Tag Archives: mathematics

The Impact of Jim Simons

The obituaries have been weirdly relevant lately.

First, a couple weeks back, Daniel Dennett died. Dennett was someone who could have had a huge impact on my life. Growing up combatively atheist in the early 2000’s, Dennett seemed to be exploring every question that mattered: how the semblance of consciousness could come from non-conscious matter, how evolution gives rise to complexity, how to raise a new generation to grow beyond religion and think seriously about the world around them. I went to Tufts to get my bachelor’s degree based on a glowing description he wrote in the acknowledgements of one of his books, and after getting there, I asked him to be my advisor.

(One of three, because the US education system, like all good games, can be min-maxed.)

I then proceeded to be far too intimidated to have a conversation with him more meaningful than “can you please sign my registration form?”

I heard a few good stories about Dennett while I was there, and I saw him debate once. I went into physics for my PhD, not philosophy.

Jim Simons died on May 10. I never spoke to him at all, not even to ask him to sign something. But he had a much bigger impact on my life.

I began my PhD at SUNY Stony Brook with a small scholarship from the Simons Foundation. The university’s Simons Center for Geometry and Physics had just opened, a shining edifice of modern glass next to the concrete blocks of the physics and math departments.

For a student aspiring to theoretical physics, the Simons Center virtually shouted a message. It taught me that physics, and especially theoretical physics, was something prestigious, something special. That if I kept going down that path I could stay in that world of shiny new buildings and daily cookie breaks with the occasional fancy jar-based desserts, of talks by artists and a café with twenty-dollar lunches (half-price once a week for students, the only time we could afford it, and still about twice what we paid elsewhere on campus). There would be garden parties with sushi buffets and late conference dinners with cauliflower steaks and watermelon salads. If I was smart enough (and I longed to be smart enough), that would be my future.

Simons and his foundation clearly wanted to say something along those lines, if not quite as filtered by the stars in a student’s eyes. He thought that theoretical physics, and research more broadly, should be something prestigious. That his favored scholars deserved more, and should demand more.

This did have weird consequences sometimes. One year, the university charged us an extra “academic excellence fee”. The story we heard was that Simons had demanded Stony Brook increase its tuition in order to accept his donations, so that it would charge more similarly to more prestigious places. As a state university, Stony Brook couldn’t do that…but it could add an extra fee. And since PhD students got their tuition, but not fees, paid by the department, we were left with an extra dent in our budgets.

The Simons Foundation created Quanta Magazine. If the Simons Center used food to tell me physics mattered, Quanta delivered the same message to professors through journalism. Suddenly, someone was writing about us, not just copying press releases but with the research and care of an investigative reporter. And they wrote about everything: not just sci-fi stories and cancer cures but abstract mathematics and the space of quantum field theories. Professors who had spent their lives straining to capture the public’s interest suddenly were shown an audience that actually wanted the real story.

In practice, the Simons Foundation made its decisions through the usual experts and grant committees. But the way we thought about it, the decisions always had a Jim Simons flavor. When others in my field applied for funding from the Foundation, they debated what Simons would want: would he support research on predictions for the LHC and LIGO? Or would he favor links to pure mathematics, or hints towards quantum gravity? Simons Collaboration Grants have an enormous impact on theoretical physics, dwarfing many other sources of funding. A grant funds an army of postdocs across the US, shifting the priorities of the field for years at a time.

Denmark has big foundations that have an outsize impact on science. Carlsberg, Villum, and the bigger-than-Denmark’s GDP Novo Nordisk have foundations with a major influence on scientific priorities. But Denmark is a country of six million. It’s much harder to have that influence on a country of three hundred million. Despite that, Simons came surprisingly close.

While we did like to think of the Foundation’s priorities as Simons’, I suspect that it will continue largely on the same track without him. Quanta Magazine is editorially independent, and clearly puts its trust in the journalists that made it what it is today.

I didn’t know Simons, I don’t think I even ever smelled one of his famous cigars. Usually, that would be enough to keep me from writing a post like this. But, through the Foundation, and now through Quanta, he’s been there with me the last fourteen years. That’s worth a reflection, at the very least.

Getting It Right vs Getting It Done

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With all the hype around machine learning, I occasionally get asked if it could be used to make predictions for particle colliders, like the LHC.

