My name is Yorus Kla. I'm a PhD student

here at the MPI MIS in in light.

>> And I'm Veronica. I'm also a PhD student

here. And also today we have Nema. And

could you maybe introduce yourself very

quickly?

>> Yeah, I'm Neimar Kani Hamemed. I'm a

theoretical physicist at the Institute

for Advanced Study in Princeton.

>> Okay. Good to have you, Nema.

Um so we would like to start out slowly

and all the way back from um and ask you

basically is there a particular reason

why you entered the field of physics or

science in general?

>> Yeah. Well, I mean I think uh um

probably like most people who end up in

uh in in in science. I I I loved uh

nature as a kid. Um uh actually I was

most uh fascinated by uh animals um for

a long time you know sort of natural

history. I wanted I would sort of catch

frogs and toads and snakes and things

like that and uh and attempt to study

them. Um and uh so I wanted to be a

naturalist for a long time but I'm the

child of two physicists and I'd like to

say it was my active teenage rebellion

to become a physicist. They definitely

did not want me to be a to be a

physicist. Um and uh uh also I loved

math from a from a from a young age. I

loved math and then I you know I put two

and two together that there was

something you could do with your life

that put these things about the natural

world and the world of mathematics

together. Actually I can say very

specifically the moment uh I decided I

was going to be a theoretical physicist.

Um

>> uh I think I was maybe 12 or 13 years

old. Um and um uh like most kids of that

uh era in the ' 80s, you know, I was

fascinated by the space shuttle going

going going up and down.

>> And I'd heard this number that you have

to sort of fire the rockets of the space

shuttle. So it goes at 11 km a second to

get out of the earth's uh gravitational

field. And you know, I wondered how do

they figure out that number 11 km a

second? Did they try 3 km a second?

Nope. Four? Nope. Five? Nope. You know

that. And at some point, woo, it goes at

11, right? some expensive

>> and uh yeah it sounds sounds expensive

and dangerous and my my uh my uh my my

father um explained to me uh really

basic things energy conservation

Newton's law I didn't know any of these

things but um but he just sort of

sketched out in a few lines uh the

formula v^2= 2gm over r for how you

could figure out escape velocity and

that just completely blew me away that

that you could figure that out and that

it was something a kid could understand

and a kid could do and now that I had

formula. I had the answer for the Earth.

I had it for Jupiter. I had for getting

out of solos. I had it for for

everything in one shot. And that just

kind of blew me away that there was a

not only some sort of beauty and wonder

in the natural world, but some kind of

power as well in understanding it. Um

and that uh and that uh that really

hooked me and and around that time I I

really sort of decided fairly seriously

that I wanted to be a theoretical

physicist and uh and oriented my

life to start trying to to do that

>> and in all of this path since you were

12 years old until nowadays that uh I

mean it's a long time thinking about

physics of course do you have any

particular role model or role models

that were important? Oh, that's a great

question because I think um probably if

you ask most people I don't know if

people would have similar answers. Um uh

you know there's uh uh there's of course

uh heroes we have in all of uh all of

physics Newton Einstein Maxwell Dak

these people and um uh you know when I

was a kid growing up or or learning

physics there were these sort of gods

out there but I didn't think about them

too much other than thanking them. Thank

you Newton you know for uh for giving us

uh f equals ma but um I was sort of much

more fascinated as I said with the sort

of ability to use uh uh physics to to

explain things in the world around us.

