I got an email from a physics major asking for some advice about graduate programs. He said it would be okay if I posted it here. Maybe you can help out!

Prof. Baez,

My name is Blake Pollard, I am an undergraduate physics major at Columbia University graduating next week. I agree very much with the premise of and the need for the Azimuth Project and would like to help out. Though my passion is physics, most of my undergraduate research has been in climate and sustainability. I would really like to find a graduate program enabling me to do both physics and something useful for the environmental movement, hence I haven’t committed to a Ph.D. program in pure physics. I studied category theory a bit here at Columbia from Lauda, and took some representation theory with Khovanov, but I think (at least at this point in time) my calling in physics is geometrical algebras. I was planning on spending a year off reading on my own, trying to do some work, and making the decision between environmental, physics, or mathematics graduate studies. Your blog served me well as a guidepost in my early college years for reading good stuff, and would appreciate any advice you have on:

1) graduate programs where I could do work on both mathematical physics and the environment

2) good people/places/projects that I could participate in in the coming year.

The Azimuth Project web resources have already been helpful in finding people to reach out to, but I figured you might have something or someone popping out of your head in particular.

I have programming experience in data mining, numerical simulations, remote sensing, and just having fun programming; decent math/physics background; and really just want to find a good place where good people are working hard. Like Göttingen way back in the day. Sorry for the longish email.

Thank you in advance for your time,

Blake S. Pollard

Applied Physics 2011

In a later email he added a bit more detail:

I think most people, though, would associate my goals with doing some physical modeling/analysis of environmental systems/problems, maybe a statistical-physical hybrid. That is probably what I would do in a PhD program on the environmental side of things. But I’m more thinking of having an advisor who does research in mathematical physics, while applying myself on the side to some problem related to the environment, like Google’s 20% projects. Probably it’s a bit too inter-departmental and too flexible for there to be a formal program for this (plus I’d likely be too busy!).

It seems though the answer might be simply doing a PhD in environmental sciences and doing physics in my spare time. Just organizing my own thoughts.

Are there any good grad programs that involve a mix of mathematical or theoretical physics and environmental science? I’ll take any good answers I get and add them to the Azimuth Wiki.

The Center for Atmospheric and Ocean Science at the Courant Institute (NYU) is strong in mathematical physics, and has people who do atmosphere/ocean fluid dynamics, stochastic dynamics, multiscale modeling, and glacier mechanics. Check out their faculty and research pages. It could be a strong all-around option.

Last year the UCLA Institute for Pure and Applied Mathematics (IPAM) hosted an extended workshop, Model and Data Hierarchies for Simulating and Understanding Climate. I didn’t attend, but there were a lot of mathematical physicists participating (mostly in numerical analysis and stochastic dynamics/statistical physics). It might be worth looking through the list to see if any institutions stand out (e.g., as being well represented).

If UK or other European programs are of interest, one could look at the participants of the Mathematical and Statistical Approaches to Climate Modelling and Prediction workshop in Cambridge, which I did attend. Many of the participants were statisticians, but there was a strong contingent of statistical physicists working on stochastic dynamics; see the particpants of the Stochastic Methods in Climate Modelling sub-workshop.

Another approach would be to pick a topic area and find out who’s good in that field and where they are.

(For statistical/physical modeling I’d specifically check out Majda or Kleeman at NYU. I don’t know about environmental applications of geometric algebra.)

Nathan wrote:

That’s a fun exercise. The organizing committee consisted of

• Amy Braverman (Jet Propulsion Laboratory).

• Rupert Klein (Freie Universität Berlin, Mathematics).

• Andrew Majda (New York University, Courant Institute of Mathematical Sciences).

• Olivier Pauluis (New York University, Courant Institute of Mathematical Sciences).

• Bjorn Stevens (Max Planck Institute for Meteorology).

Two from the Courant Institute! Blake said he wanted someplace “like Göttingen way back in the day”. Well, the Courant Institute was set up as a kind of replacement for Göttingen during World War II. Clicking on Andrew Majda’s name we soon find ourselves at the Center for Atmosphere Ocean Science, part of the Courant Institute of Mathematical Sciences, which is itself affiliated with the mathematics department at New York University.

How much contact do math or physics grad students at NYU have with research taking place at the Center for Atmosphere Ocean Science?

John wrote:

I don’t know, but CAOS has its own graduate program too.

Oh, interesting. Since Blake is at Columbia it should be easy for him to check out these options.

You might want to look into some of nodes in the Mathematics and Climate Research Network.

Nice! I hadn’t known about that!

It might be useful to check into places working on network theory. This topic tends to be exceptionally multidisciplinary in nature and relates biological and environmental sciences with mathematics and physics.

For example, my friend Phillip Staniczenko did a PhD in physics from Oxford, but ended up working at CABDYN in the business school. He did research on food webs. He later left and went to U Chicago, to join the Department of Ecology & Evolution, in this group.