Physicists do use machine learning these days, to be clear. There are tricks and heuristics, ways to quickly classify different particle collisions and speed up computation. But if you’re imagining something that replaces particle physics calculations entirely, or even replace the LHC itself, then you’re misunderstanding what particle physics calculations are for.

Why do physicists try to predict the results of particle collisions? Why not just observe what happens?

Physicists make predictions not in order to know what will happen in advance, but to compare those predictions to experimental results. If the predictions match the experiments, that supports existing theories like the Standard Model. If they don’t, then a new theory might be needed.

Those predictions certainly don’t need to be made by humans: most of the calculations are done by computers anyway. And they don’t need to be perfectly accurate: in particle physics, every calculation is an approximation. But the approximations used in particle physics are controlled approximations. Physicists keep track of what assumptions they make, and how they might go wrong. That’s not something you can typically do in machine learning, where you might train a neural network with millions of parameters. The whole point is to be able to check experiments against a known theory, and we can’t do that if we don’t know whether our calculation actually respects the theory.

That difference, between caring about the result and caring about how you got there, is a useful guide. If you want to predict how a protein folds in order to understand what it does in a cell, then you will find AlphaFold useful. If you want to confirm your theory of how protein folding happens, it will be less useful.

Some industries just want the final result, and can benefit from machine learning. If you want to know what your customers will buy, or which suppliers are cheating you, or whether your warehouse is moldy, then machine learning can be really helpful.

Other industries are trying, like particle physicists, to confirm that a theory is true. If you’re running a clinical trial, you want to be crystal clear about how the trial data turn into statistics. You, and the regulators, care about how you got there, not just about what answer you got. The same can be true for banks: if laws tell you you aren’t allowed to discriminate against certain kinds of customers for loans, you need to use a method where you know what traits you’re actually discriminating against.

So will physicists use machine learning? Yes, and more of it over time. But will they use it to replace normal calculations, or replace the LHC? No, that would be missing the point.

Models, Large Language and Otherwise

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In particle physics, our best model goes under the unimaginative name “Standard Model“. The Standard Model models the world in terms of interactions of different particles, or more properly quantum fields. The fields have different masses and interact with different strengths, and each mass and interaction strength is a parameter: a “free” number in the model, one we have to fix based on data. There are nineteen parameters in the Standard Model (not counting the parameters for massive neutrinos, which were discovered later).

In principle, we could propose a model with more parameters that fit the data better. With enough parameters, one can fit almost anything. That’s cheating, though, and it’s a type of cheating we know how to catch. We have statistical tests that let us estimate how impressed we should be when a model matches the data. If a model is just getting ahead on extra parameters without capturing something real, we can spot that, because it gets a worse score on those tests. A model with a bad score might match the data you used to fix its parameters, but it won’t predict future data, so it isn’t actually useful. Right now the Standard Model (plus neutrino masses) gets the best score on those tests, when fitted to all the data we have access to, so we think of it as our best and most useful model. If someone proposed a model that got a better score, we’d switch: but so far, no-one has managed.

Physicists care about this not just because a good model is useful. We think that the best model is, in some sense, how things really work. The fact that the Standard Model fits the data best doesn’t just mean we can use it to predict more data in the future: it means that somehow, deep down, that the world is made up of quantum fields the way the Standard Model describes.

If you’ve been following developments in machine learning, or AI, you might have heard the word “model” slung around. For example, GPT is a Large Language Model, or LLM for short.

Large Language Models are more like the Standard Model than you might think. Just as the Standard Model models the world in terms of interacting quantum fields, Large Language Models model the world in terms of a network of connections between artificial “neurons”. Just as particles have different interaction strengths, pairs of neurons have different connection weights. Those connection weights are the parameters of a Large Language Model, in the same way that the masses and interaction strengths of particles are the parameters of the Standard Model. The parameters for a Large Language Model are fixed by a giant corpus of text data, almost the whole internet reduced to a string of bytes that the LLM needs to match, in the same way the Standard Model needs to match data from particle collider experiments. The Standard Model has nineteen parameters, Large Language Models have billions.

Increasingly, machine learning models seem to capture things better than other types of models. If you want to know how a protein is going to fold, you can try to make a simplified model of how its atoms and molecules interact with each other…but instead, you can make your model a neural network. And that turns out to work better. If you’re a bank and you want to know how many of your clients will default on their loans, you could ask an economist to make a macroeconomic model…or, you can just make your model a neural network too.

