Ahead of the Season 2 premiere, the writer, a physicist by training, asked around. The answer? It’s complicated.

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[A more technical post follows] My most recent paper, out on the arXiv today, is very exciting to me because it seems to be a genuinely new way of computing some important quantities and it is devilishly simple. So simple that I worried for months that it is all super-obvious to everyone. But another voice within me said to myself: Well if it is so obvious, why has nobody published it? Another (paranoid) voice within said: Maybe someone has published this method, and I just can't find it in the literature... Well, I decided that the best way to find out for sure is to put it on the arXiv and within a short time someone will email to say that I missed their important work. So, while I wait for that email (as I start writing it's only been 30 minutes since it has been "out there", so there's time), let me say a few things about why I like the many results in the paper. I was already pleased enough with the core part of the paper that I was going to write a swift four-pager about it back in February. The core point being that I figured out how to build on work I'd done in a paper back in 2024 (expanded on with followup work I did with Wasif Ahmed and Krishan Saraswat, a student and postoc). Back in 2024, I found (here) a really nice way (almost miraculous in how it worked) of writing all the corrections to the spectral density of a class of models in terms of one function and its derivatives. It was obtainable from one simple ordinary differential equation (ODE) called the Gel'fand-Dikii equation, which takes in the function as input. The ODE is for a special quantity called the diagonal resolvent . You integrate that quantity with respect to and you're more or less home. In general, it is a messy quantity. but just when the function obeys the "string equation" it is supposed to (as dictated by the governing model's physics), then is a total derivative (a seeming miracle-see later), and the corrections it gives to the density become of just the right form! Those corrections can be called where the is the order in perturbation theory. is leading order, is the torus, the double torus, etc. Indeed is the number of handles or "genus" of an associated Riemann surface. The one on the other hand, corresponds to the one energy entry available when just discussing the density . All the end up being written nicely in terms of a function and its derivatives, evaluated at a special point. An already nice feature (among many) of the construction was that this one ODE, recursively solved, gave rise to the of many different problems across a range, including certain random matrix models, gravity problems, intersection theory and topology, and so on. All you need to do is change the function . Moreover, for this (wide) class of problems, you can compute the desired results faster and with way less machninery than other methods, such as topological recursion, which was interesting. This includes very famous problems like the Weil-Petersson volumes (of the compactified moduli space of Riemann surfaces with genus and boundaries) and generalisations. Another nice feature is that you also get non-perturbative data beyond the genus expansion, an aspect I explored recently (in this paper) with student Joao Rodrigues, and expert in resurgence techniques. The core breakthrough of the new paper is this: [...] Click to continue reading this post →

YouTube video by UC Santa Barbara

Well, I can now officially mention that I've been part of the filmmaking team (in a way) working hard to bring you an enjoyable and interesting Fantastic Four movie! I think it has been about two and a half years (?) since this all began. This was a nearly perfect model of how science consulting can work in film. I worked with everyone, wherever I was needed, with the director, writers, producers, director of photography, VFX teams, set design, and so on. They made me feel welcome and part of whatever creative team I was talking to, which was great. They were open to lots of ideas right from when they were starting out thinking about tone, story ideas, and so forth, right through to final (key) tweaks right at the end of the process as recently as mere weeks ago. It began early on with with having great conversations Matt Shakman and his writing team about the fact that Reed Richards is first and foremost a curiosity-driven physicist (and so quite different from the engineer we have in Tony Stark that we see RdJ bring out so well), and how things like his dedication to his work (and his outlook on things that comes from such work) might play out in terms of family dynamic, personal relationships, etc., - Without it turning into the tedious cliches about scientists somehow not being able to navigate the world of human relationships. Obviously, I could speak to this as a physicist who works on precisely the things Reed works on, as well as a family man, and as well as someone who remembers that it's still all about telling a story. And there are so many stories to tell at that intersection... Anyway, I think these early conversations (as well as suggestions I made in many sets of notes along the way) helped inform (even if only a little bit? who knows?) what Pedro Pascal brought to the character. This aspect of the film is one of the things I'm most pleased about seeing up on screen. Beyond that, you'll see lots of things I gave them that I'm also delighted to see made it to the film, in many scenes. This includes (but not limited to!): [...] Click to continue reading this post →

Some years ago I speculated that it would nice if a certain mathematical object existed, and even nicer if it satisfy an ordinary differential equation of a special sort. I was motivated by a particular physical question, and it seemed very natural to me to imagine such an object... So natural that I was sure that it must already have been studied, the equation for it known. As a result, every so often I'd go down a rabbit hole of a literature dig, but not with much success because it isn't entirely clear where best to look. Then I'd get involved with other projects and forget all about the matter. Last year I began to think about it again because it might be useful in a method I was developing for a paper, went through the cycle of wondering, and looking for a while, then forgot all about it in thinking about other things. Then, a little over a month ago at the end of March, while starting on a long flight across the continent, I started thinking about it again, and given that I did not have a connection to the internet to hand, took another approach: I got out a pencil and began mess around in my notebook and just derive what I thought the equation for this object should be, given certain properties it should have. One property is that it should in some circumstances reduce to a known powerful equation (often associated with the legendary 1975 work of Gel'fand and Dikii*) satisfied by the diagonal resolvent $latex {widehat R}(E,x) {=}langle x|({cal H}-E)^{-1}|xrangle$ of a Schrodinger Hamiltonian $latex {cal H}=-hbar^2partial^2_x+u(x)$. It is: $latex 4(u(x)-E){widehat R}^2-2hbar^2 {widehat R}{widehat R}^{primeprime}+hbar^2({widehat R}^prime)^2 = 1 .$ Here, $latex E$ is an energy of the Hamiltonian, in potential $latex u(x)$, and $latex x$ is a coordinate on the real line. The object itself would be a generalisation of the diagonal resolvent $latex {widehat R}(E,x)$, although non-diagonal in the energy, not the [...] Click to continue reading this post →

As PST ART winds down, join us for Open House, a free, day-to-night exploration of art and science presented by Getty. Highlights include the taping of a...

Thanks to everyone who made all those kind remarks in various places last month after my mother died. I've not responded individually (I did not have the strength) but I did read them all and they were deeply appreciated. Yesterday would’ve been mum‘s 93rd birthday. A little side-note occurred to me the other day: Since she left us a month ago, she was just short of having seen two perfect square years. (This year and 1936.) Anyway, still on the theme of playing with numbers, my siblings and I agreed that as a tribute to her on the day, we would all do some kind of outdoor activity for 93 minutes. Over in London, my brother and sister did a joint (probably chilly) walk together in Regents Park and surrounds. I decided to take out a piece of the afternoon at low tide and run along the beach. It went pretty well, [...] Click to continue reading this post →

We show that random matrix models are a natural tool for understanding the appearance of a large gap in the microstate spectrum of black holes when there is a high degeneracy of states, in a variety o...