# Tidbits from the High Table of Physics

This evening, I was lucky enough to dine with Brenda Penante, Stephane Launois, Lionel Mason, Nima Arkani-Hamed, Tom Lenagan and David Hernandez. Here for your delectation are some tidbits from the conversation.

• The power of the renormalisation group comes from the fact that the $1$-loop leading logarithm suffices to fix the leading logarithm at all loops. Here’s a reference.
• The BPHZ renormalisation scheme (widely seen in the physics community as superseded by the Wilsonian renormalisation group) has a fascinating Hopf algebra structure.
• The central irony of QFT is thus. IR divergences were discovered before UV divergences and “solved” almost instantly. Theorists then wrangled for a couple of decades over the UV divergences, before finally Wilson laid their qualms to rest. At this point the experimentalists came back and told them that it was the IR divergences that were the real problem again. (This remains true today, hence the motivation behind my work on soft theorems).
• IR divergences are a consequence of the Lorentzian signature. In Euclidean spacetime you have a clean separation of scales, but not so in our world. (Struggling to find a reference for this, anybody know of one?)
• The next big circular collider will probably have a circumference of 100km, reach energies 7 times that of the LHC and cost at least £20 billion.
• The Fourier transform of any polynomial in $cos(x)$ with roots at $\pm (2i+1) / (2n+1)$ for $1 \leq i \leq n-1$ has all positive coefficients. This is equivalent to the no-ghost theorem in string theory, proved by Peter Goddard, and seems to require some highly non-trivial machinery. (Again, does anyone have a reference?)

and finally

• Never, ever try to copy algebra into Mathematica late at night!

# Using Thunderbird Client with Office 365

I’ve just wasted a good half hour trying to migrate my email to an Office365 SMTP server. It seems that QMUL have decided to discontinue their in-house email server, but have not provided sufficient details about the new settings needed for email clients.

So here they are, in case anyone else runs into difficulties.

SMTP server : smtp.office365.com
Port : 587 (not the default)
Encryption : STARTTLS (not SSL/TLS)

I imagine that similar settings should work for other institutions which have moved to an Office365 system.

# Why Should Undergraduates Attend Classes?

I’ve just finished teaching classes for the Quantum Mechanics B course here at Queen Mary. It’s been an enjoyable few weeks, watching the students grapple with bra-ket notation, spherical harmonics and the Stern-Gerlach experiment. All in all, I’ve found it rather rewarding.

A perennial bugbear is that many undergraduates don’t turn up for the classes. Although nominally compulsory, the university rarely imposes any sanctions for lack of attendance. It’s natural to wonder whether there’s any benefit in running the sessions!

I decided to do some elementary analysis to determine any correlation between class attendance and performance. Fortunately, the results were favourable – students who come to class tend to do better than those who don’t. And what’s more, the gap widens as the term goes on!

I’d like to conclude that this effect is due to the usefulness of my teaching, of course. But my scientific brain doesn’t allow such an easy deduction. After all, correlation does not imply causation! To say anything more we’d need a control study, which is unlikely to happen any time soon!

Still, I can now tell my undergraduate students that they’re more likely to succeed if they come to class. Flawed logic aside, surely that means I’m doing something right?

I’m now about to finish my first year as a PhD student. Along the way I’ve done a lot of physics! Some of the concepts are very hard. I’ve sure spent my fair share of hours battling with abstract maths! But I’ve learnt something much tougher and infinitely more valuable in the past 12 months – how to do research.

The blessing and curse of research is it’s very hard to teach. You need just the right combination of perserverance, creativity and inspiration. Unlike most forms of employment, science is wonderfully, frustratingly unpredictable!

There’s one principle that stands out through every success and failure this year. Ask the obvious question! Whether in a seminar, a conversation with colleagues or in front of your desk, never be afraid to say something stupid. Often it’s the most basic idea which leads to the richest consequences.

At the end of the day, research is something of a confidence game. It’s a bit similar to my limited experience on a snooker table. If I think I’m going to win, I usually do. But when those doubts creep in, it’s much harder to keep the break going!