uh you know along those lines um just as

a maybe a tangential comment in this

direction I was not personally

especially inspired by popular books

about physics they had they were almost

I I mean I wouldn't say uh explicitly

repulsive but definitely at most neutral

um uh because I could tell they were not

giving me the real deal you know that uh

and I was learning the real deal already

you know myself so I could figure out

where the rainbows were in the sky or

where you saw Mirage or you know uh

other things that that was possible to

figure out uh myself. Um so in that

sense the people who were the most

important to me uh early on were either

you know somewhat older kids who knew

things that could teach me um or you

know I had a few fantastic teachers um

uh I had an amazing uh physics teacher

when I was in uh grade 10. Uh his name

was John Wy um who had just gotten his

PhD um uh from the University of

Toronto. I grew up in Toronto in Canada

and um uh and you know could just tell

that I was crazy about physics and um

one of the most like amazing uh moments

of my intellectual life. Maybe one of

the most contentful sort of 90 seconds I

had was when he stared over my shoulder

and saw that I was, you know, working on

some complicated problem with incline

planes and balls and things like that,

which I sort of love to do. And he said,

"You know what? All these questions are

trivial. Um, you can solve them all in

one line with one method." I'm like,

"Get out of here. That's impossible. You

know, I'm I'm I'm I'm the world's expert

on complicated monkeys and pulleys and

fly planes. You know, you're telling me

there's a way of doing it any old schmo

can do." And he said, "Yes." and he

wrote down the lrangeian you know and he

did the whole thing in 90 seconds you

know he said you all you do is you write

down kinetic energy minus potential

energy then you write down this equation

he didn't derive anything he just wrote

down the oil lrange equation and as he

went said do you know what a partial

derivative is I said no he said just

pretend all the all the variables are

constant I'm like okay you know I can do

that I can do that and he went away and

then I'm like holy crap this can't

possibly work and I remember trying it

on the very first problem was not some

Mickey Mouse problem cuz I I I wanted to

see if this thing really worked. So I

did the problem of the, you know, mass

on a string spinning around attached to

a weight through the hole in the table.

I set it all up. I followed what he

said. I got the equations I knew you're

supposed to get

>> and it changed my life. You know that um

it really did change change my life

because I I appreciated not only is

physics amazing and you use it to

predict things in the world around you,

but there's structures underneath it.

There are some sort of deep structures

underneath it and that and that you're

not done when you get the first set like

F equals MA. you can sort of keep on

going, discover other things about that

that exploring the sort of structures

themselves is something uh meaningful.

Anyway, so here's an example. I mean, he

was incredibly important, not not like a

godlike role model per se, but those are

the most important people to me. It was

the people directly around me. You know,

when I was in graduate school, it was

like these slightly older graduate

students who sort of, you know, showed

me all the tricks tricks of the trade so

I wouldn't have to uh I wouldn't have to

flounder around. uh I think sort of much

later when I became uh you know not only

started doing research but you know

started having plans and sort of ideas

for what I wanted to spend years and

years of my life doing at that point we

could talk about uh the more

conventional sort of role model I guess

and there my answer is totally cliche um

but maybe uh hopefully not entirely

cliche reasons is probably Einstein um

and it's Einstein uh only because like

Newton and Maxwell are Martians uh sorry

and maybe not Maxwell I meant Newton

Durac uh people like that are clearly

have some sort of CPU and mental ability

that's uh not comparable uh certainly to

me or really most most most of people um

um uh you know Newton in in the

Principia would wake up in the morning

and decide he wanted to calculate square

root of two to 20 decimal places for fun

because he just discovered the binomial

expansion you know that's not that's not

uh that's not not me uh but uh I'm also

Einstein. Let me make that clear. Let me

make that very very clear. But um but

his his sort of the way he went about uh

doing physics and um uh was not driven

by some monstrous CPU. Of course, he had

an unworldly physical intuition, but he

made so many mistakes. You know, he made

so many elementary mistakes. He was

struggling for a long time. What he had

more than anything is some like

unbelievable

drive and will to stick with a hard

problem. ignore what everyone was

saying. No one believed him. No one

cared. Up, down. But somehow he had this

sort of drive to keep on going for years

and years and years until something made

sense. And uh that I find incredibly

inspiring. I mean that that's very very

difficult to do. But I've tried sort of

consciously very consciously in my life

to you know go longer and longer periods

without making progress uh before

getting freaked out and switching to

something else. and you know Einstein's

example you know other people uh you

know there's maybe more examples in in

in in math the wilds Pearlman people

like that um but it's this kind of uh

sticking to something with some

particular vision of what what might uh

uh what might happen um and uh

continuing until you get there has been

has been in some more concrete way uh

inspiring to me.

>> All right. All right. Okay. This is also

already good. you're moving a bit

further into your career already.

>> Okay.

>> So, and the followup on this would be so

one of the most prominent research

aspects that came out of your research

life um that interest us here lots is

the amplitude. Yes.

>> Is there is there like a bit of a story

how you came to think about it and how

it developed? How did you end up

defining it?

>> Oh yes. I mean it's uh um my work uh uh

even starting in uh graduate school and

through to about 2008 so about you know

15 years the first sort of 15 years of

my uh of my um uh I started grad school

in 93 okay so so that that period of my

life um I was not doing mathematical

things at all I mean I was uh most

interested in um uh in uh uh thinking

about theories for what we might see at

the large adon collider that sort of

attack problems of particle physics.