I’m not an expert on the locations of network theory groups, but I assume one could find many.

I should also mention that geometric algebra (aka Clifford algebra) is already used regularly in quantum network theory. It was even used to form the backbone of some of the complexity results on quantum evolutions that are efficient to simulate using classical computers (Gottesman–Knill theorem).

It is likely also highly relevant to other types of networks, though I’m not sure of any work done on that yet.

Can’t offer a lot of advice other than trying to convince a program to give a degree title of “Statistical Mechanic”. IMO, a lot of the interesting stuff is in the periphery of academia, at the crossroads of physics, math, sociology, politics, ecology, and economics.

Hi. I’m the friend Jacob is referring to. Ecology is a fun area to apply physics-based techniques: with larger and more complex data sets emerging, the field is crying out for better analytical approaches (both for modelling ecosystems and for extracting information from data).

The Oxford group is excellent for more general research on networks (lots of “former” physicists and mathematicians working there on a variety of problems). But, common with most Universities in the UK, there is no explicit graduate program.

I’m now in a fantastic group at UChicago (based in Ecol & Evo) that comprises theoreticians from a range of backgrounds (physics, comp sci, stats). Our focus is theoretical community ecology (food webs, population dynamics and general analytical methods) than climate or species-specific work, but we also do more general network theory. (And there is the excellent NICO research cluster at Northwestern nearby.)

The graduate programs at UChi are supposedly very good and I’m sure you could cherry-pick courses from different departments (UChi has a very good math and stats dept, and [of course] physics dept). There are also good opportunities for doing research very quickly in my group–we have undergrads getting first-author papers into good journals. There’s a PhD candidate in the group who is happily taking courses in eco and stats and the group head teaches a nice theoretical ecology course.

Hope that’s helpful, get in touch if you want to know more.

I’m sure I’m saying something well known, but because UK first degrees are generally much more focussed than American first degrees, that tends to mean that the things that the taught part of a US graduate program address tend not to be dealt with informally as an add-on to research.

This probably doesn’t apply to mathematical physics but in the UK in more applied areas it’s relatively common to get a PhD place working on a specific project grant, which means that while you have some freedom in the precise problem you work on (particularly if it becomes clear an issue unanticipated in the grant proposal is going to block all the plans), the “mid-level problem area” in which you’re working is decided from the time you start. (This was certainly the case in my PhD in computer science.) Whether you feel you can commit to this when you’re still investigating what interests you is a key issue in considering doing a PhD in the UK.

I’ve heard it said that to get the best of both worlds, you should do your undergraduate work in the UK and your graduate work in the US. The first prepares you to instantly dive into research when you become a grad student, and then the second gives you lots of time to take courses and make sure you know what you’re interested in before doing a thesis. (It’s always good to write and publish papers

beforedoing a thesis, so being ready to hit the ground running is not wasted.)I think there’s a lot of trade-offs (although I’ve only second-hand knowledge of the US system). Because the US system is built around giving the freedom to choose whatever stuff fulfils requirements and it’s not unusual for people to take different numbers of years, it’s probably easier to make enough of a connections to get the stimulation to produce a paper whilst an undergrad. In the UK it (used to be) a relatively fixed-format 3 year course with few “breathing spaces” and is rare to be able to write a paper (except in the experimental sciences where you might get your name on a paper for “primarily labwork”). My impression is that even the really high-flyers on my (mathematics) degree course focussed even more on exams if they had spare time. My view of the difference is that the UK is more suitable than the US if you don’t feel like sitting in courses outside your main interest

as part of what you’re paying for at university. (Following Mark Twain I never let my schooling interfere with my education.)One practical upshot of this difference is that embarking on a PhD after doing a related undergrad degree the basic knowledge known is a lot more uniform; I gather the taught part of US grad school is partly because even with a “major” in X two US undergrads could have studied vastly different areas of the subject. (I “moved” from mathematics undergrad to computer science PhD via an intermediate MSc.)

But the point I really wanted to make was that, in considering a graduate degree in a more “experimental” subject — such as environmental areas — there may be “support expenses” like data collection field trips, machinery, lab workers, etc, which are paid for from a specific grant. Thus starting an associated PhD there’s a lot less freedom than a more “pencil and paper” subject area. (It sounds like Blake’s primary interest is in mathematical physics so this doesn’t apply, but I thought it worth mentioning in the general discussion.)

John wrote:

David wrote:

Just to clarify: I wasn’t talking about publishing papers while still an undergrad; I was talking about doing it as a grad student before you start work on your thesis.

You see, in the US there’s enough time in grad school for mathematicians or theoretical physicists to do this. They spend 2 years doing coursework, but if they’re ambitious and smart, they can be writing papers at the same time.