That’s why it’s so important that scientists communicate. Sadly the human brain doesn’t seem to be wired up to think deeply and laterally simultaneously. Regular breaks for discussion, evaluation and presentation of your work are vital!

I’ve had my clearest thoughts on walks to the tube, after chatting over coffee or writing a blog post. Although the life of a scientist might appear relaxed, ours is not a job where you can just clock in and out!

Asking the obvious question is not just important for researchers. Students, journalists, politicians, civil servants, lawyers, managers, even executives pose simple questions every day. In fact, it’s when public figures disguise their questions and answers with complex language that we struggle to relate.

A stupid, obvious question can do no harm. And more often than not, it’s exactly what you need to say.

# Back From Holiday

refreshed, revived and ready to start this blog in earnest. Alas, no real post today! Nevertheless I have been working behind the scenes putting the finishing touches to the necessary background material. Okay, it is more than a little dry, and probably terrifying to the uninitiated. Don’t worry – I won’t need to use all of it right away. It should serve as a touchstone (for me as much as you) to ensure that I’m doing everything on a firm mathematical footing.

Talking of well written introductory books, I feel obliged to join the long list of individuals who have publicly praised Roger Penrose’s great work, The Road to Reality. I’ve owned the volume for several years, dipped into it now and then, but only over the past seven days have I truly appreciated its depth and scope. Certainly a worthwhile investment if you are interested in science at a more than superficial level!

Finally, if you find yourself at a loss for entertainment any time in the next few days I’d heartily endorse the fantastic Beethoven Prom Series currently in progress. I had been a little skeptical about this rather ‘obvious’ choice of repertoire, but Baremboim’s expert musicianship has won me over. Also they are really good pieces, after all.

I promise a proper post tomorrow – we’ll be talking about Affine Varieties. They’re not as scary as they sound, honest!

# Apologies For My Absence

in the last 24 hours. I have been attempting to decide where I should focus my mathematical energies. In the short term, how do I best use this blog? In the long term, what should I study for a PhD? This has been daunting, terrifying, exciting, confusing and time-consuming in equal measures, and will continue to be.

I am presently off on holiday for a week, which should be a good chance to get my thoughts in order. When I return the mathematical content will begin in earnest. I hope this gives you all an opportunity to brush up on the suggested background material, should you need to!

I leave you with this amusing and inspiring article.

# And Now For Something Completely Different…

A far more seasoned blogger has something to say here. Today it’s a dissection of Fox News. And it’s even for charity. Head across while you wait for me to write something meaningful.

# So What Exactly Are We Doing Here?

Good afternoon. Over the next 12 weeks or so, this blog will grow into a collection of (mostly mathematical) ideas. If you’re at all interested in String Theory, Algebraic Geometry or Quantum Mechanics I should have something worthwhile to tell you. If you already don’t know what I’m talking about, don’t worry – I’ll attempt to make a great deal of what I write accessible to the diligent layman! I’ll start slowly and try not to lose people along the way. Hopefully this will end up being a cute introduction to a fascinating part of maths for people from all kinds of backgrounds.

The aim is to post about once a day, with the style being something between popular science and academic coursebook. I’ll try to tag posts accordingly, so it’s easy to tell what audience I’m pitching to. The first few days may be an extremely brief recap of some very foundational material to provide some explanation and background for non-mathematicians.

Occasionally I might discuss/opine/rant about other things, including music, sport, and just why we are getting quite so much rain. I hope this will provide a (necessary?) break from the maths. I’ll happily take requests for a post on a particular topic, but I can’t promise to become an instant expert.

Finally I can’t guarantee that everything I write will be entirely correct on first posting. Some of this material I’m learning for the first time myself, and it might take a couple of iterations before I fully grasp the concepts. If you think I’ve been unclear or don’t understand something, please do comment.

If you are still with me, well done! No more administrative faff, I promise! Have a couple of contrasting YouTube videos for your efforts, here and here.