There's a one of the great problems of

uh one of the great mysteries in nature

is we don't understand why the universe

is big. Um and that's because there's

sort of increasingly violent quantum

mechanical fluctuations at shorter and

shorter distances in the vacuum. What uh

seemingly create uh destroy any

possibility of of a macroscopic

universe. Uh and yet here we are. The

universe is very big. The universe has

large things in it. And uh those are

turn out to be huge mysteries we still

don't uh understand. If we take for

granted that the universe is big and

that it has big things in it. This is

tantamount to the existence of very

large sort of hierarchies of scale

between very microscopic length scale

like the like the plunk scale where

where where gravity gets strong spaceime

breaks down etc etc. And the much larger

scales in the universe all the way out

to the size of the observable universe

sort of six orders of magnitude between

the plunk length and the size of the

universe. and many other scales that

populate things in between that are very

well separated from each other. And the

big mystery is why quantum fluctuations

don't sort of crash all those scales on

top of each other. So it's not an

esoteric question. It's some very basic

question about the world around us. Um

uh you know when when I was in

undergraduate uh I mentioned even as a

kid I loved math and I loved physics. I

love both of them. I just all love

physics always very slightly more very

very slightly more but it was a very

slight thing. It was very difficult for

me to sort of choose definitely to be a

theoretical physicist and not a not a a

mathematician. But that choice kind of

affected a lot uh uh what I did because

I always had in back of my mind if I was

going to do something more mathematical

and formal uh I wasn't going to do

something sort of half-ass, I might as

well be a mathematician if I'm going to

do that, not you know. Um so so you know

I polarized more into questions that

would have uh uh direct contact with

experiment and that's that's really what

what I what I focused on and what I

worked on. Anyway, there's many twists

and turns in this story, but um uh but

uh in the mid 2000s uh me and many other

people uh started becoming alive to a

very different possibility for what

might explain uh these mysteries like uh

why the universe is big, why it has big

things in it. um uh related to ideas of

uh uh the possibility that uh uh the

constants of nature, what we think of as

a constants of nature. And these

mysteries about the vastness of the

universe are related to some of the

constants of nature like uh the vacuum

energy, the cosmological constant uh

it's called the cosmological constant or

uh the the the the constant that

controls the mass of the Higs particle.

Why these constants have seemingly

absurdly minuscule values compared to

what you would have sort of naturally

expected them to have.

>> So is this about naturalness? That's

right. This is this is the entire

question that uh that technically goes

by by by the name naturalness, but it's

really this sort of very basic question

about why quantum fluctuations don't

wipe out uh uh microscopic order and uh

and a sort of possibility started

emerging that maybe the constants uh are

not actually constant and they they they

they take on different values in

different regions of uh not the

observable universe, but if you're

somehow in a god's eye picture, zoom out

to gargantuan scales, you would see that

there is a giant multiverse out there

and the constants take different values

in different places in the universe and

in most of those places um if you change

these constants a little bit the

universe is empty or doesn't have any

matter of any sort in it or any

structure in it uh uh and so um it's

lethal mostly out there but in a few

tiny spots of uh it's possible for

structure and life to emerge and that's

why we we find ourselves there anyway it

was a sort of a controversial idea it's

still a controversial idea uh but people

tried to make sort of more proper for

theoretical sense of it. They tried and

they failed and uh they uh and I tried

and I failed. Many people tried and

failed. Um but these questions sort of

convinced me that uh we did need to

learn even for questions of direct

relevance to experiment you know not uh

you know questions up at the the the

scale having to do with quantum gravity

and so on that one way or another we

needed to figure out how to make sense

of quantum mechanics and cosmology uh

all in the same sentence. Right? that um

uh that that we couldn't factoriize

these sort of deep conceptual questions

about quantum mechanics in in the

universe from the more practical seeming

questions of the sort of structure of

our vacuum. And uh that's a very hard

question. But when you start backing up

from that question, at least I found

myself running into a simpler version of

all these problems where you try to uh

it was clear you somehow have to

reconceptualize what quantum mechanics,

spacetime, and the vacuum are about.

That's sort of that's I think completely

clear that continues to be clear today.