Indeed, it’s quite common for good students in these fields to have published a few papers before submitting their thesis. I force all my students to do it: if they can’t finish writing a paper in time for their oral exam, I won’t take them on as PhD students. But I help them do it. I figure if they leave grad school not yet having experienced the whole process of submitting papers to journals, responding to referees’ criticisms, etcetera, they don’t really know what their chosen profession is like.

Ah, right. There have been very, very occasional instances of papers published by undergrad — such as Roger Penrose’s paper on matrix pseudo-inverses — which probably predisposed me to misunderstanding what you were saying.

Jacob and Phillip mentioned CABDYN. That stands for “Complex Agent-Based Dynamic Networks” — it’s highly interdisciplinary program which, true to its name, is part of a network of groups, including the Institute for Science, Innovation and Society at the Saïd Business School, the Oxford Complex Systems Group in the Physics Department, and the Nuffield Network of Network Researchers (NNNR) at Nuffield College. I don’t know enough about it, but I know that Geise Reinert is involved: she helped run the Tutorials on Discrete Mathematics and Probability in Networks and Population Biology here in Singapore, which I blogged about last week.

All this is very interesting, but I’m curious about how much these groups collaborate with people working to understand or deal with climate change, renewable energy and the like. Oxford has a

lotof institutes and programs related to these issues! As you’ll see, this page has links to all these:• 21st Century Ocean Institute

• Biodiversity Institute

• Institute for Carbon and Energy Reduction in Transport

• Institute for Science, Innovation and Society

• Oxford Centre for Tropical Forests

• Oxford Geoengineering Programme

• Plants for the 21st Century Institute

• Programme in Nuclear and Energy Materials

• Programme on Globalising Tidal Power Generation

• Programme on Modelling and Predicting Climate

• Programme on Solar Energy: Organic Photovoltaics

I don’t know how easy it is for a grad student at Oxford to get involved in these programs. I hope they’re putting some thought into that.

First, let me thank you all for the replies!

I’ve been poking around the CAOS at the Courant Institute website, as well as the slew of Oxford institutes and there is surely some interesting research/projects going on at both that I wasn’t aware of.

I also was interested by some of the work being done with respect to application of network theory to environment-related problems. I think I have to do some more reading before I can tell you what quantum network theory is, but reading some of the old papers and looking through some of the current work being done it seems to be a good fit as a subject where PhD studies in mathematical physics could be completed with an eye towards more practical applications, environmental or of a wider variety.

Thanks again! I’ll try to keep you posted about what I find and don’t find.

Good luck! It would be very nice if you keep us posted here about what you find out and what you decide to do.

I’m busy trying to extend techniques developed in quantum network theory (which I’ve been working on for years) to more practical applications, and I have a feeling that this will be a growing area in the next 5-10 years. If you don’t know this book already, I recommend it as a place to get started:

• Bob Coecke, editor,

New Structures for Physics, Springer, Berlin, 2011.It’s an intimidatingly fat book, but the articles are all expository, they can be read independently, and many of them are available for free here, here and here.

Hey all.

I know this post has been dead for a minute but I figured I’d update you all with where I’m at. I actually moved to Hawaii and am a private tutor living on the North Shore of Oahu…. chasing some waves! I’ve embarked upon my grad school apps though and some of you will probably be hearing from me. I’m definately submitting applications to Oxford and Cambridge, as Oxford has the many centres/groups discussed above and Cambridge has a Geometrical Algebra group of which Chris Doran used to be a part (he was visiting Columbia while I was an undergrad). I’ll also be applying to UChicago as Staniczenko’s group sounds like fun and their physics department is great. The UC’s are also on my list, Riverside and Irvine, even with Baez in Singapore, my former roommate is doing is math PhD at Davis, which seems like a good spot, and of course Berkley, Santa Barbara, and Santa Cruz as I’d still like to be able to surf for the next 5 years. Also Lauda (I sat in on category theory with him at Columbia and was fortunate enough to take rep theory with Khovanov) is now at USC, which could be good. Penn State also might have something to offer with Ashketar’s group in loop quantum gravity. I’m really looking now for a solid physics program where there is exciting inter-disciplinary work. This post ended up being more than helpful and I spent many a night getting lost clicking links from where this leads.

I’ve been keeping busy with Lounesto’s book on Clifford Algebras and Spinors as well as Penrose’s two volumes on spacetime, spinors and twistors. Thanks again all for the replies.

Blake

Thanks for the update, Blake! Good luck!

I’ll be back at Riverside by the time you get there, if there’s where you happen to go: I’ll return in September 2012.

Of course, I won’t be wanting to talk about loop quantum gravity, representation theory, Clifford algebras, spinors or twistors. I’m focused on this ‘network theory’ project, and I’m looking for grad students who want to work on that.