In physics, we think that the best model is the model that is closest to reality. Clearly, though, this can’t be what’s going on here. Real proteins don’t fold based on neural networks, and neither do real economies. Both economies and folding proteins are very complicated, so any model we can use right now won’t be what’s “really going on”, unlike the comparatively simple world of particle physics. Still, it seems weird that, compared to the simplified economic or chemical models, neural networks can work better, even if they’re very obviously not really what’s going on. Is there another way to think about them?

I used to get annoyed at people using the word “AI” to refer to machine learning models. In my mind, AI was the thing that shows up in science fiction, machines that can think as well or better than humans. (The actual term of art for this is AGI, artificial general intelligence.) Machine learning, and LLMs in particular, felt like a meaningful step towards that kind of AI, but they clearly aren’t there yet.

Since then, I’ve been convinced that the term isn’t quite so annoying. The AI field isn’t called AI because they’re creating a human-equivalent sci-fi intelligence. They’re called AI because the things they build are inspired by how human intelligence works.

As humans, we model things with mathematics, but we also model them with our own brains. Consciously, we might think about objects and their places in space, about people and their motivations and actions, about canonical texts and their contents. But all of those things cash out in our neurons. Anything we think, anything we believe, any model we can actually apply by ourselves in our own lives, is a model embedded in a neural network. It’s quite a bit more complicated neural network than an LLM, but it’s very much still a kind of neural network.

Because humans are alright at modeling a variety of things, because we can see and navigate the world and persuade and manipulate each other, we know that neural networks can do these things. A human brain may not be the best model for any given phenomenon: an engineer can model the flight of a baseball with math much better than the best baseball player can with their unaided brain. But human brains still tend to be fairly good models for a wide variety of things. Evolution has selected them to be.

So with that in mind, it shouldn’t be too surprising that neural networks can model things like protein folding. Even if proteins don’t fold based on neural networks, even if the success of AlphaFold isn’t capturing the actual details of the real world the way the Standard Model does, the model is capturing something. It’s loosely capturing the way a human would think about the problem, if you gave that human all the data they needed. And humans are, and remain, pretty good at thinking! So we have reason, not rigorous, but at least intuitive reason, to think that neural networks will actually be good models of things.

A Significant Calculation

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Particle physicists have a weird relationship to journals. We publish all our results for free on a website called the arXiv, and when we need to read a paper that’s the first place we look. But we still submit our work to journals, because we need some way to vouch that we’re doing good work. Explicit numbers (h-index, impact factor) are falling out of favor, but we still need to demonstrate that we get published in good journals, that we do enough work, and that work has an impact on others. We need it to get jobs, to get grants to fund research at those jobs, and to get future jobs for the students and postdocs we hire with those grants. Our employers need it to justify their own funding, to summarize their progress so governments and administrators can decide who gets what.

This can create weird tensions. When people love a topic, they want to talk about it with each other. They want to say all sorts of things, big and small, to contribute new ideas and correct others and move things forward. But as professional physicists, we also have to publish papers. We can publish some “notes”, little statements on the arXiv that we don’t plan to make into a paper, but we don’t really get “credit” for those. So in practice, we try to force anything we want to say into a paper-sized chunk.

That wouldn’t be a problem if paper-sized chunks were flexible, and you can see when journals historically tried to make them that way. Some journals publish “letters”, short pieces a few pages long, to contrast with their usual papers that can run from twenty to a few hundred pages. These “letters” tend to be viewed as prestigious, though, so they end up being judged on roughly the same standards as the normal papers, if not more strictly.

What standards are those? For each journal, you can find an official list. The Journal of High-Energy Physics, for example, instructs reviewers to look for “high scientific
quality, originality and relevance”. That rules out papers that just reproduce old results, but otherwise is frustratingly vague. What constitutes high scientific quality? Relevant to whom?

In practice, reviewers use a much fuzzier criterion: is this “paper-like”? Does this look like other things that get published, or not?

Each field will assess that differently. It’s a criterion of familiarity, of whether a paper looks like what people in the field generally publish. In my field, one rule of thumb is that a paper must contain a significant calculation.

A “significant calculation” is still quite fuzzy, but the idea is to make sure that a paper requires some amount of actual work. Someone has to do something challenging, and the work shouldn’t be half-done: as much as feasible, they should finish, and calculate something new. Ideally, this should be something that nobody had calculated before, but if the perspective is new enough it can be something old. It should “look hard”, though.