Uh but um uh but trying to do that in

the directly in the context of these

cosmological questions seemed too

difficult. And so I sort of tried to

back up to the first setting in which it

seemed like you could do something about

it. Um and uh so time has to be

important just like it's important in

cosmology. Dynamics has to be important.

You have to think about some questions

where quantum mechanics and spaceime

matter at order 100% you know in some

vivid way. And so uh scattering of

elementary particles was the sort of

obvious uh uh version of that uh

question. I had also learned um first

through the sort of famous paper of

Edward Whitten in 2003 um you know with

some vision for what an alternate theory

of scattering amplitudes might be. I was

not working on the subject at all but I

knew this seemed like a big deal. And

secondly, through the work of some

brilliant young people who also later

collaborated with Edward about these

things, including uh Freddy Kachazo uh

and Ruth Bridto who's uh uh here who

were both students at uh Harvard uh when

I was when I was there. I knew that

something was a foot in this world of of

amplitudes that there were you know very

basic facts about quantum field theory

that uh were being understood in new

ways. Um and uh that I found very very

striking. You know, I I thought of

myself as someone who maybe didn't know

all the fancy esoterica of uh what was

going on in uh field theory, but I I

understood the basics. I thought cold,

right? And then, you know, I remember

Freddy telling me some amazing things uh

that uh were associated with the famous

BCFW recursion relations, but they

involved some simple properties of uh

amplitudes that I just simply didn't

know. And of course, nobody knew before

they discovered them. So that that I

found uh very striking that there was

something going on uh right under our

noses that that we didn't understand.

