the NSF standard. So be sure to read the application guidelines the NSF provides, and follows them all to the letter. You don’t want to spend a bunch of time preparing your application, waiting anxiously for the announcement date only to find out that all your work was for naught because you used “exactly 12 point line spacing” and not “singled-space or greater line spacing” . (It is also a good idea to check the uploaded copies of your statements to make sure nothing weird happened during the conversion process.)
Personal Statement: As the name suggests personal statements are personal, and so there is very little I can say about them that would be universally applicable. That said, my one piece of advice is to be genuine, and use the personal statement as a stage to share your story. Every other part of the NSF application — with perhaps exception of the research statement – is clinical: test scores, GPA, etc. so use your personal statement to give your application personality and depth. Oh, and be sure your personal statement is completely free of grammatical and spelling mistakes. A statement riddled with errors makes you come off as unprofessional and someone who did not take the application process seriously.
Research Statement: Writing a research statement can be a daunting task – it was for me. In order to write a good research statement you not only need to have an idea of what is currently going on in a field (hard), but also you need to have some reasonable open problems you can discuss solving (really hard). For this reason I strongly encourage you to reach out and find an advisor who can help you draft your research statement. In particular, more seasoned researchers, i.e. professors, have a much better understanding of the current state of the field, and can aid you in deciding what is worth writing about. In my first research statement I included a few open questions I had found in various pre-prints, and said I would like to answer them. This in itself is a good thing, however, it turns out that many of the questions I included were notoriously difficult. In fact, when preparing my second research statement, one of the professors I consulted told me that it was thought many of the statements I had said I want to prove were false! So having a professor guide you with your research statement is vital. Oh, and again be sure to proofread your statements for grammar and spelling errors.
Broader Impact: One of the areas on which your application will be judged is its “broader impacts”. This is probably the criterion that confused me the most when I first applied. First, what in the world are broader impacts? Well, the NSF’s website says the broader impact criteria, “Encompasses the potential to benefit society and contribute to the achievement of specific, desired societal outcomes.” Okay so that definition is not particular helpful, especially for mathematics. I mean, for those doing research in biomedical engineering or health science, the impact of their research on world around is probably fairly evident. However, it is much less clear how research focused on algebraic geometry, or most other fields of pure math, potentially benefit society. (This is not to say that these fields do not have practical and often times hugely beneficial applications to the real world.)
With this in mind when I was preparing my first application and stumbled upon this problem, I did the first thing every student raised in the 21st century does; I turned to Google. In particular, I spent time digging up every possible applications of algebraic geometry and commutative algebra. I then proceeded to jam all of these references into the final paragraph of my research statement. The result of this was the following:
“My interests and proposed research in “Boij-Soderberg” theory is driven primarily by the beauty of recent results, and not necessarily by any particular application. However, results in pure algebraic geometry often lead to advancements in other fields, such as biological and chemical modeling, statistics, and computer aided design [3,4,5]. Further, the study of free resolutions lends itself nicely to computational experimentation, as computer algebra packages such as Macaulay2 are capable of calculating the Betti diagrams of various resolutions. Thus, the proposed research project has the opportunity to engage other members of the mathematical community, including undergraduates, via computational exploration and the development of additional software packages for Macaulay2.”
Garbage! This is complete garbage. It is the citation heavy fluff that is more at home in an essay a high school student is doing everything in their power to meet the page requirement; not a serious research proposal. Moreover, it is clear that this passage clearly lacks any sense of conviction. It makes the reader believe the writer has no interest in broader impacts.
So if I think the above broader impacts statement stinks what exactly are those studying theoretical mathematics supposed to do? The answer – given to me by a professor I talked to, see another reason to find a mentor — that worked for me is to speak about the broader impacts I have as a person, not the broader impacts of my research. So in my second application the above paragraph was replaced with the following passage:
“I have been actively involved in outreach programs — as an administrator and volunteer for the Michigan Math Circle, course assistant for Michigan Math and Science Scholars summer program, as a guest lecturer at my local high school, etc — aimed interesting K-12 students in STEM fields. Since arriving at the University of Wisconsin, I continue to remain engaged in these ways. I gave a talk for the Madison Math Circle, and am looking to take a larger role in this circle next semester. Additionally, I am a mentor through the university’s Bonding Undergraduates and Graduate Students program.
During the summer of 2014, I organized a weekly seminar, where older undergraduates gave lectures on interesting mathematics not necessarily covered in the usual courses. This semester, I am taking an active role in the graduate student algebraic geometry seminar. In the future, I hope to take a more administrative role in organizing this seminar. I find algebraic geometry appealing because in certain cases one is actually able to do explicit computations — for example using Macaulay 2. I plan to establish a reading group of graduate students and other interested members (undergraduates, postdocs, etc.) to gain a better understanding of how to effectively use Macaulay 2.”
This passage says so much more about the applicant than the first broader impact paragraph. It makes it clear they view mathematics as more than just research and is willing to work to benefit society. In summary don’t limit your broader impacts just to your research, but instead use it to speak about yourself and give your application further depth and personality. (Again despite possibly sounding like a looped YouTube video, because who uses records these days, proofread your broader impacts and then proofread it again.)
Well that pretty much sums of all of the advice I can squeeze out of my experience with the NSF-GRFP. I should also say that most of this advice is not original to me, but instead is my synthesis of all the advice and guidance given to me by others. So thank you to those who helped me in the past, and hopefully this column can be my form of paying it forward. Best of luck applying and see you all next month!!!
 About The Program. Graduate Research Fellowship Program, National Science Foundation. http://www.nsfgrfp.org/general_resources/about
 Statement Formatting FAQ. Graduate Research Fellowship Program, National Science Foundation. https://www.nsfgrfp.org/applicants/faqs
 Theory and applications of lattice point methods for binomial ideals. In Combinatorial Aspects of Com- mutative Algebra and Algebraic Geometry, number 6 in Abel Symposia.
 Bert Juttler and Ragni Piene, editors. Geometric Modeling and Algebraic Geometry. Springer, 2008.
 L. Pachter and B. Sturmfels. Algebraic Statistics for Computational Biology. Cambridge University Press, August 2005.