That’s a fine way to judge whether someone is working hard, which is something we sometimes want to judge. But since we’re incentivized to make everything into a paper, this means that every time we want to say something, we want to accompany it with some “significant calculation”, some concrete time-consuming work. This can happen even if we want to say something that’s quite direct and simple, a fact that can be quickly justified but nonetheless has been ignored by the field. If we don’t want it to be “just” an un-credited note, we have to find some way to turn it into a “significant calculation”. We do extra work, sometimes pointless work, in order to make something “paper-sized”.

I like to think about what academia would be like without the need to fill out a career. The model I keep imagining is that of a web forum or a blogging platform. There would be the big projects, the in-depth guides and effortposts. But there would also be shorter contributions, people building off each other, comments on longer pieces and quick alerts pinned to the top of the page. We’d have a shared record of knowledge, where everyone contributes what they want to whatever level of detail they want.

I think math is a bit closer to this ideal. Despite their higher standards for review, checking the logic of every paper to make sure it makes sense to publish, math papers can sometimes be very short, or on apparently trivial things. Physics doesn’t quite work this way, and I suspect part of it is our funding sources. If you’re mostly paid to teach, like many mathematicians, your research is more flexible. If you’re paid to research, like many physicists, then people want to make sure your research is productive, and that tends to cram it into measurable boxes.

In today’s world, I don’t think physics can shift cultures that drastically. Even as we build new structures to rival the journals, the career incentives remain. Physics couldn’t become math unless it shed most of the world’s physicists.

In the long run, though…well, we may one day find ourselves in a world where we don’t have to work all our days to keep each other alive. And if we do, hopefully we’ll change how scientists publish.

IPhT-60 Retrospective

Physics’ Unique Nightmare

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Halloween is coming up, so let’s talk about the most prominent monster of the physics canon, the nightmare scenario.

Not to be confused with the D&D Nightmare, which once was a convenient source of infinite consumable items for mid-level characters.

Right now, thousands of physicists search for more information about particle physics beyond our current Standard Model. They look at data from the Large Hadron Collider to look for signs of new particles and unexpected behavior, they try to detect a wide range of possible dark matter particles, and they make very precise measurements to try to detect subtle deviations. And in the back of their minds, almost all of those physicists wonder if they’ll find anything at all.

It’s not that we think the Standard Model is right. We know it has problems, deep mathematical issues that make it give nonsense answers and an apparent big mismatch with what we observe about the motion of matter and light in the universe. (You’ve probably heard this mismatch called dark matter and dark energy.)

But none of those problems guarantee an answer soon. The Standard Model will eventually fail, but it may fail only for very difficult and expensive experiments, not a Large Hadron Collider but some sort of galactic-scale Large Earth Collider. It might be that none of the experiments or searches or theories those thousands of physicists are working on will tell them anything they didn’t already know. That’s the nightmare scenario.

I don’t know another field that has a nightmare scenario quite like this. In most fields, one experiment or another might fail, not just not giving the expected evidence but not teaching anything new. But most experiments teach us something new. We don’t have a theory, in almost any field, that has the potential to explain every observation up to the limits of our experiments, but which we still hope to disprove. Only the Standard Model is like that.

And while thousands of physicists are exposed to this nightmare scenario, the majority of physicists aren’t. Physics isn’t just the science of the reductionistic laws of the smallest constituents of matter. It’s also the study of physical systems, from the bubbling chaos of nuclear physics to the formation of planets and galaxies and black holes, to the properties of materials to the movement of bacteria on a petri dish and bees in a hive. It’s also the development of new methods, from better control of individual atoms and quantum states to powerful new tricks for calculation. For some, it can be the discovery, not of reductionistic laws of the smallest scales, but of general laws of the largest scales, of how systems with many different origins can show echoes of the same behavior.

Over time, more and more of those thousands of physicists break away from the nightmare scenario, “waking up” to new questions of these kinds. For some, motivated by puzzles and skill and the beauty of physics, the change is satisfying, a chance to work on ideas that are moving forward, connected with experiment or grounded in evolving mathematics. But if your motivation is really tied to those smallest scales, to that final reductionistic “why”, then such a shift won’t be satisfying, and this is a nightmare you won’t wake up from.

Me, I’m not sure. I’m a tool-builder, and I used to tell myself that tool-builders are always needed. But I find I do care, in the end, what my tools are used for. And as we approach the nightmare scenario, I’m not at all sure I know how to wake up.

