My Research: FAQ

Nigel Goldenfeld

What are your areas of research?

My research is mainly (but not exclusively) in areas related to biology, condensed matter physics, statistical physics and applied mathematics. I work closely with a number of other faculty both here and elsewhere, and both experimentalists and theorists. Some of my recent work has been in collaboration with Professors Carl Woese, Bruce Fouke, Gustavo Gioia, Jon Dantzig and Yoshi Oono and also the condensed matter experimental groups at Urbana and elsewhere. Key themes of my research are the emphasis on describing and predicting real experiments, the development of special tools to cope with systems spanning many disparate scales of space and time, the use of renormalization group methods, and the creative use of computers to augment pencil and paper thinking.

Please see my group's web site for more details of my current research activities and highlights of my past work.

How big is your group? Will I ever see you?

My group contains 4-5 students, and typically 1 or 2 postdocs. Sometimes I have senior visitors too. I keep my group small so that I can personally interact with my students as closely as possible.

Is funding available?

My research has been continuously funded by the National Science Foundation since 1985, as well as by grants from the Department of Energy and NASA. I do not seek or accept funding from overtly military agencies. I believe that students benefit from teaching, and so try to ensure that they spend some time being a TA, even though I have funds to support them.

What preparation should I have?

My research invariably involves a mixture of computational and analytical work. I do not generally use computers to do conceptually simple problems that happen to be complicated due to excessive realism. Instead, I try to use computers as a tool to uncover the qualitative properties and mathematical structure of problems. Prospective students must be comfortable with treating computational physics and analytical physics on an equal footing. The language of modern day condensed matter physics includes quantum field theory, statistical mechanics, fluid dynamics and partial differential equations. I hope that my students will learn these subjects as they embark on research. Although some basic knowledge is required, I believe that one should develop or learn skills on the job. I don't expect my students to "learn everything first, then apply it".

The most important preparation is to develop a sense of curiosity and fun. You cannot do physics without wanting to ask questions. It is almost certain that all the ideas I have about future research directions will not be right. So students must be prepared to face tough challenges. I always try to start off my students with what looks like a relatively simple problem, to gain confidence and get some results relatively quickly.

What should I read before joining your group?

(1) Applied mathematics.

Bender and Orszag, Advanced Mathematical Methods for Scientists and Engineers. Simply the best book in applied mathematics.  For our purposes, the parts in the last chapters on global asymptotics are most relevant: multiple scales, boundary layer theory, WKB, in short - singular perturbation theory methods.  Some of my work has been directed towards unifying these methods using renormalization group theory.   See my recent review article (described here) and our original paper on unifying singular perturbation theory.  Precursor to all these RG-related techniques is my book, and especially the standalone chapter 10.  This itself is a development of Barenblatt's book on scaling and asymptotics in nonequilibrium problems.

(2) Biology. 

Most biology books are awful, in my opinion. I find the subject difficult to learn, and you probably will also if you are attracted to the intellectual style of my work.  By far the nicest read is the Problems in Biology by Maynard Smith, written 20 years or so ago, but still very relevant.  The last chapters or so directly relate to my own research agenda.  Although written for the general public, he approaches biology from a physicist's perspective.  The other book I would recommend is Ptashne's Genetic Switch book, which describes modern gene regulation in a simple way without too much chemistry or jargon.  It cries out for mathematisation, which is really what is systems biology; the place to start there is Uri Alon's book.

(3) Mainstream physics.  I suggest you browse the web sites for my courses, which have some recommended books and brief descriptions.  You can get these from my home page.

How long do your students take to graduate?

I try to have my students graduate in four years. If a student has a particular (e.g. personal) reason to want to stay a fifth year, I will try to accomodate that. Four years should be sufficient to get worthwhile scientific results, and attain enough scientific maturity to compete effectively in either the academic or real worlds.

What do your students do after they graduate?

So far, I have supervised 13 students to completion of Ph.D and 16 postdocs. Two students have left physics for other careers early on in their research. The students who completed a Ph.D all had the opportunity to do good postdocs (and were accepted for top choice postdoctoral positions), and some have chosen to go on to postdocs and research in physics or biology, but not all. One former student is raising his children and working on physics education, several others work on Wall Street, one has transitioned into science policy areas. Details are on my group's web site "people" page.

Updated by Nigel Goldenfeld
October 2021