Stories Backwards and Forwards

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You can always start with “once upon a time”…

I come up with tricks to make calculations in particle physics easier. That’s my one-sentence story, or my most common one. If I want to tell a longer story, I have more options.

Here’s one longer story:

I want to figure out what Nature is telling us. I want to take all the data we have access to that has anything to say about fundamental physics, every collider and gravitational wave telescope and ripple in the overall structure of the universe, and squeeze it as hard as I can until something comes out. I want to make sure we understand the implications of our current best theories as well as we can, to as high precision as we can, because I want to know whether they match what we see.

To do that, I am starting with a type of calculation I know how to do best. That’s both because I can make progress with it, and because it will be important for making these inferences, for testing our theories. I am following a hint in a theory that definitely does not describe the real world, one that is both simpler to work with and surprisingly complex, one that has a good track record, both for me and others, for advancing these calculations. And at the end of the day, I’ll make our ability to infer things from Nature that much better.

Here’s another:

Physicists, unknowing, proposed a kind of toy model, one often simpler to work with but not necessarily simpler to describe. Using this model, they pursued increasingly elaborate calculations, and time and time again, those calculations surprised them. The results were not random, not a disorderly mess of everything they could plausibly have gotten. Instead, they had structure, symmetries and patterns and mathematical properties that the physicists can’t seem to explain. If we can explain them, we will advance our knowledge of models and theories and ideas, geometry and combinatorics, learning more about the unexpected consequences of the rules we invent.

We can also help the physicists advance physics, of course. That’s a happy accident, but one that justifies the money and time, showing the rest of the world that understanding consequences of rules is still important and valuable.

These seem like very different stories, but they’re not so different. They change in order, physics then math or math then physics, backwards and forwards. By doing that, they change in emphasis, in where they’re putting glory and how they’re catching your attention. But at the end of the day, I’m investigating mathematical mysteries, and I’m advancing our ability to do precision physics.

(Maybe you think that my motivation must lie with one of these stories and not the other. One is “what I’m really doing”, the other is a lie made up for grant agencies.
Increasingly, I don’t think people work like that. If we are at heart stories, we’re retroactive stories. Our motivation day to day doesn’t follow one neat story or another. We move forward, we maybe have deep values underneath, but our accounts of “why” can and will change depending on context. We’re human, and thus as messy as that word should entail.)

I can tell more than two stories if I want to. I won’t here. But this is largely what I’m working on at the moment. In applying for grants, I need to get the details right, to sprinkle the right references and the right scientific arguments, but the broad story is equally important. I keep shuffling that story, a pile of not-quite-literal index cards, finding different orders and seeing how they sound, imagining my audience and thinking about what stories would work for them.

Amplitudes 2023 Retrospective

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I’m back from CERN this week, with a bit more time to write, so I thought I’d share some thoughts about last week’s Amplitudes conference.

One thing I got wrong in last week’s post: I’ve now been told only 213 people actually showed up in person, as opposed to the 250-ish estimate I had last week. This may seem fewer than Amplitudes in Prague had, but it seems likely they had a few fewer show up than appeared on the website. Overall, the field is at least holding steady from year to year, and definitely has grown since the pandemic (when 2019’s 175 was already a very big attendance).

It was cool having a conference in CERN proper, surrounded by the history of European particle physics. The lecture hall had an abstract particle collision carved into the wood, and the visitor center would in principle have had Standard Model coffee mugs were they not sold out until next May. (There was still enough other particle physics swag, Swiss chocolate, and Swiss chocolate that was also particle physics swag.) I’d planned to stay on-site at the CERN hostel, but I ended up appreciated not doing that: the folks who did seemed to end up a bit cooped up by the end of the conference, even with the conference dinner as a chance to get out.

Past Amplitudes conferences have had associated public lectures. This time we had a not-supposed-to-be-public lecture, a discussion between Nima Arkani-Hamed and Beate Heinemann about the future of particle physics. Nima, prominent as an amplitudeologist, also has a long track record of reasoning about what might lie beyond the Standard Model. Beate Heinemann is an experimentalist, one who has risen through the ranks of a variety of different particle physics experiments, ending up well-positioned to take a broad view of all of them.

It would have been fun if the discussion erupted into an argument, but despite some attempts at provocative questions from the audience that was not going to happen, as Beate and Nima have been friends for a long time. Instead, they exchanged perspectives: on what’s coming up experimentally, and what theories could explain it. Both argued that it was best to have many different directions, a variety of experiments covering a variety of approaches. (There wasn’t any evangelism for particular experiments, besides a joking sotto voce mention of a muon collider.) Nima in particular advocated that, whether theorist or experimentalist, you have to have some belief that what you’re doing could lead to a huge breakthrough. If you think of yourself as just a “foot soldier”, covering one set of checks among many, then you’ll lose motivation. I think Nima would agree that this optimism is irrational, but necessary, sort of like how one hears (maybe inaccurately) that most new businesses fail, but someone still needs to start businesses.

Michelangelo Mangano’s talk on Thursday covered similar ground, but with different emphasis. He agrees that there are still things out there worth discovering: that our current model of the Higgs, for instance, is in some ways just a guess: a simplest-possible answer that doesn’t explain as much as we’d like. But he also emphasized that Standard Model physics can be “new physics” too. Just because we know the model doesn’t mean we can calculate its consequences, and there are a wealth of results from the LHC that improve our models of protons, nuclei, and the types of physical situations they partake in, without changing the Standard Model.

We saw an impressive example of this in Gregory Korchemsky’s talk on Wednesday. He presented an experimental mystery, an odd behavior in the correlation of energies of jets of particles at the LHC. These jets can include a very large number of particles, enough to make it very hard to understand them from first principles. Instead, Korchemsky tried out our field’s favorite toy model, where such calculations are easier. By modeling the situation in the limit of a very large number of particles, he was able to reproduce the behavior of the experiment. The result was a reminder of what particle physics was like before the Standard Model, and what it might become again: partial models to explain odd observations, a quest to use the tools of physics to understand things we can’t just a priori compute.

On the other hand, amplitudes does do a priori computations pretty well as well. Fabrizio Caola’s talk opened the conference by reminding us just how much our precise calculations can do. He pointed out that the LHC has only gathered 5% of its planned data, and already it is able to rule out certain types of new physics to fairly high energies (by ruling out indirect effects, that would show up in high-precision calculations). One of those precise calculations featured in the next talk, by Guilio Gambuti. (A FORM user, his diagrams were the basis for the header image of my Quanta article last winter.) Tiziano Peraro followed up with a technique meant to speed up these kinds of calculations, a trick to simplify one of the more computationally intensive steps in intersection theory.

The rest of Monday was more mathematical, with talks by Zeno Capatti, Jaroslav Trnka, Chia-Kai Kuo, Anastasia Volovich, Francis Brown, Michael Borinsky, and Anna-Laura Sattelberger. Borinksy’s talk felt the most practical, a refinement of his numerical methods complete with some actual claims about computational efficiency. Francis Brown discussed an impressively powerful result, a set of formulas that manages to unite a variety of invariants of Feynman diagrams under a shared explanation.

Tuesday began with what I might call “visitors”: people from adjacent fields with an interest in amplitudes. Alday described how the duality between string theory in AdS space and super Yang-Mills on the boundary can be used to get quite concrete information about string theory, calculating how the theory’s amplitudes are corrected by the curvature of AdS space using a kind of “bootstrap” method that felt nicely familiar. Tim Cohen talked about a kind of geometric picture of theories that extend the Standard Model, including an interesting discussion of whether it’s really “geometric”. Marko Simonovic explained how the integration techniques we develop in scattering amplitudes can also be relevant in cosmology, especially for the next generation of “sky mappers” like the Euclid telescope. This talk was especially interesting to me since this sort of cosmology has a significant presence at CEA Paris-Saclay. Along those lines an interesting paper, “Cosmology meets cohomology”, showed up during the conference. I haven’t had a chance to read it yet!

Just before lunch, we had David Broadhurst give one of his inimitable talks, complete with number theory, extremely precise numerics, and literary and historical references (apparently, Källén died flying his own plane). He also remedied a gap in our whimsically biological diagram naming conventions, renaming the pedestrian “double-box” as a (in this context, Orwellian) lobster. Karol Kampf described unusual structures in a particular Effective Field Theory, while Henriette Elvang’s talk addressed what would become a meaningful subtheme of the conference, where methods from the mathematical field of optimization help amplitudes researchers constrain the space of possible theories. Giulia Isabella covered another topic on this theme later in the day, though one of her group’s selling points is managing to avoid quite so heavy-duty computations.

The other three talks on Tuesday dealt with amplitudes techniques for gravitational wave calculations, as did the first talk on Wednesday. Several of the calculations only dealt with scattering black holes, instead of colliding ones. While some of the results can be used indirectly to understand the colliding case too, a method to directly calculate behavior of colliding black holes came up again and again as an important missing piece.

The talks on Wednesday had to start late, owing to a rather bizarre power outage (the lights in the room worked fine, but not the projector). Since Wednesday was the free afternoon (home of quickly sold-out CERN tours), this meant there were only three talks: Veneziano’s talk on gravitational scattering, Korchemsky’s talk, and Nima’s talk. Nima famously never finishes on time, and this time attempted to control his timing via the surprising method of presenting, rather than one topic, five “abstracts” on recent work that he had not yet published. Even more surprisingly, this almost worked, and he didn’t run too ridiculously over time, while still managing to hint at a variety of ways that the combinatorial lessons behind the amplituhedron are gradually yielding useful perspectives on more general realistic theories.

Thursday, Andrea Puhm began with a survey of celestial amplitudes, a topic that tries to build the same sort of powerful duality used in AdS/CFT but for flat space instead. They’re gradually tackling the weird, sort-of-theory they find on the boundary of flat space. The two next talks, by Lorenz Eberhardt and Hofie Hannesdottir, shared a collaborator in common, namely Sebastian Mizera. They also shared a common theme, taking a problem most people would have assumed was solved and showing that approaching it carefully reveals extensive structure and new insights.

Cristian Vergu, in turn, delved deep into the literature to build up a novel and unusual integration method. We’ve chatted quite a bit about it at the Niels Bohr Institute, so it was nice to see it get some attention on the big stage. We then had an afternoon of trips beyond polylogarithms, with talks by Anne Spiering, Christoph Nega, and Martijn Hidding, each pushing the boundaries of what we can do with our hardest-to-understand integrals. Einan Gardi and Ruth Britto finished the day, with a deeper understanding of the behavior of high-energy particles and a new more mathematically compatible way of thinking about “cut” diagrams, respectively.

On Friday, João Penedones gave us an update on a technique with some links to the effective field theory-optimization ideas that came up earlier, one that “bootstraps” whole non-perturbative amplitudes. Shota Komatsu talked about an intriguing variant of the “planar” limit, one involving large numbers of particles and a slick re-writing of infinite sums of Feynman diagrams. Grant Remmen and Cliff Cheung gave a two-parter on a bewildering variety of things that are both surprisingly like, and surprisingly unlike, string theory: important progress towards answering the question “is string theory unique?”

Friday afternoon brought the last three talks of the conference. James Drummond had more progress trying to understand the symbol letters of supersymmetric Yang-Mills, while Callum Jones showed how Feynman diagrams can apply to yet another unfamiliar field, the study of vortices and their dynamics. Lance Dixon closed the conference without any Greta Thunberg references, but with a result that explains last year’s mystery of antipodal duality. The explanation involves an even more mysterious property called antipodal self-duality, so we’re not out of work yet!

At Amplitudes 2023 at CERN

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I’m at the big yearly conference of my sub-field this week, called Amplitudes. This year, surprisingly for the first time, it’s at the very appropriate location of CERN.

Somewhat overshadowed by the very picturesque Alps

Amplitudes keeps on growing. In 2019, we had 175 participants. We were on Zoom in 2020 and 2021, with many more participants, but that probably shouldn’t count. In Prague last year we had 222. This year, I’ve been told we have even more, something like 250 participants (the list online is bigger, but includes people joining on Zoom). We’ve grown due to new students, but also new collaborations: people from adjacent fields who find the work interesting enough to join along. This year we have mathematicians talking about D-modules, bootstrappers finding new ways to get at amplitudes in string theory, beyond-the-standard-model theorists talking about effective field theories, and cosmologists talking about the large-scale structure of the universe.

The talks have been great, from clear discussions of earlier results to fresh-off-the-presses developments, plenty of work in progress, and even one talk where the speaker’s opinion changed during the coffee break. As we’re at CERN, there’s also a through-line about the future of particle physics, with a chat between Nima Arkani-Hamed and the experimentalist Beate Heinemann on Tuesday and a talk by Michelangelo Mangano about the meaning of “new physics” on Thursday.

I haven’t had a ton of time to write, I keep getting distracted by good discussions! As such, I’ll do my usual thing, and say a bit more about specific talks in next week’s post.

Cabinet of Curiosities: The Deluxe Train Set

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Stories about physics from someone who's been there