And anyway, so those were all the

motivations in uh something like 2007208

to uh stop what I was doing and and

start uh uh start thinking about uh

amplitudes. The the the year or two uh

leading up to this period I was uh it

was also uh in anticipation of the Large

Hadron Collider turning on. So I'd spent

a lot of time thinking about uh you know

very practical questions about better

ways experimentalists might look at the

data coming out of the LHC. So that's

why maybe as I said in the beginning of

the child lectures the period before

amplitude is I was mostly working with

experimental particle physicists. Uh but

um variety of reasons there was kind of

a hard stop uh um I moved to the

institute for advanced study and that

was also a great opportunity to just

sort of become a graduate student again

for a while and learn a new subject. uh

and so um yeah so that's when it started

in uh uh 2008 um but it started with

this very clear picture uh I mean I

would go to conferences and say this is

what uh I I wanted to happen you know

some some people were friendly some

people were skeptical but it was a very

clear picture that what we're looking

for is some new way of formulating what

scattering amplitudes are where we

didn't have the usual apparatus we

didn't have uh uh we weren't relying on

pictures of particle trajectories or the

evolution of the wave function in in

Hilbert's space. Um, of course, this was

not coming entirely out of the blue. We

had this sort of stunning success of

BCFW recursion was clearly organizing or

thinking in some radically different

way. Even though you could, of course,

derive it in principle. There's a

derivation from standard quantum field

theory. So, you could, if you're a

skeptic, say, okay, it's very cool. It's

a tool. It's a tool, right? It's a it's

a very cool tool. You can derive it from

field theory and so on. But it also

looked like it was organizing things in

such a radically different way that that

you you had to be able to interpret them

as coming from a different world of uh

ideas. And so that that was it. It was

really kind of a a five-year period

between 2008 and 2013 that kind of saw

this uh evolution towards ampl happen in

steps. Um uh I spent uh a year with

Freddy Kachazo visiting me at the

institute. I like to tell Freddy that I

was uh I mean I was his grad student for

that year. I told him for a while, you

know, I would be his best grad student

ever, but he's had really good grad

students since, so it might not be true

that um and uh but I learned an enormous

amount from him in that year and we

started doing uh some work together that

uh started thinking about what these

recursion relations like BCFW meant in

twister space. That was the sort of

first first step. And then that led us

to uh uh sort of drawing pictures for

how we thought about these things in a

twister space that looked eerily similar

to pictures that one of my uh real

heroes in uh all of physics uh um uh

really heroes in life uh uh Andrew

Hodgeges at Oxford um had been drawing

uh since he was Penrose student in the

70s. Okay. Um, and I'd been staring at

Andrew's papers that been sitting on my

desk for two years. For these two years,

I couldn't figure out if he was a, you

know, crackpot or a genius. Uh, and, uh,

it was it was the latter, you know,

that, but but it took two years to, uh,

to figure that out. And, uh, Freddy and

and I and and and, uh, and and and some

of my, uh, uh, students back then

started figuring out the pictures that

we're drawing looked a lot like, uh,

Andrew's pictures. And we spent a number

of weeks with our crappy pictures on the

board on one side and his beautiful

pictures on the other side and and

asking what would we have to do to our

pictures to make them look more like

Andrew's pictures and along the way

discovering all sorts of uh wonderful

things. Um uh that ended up connecting

to the to Grassmanians in some way. So

that so understanding those pictures

ended up connecting to Gusmanians. That

was a whole other fantastic set of uh

coincidences that Alex Posnikov had

worked out essentially what the

structure uh looked like just a little

while before we needed it. But we ran

into uh uh Sasha Garcro is incredibly

important in in having us think about

these things properly. We spent months

um uh interacting before we knew any of

these things with Pierre Delene uh at

the institute who uh uh you know was

another you know heroes is uh I mean

he's one of these people it's hard to be

a hero because he's on a different plane

but um but still incredibly important

sort of getting us in the oriented and

and thinking about things the right way

and so that was a sort of penultimate

step. So, so we figured out how all the

building blocks for amplitudes um were

were were or organized according to

concepts in the Gmanian and the positive

Gmanian and so on. And that was a sort

of uh so that was that then the the

final step was to sever all ties to

standard uh notions of uh field theory.

So everything up to that point, you

could if you wanted to still connect

everything back back back to some

relatively conventional uh uh ideas in

uh in field theory. And so there was

like a last period of a year and a half

or two years where uh where we we

struggled a lot to see where all of

these pieces all the ways of building

amplitudes by putting together pieces.

Uh the pieces could be thought of as in

terms of BCFW or they be thought of in

terms of onshell processes or they could

be thought of in terms of uh uh uh

building blocks in the positive grasman

but they're all still kind of Lego

blocks that were being assembled in some

way but we didn't know what they were

assembling into. And uh so that was

maybe the most everything up to the

point I was describing was a joy ride

because everything just worked more or

less out of the box. It just worked. uh

you just have to sort of head in the

right direction and it just uh it was

like uh uh walking through an open door

almost. Um the last period was much more

more difficult because uh somehow two or

three ideas had to exist in your head

simultaneously in order to see the right

thing to do next and it took us a couple

years to uh to see it. But even then it

was not totally hopeless because so many

little miracles had happened that we

just knew the thing that we're looking

for had to exist that um and there were

sort of uh experimental uh there you

know miraculous identities that the

amplitude satisfied lots of little

numerical experiments that made it clear

that the kind of object we're looking

for had to exist. So so there's a reason

not to give up even though uh it wasn't

clear uh what it was. Anyway, so that's

the uh that's the story. It was about a

sort of a 5-year period. um uh from 2008

where it all started to uh 2013 when we

ran into the object. Then yeah maybe

fast forward in then 10 years from 2013

to let's say 2023 2024

uh sort of the the this ERC grant among

which these cow lecturers make part of

the universe plus grant

>> came to be

>> and we wanted to ask you in your eyes

what is the most exciting aspect that

has came out

>> um of this universe plus grant so far?

Well, I mean, I think uh I think it's uh

to start with, I'd say it's mere

existence is exciting. Um uh I mean it

it exists because of a large number of

uh of kind of scientific things that

have happened over the past uh 10 10

years. Um uh I think that the for me

personally that that the story of of the

of the amplahedron was uh was sort of

crucial for seeing that that some vision

of this sort for what the laws of

physics might look like is possible.

Right? But of course uh it was for very

limited set of theories uh in very

special cases and so on. Um you could

say as many dimminitive things about it

as as you wanted and I would agree you

know. So, so, so, um, uh, so the goal

was try to always to get closer and

closer to describing, uh, reality. Um,

uh, my my attitude about this as a

physicist is that as we get closer to

the real world, we should expect to see

more magical structures, not less. uh

and uh that maybe contrasts a little bit

with the attitude of some more

mathematically minded physicists who uh

say well you know you see exciting

mathematical structures and toy models

that have some properties they're

integraable they have this they have

that but uh but it's sort of cool things

about mathematical physics it's unlikely

you're going to see something like that

in the real world. My attitude is the

opposite. You know the closer we get to

the real world it has to get there's

nothing more magical than than than the

real world. So, it's very unlikely. If

you believe uh uh in this deep

connection between the the Platonic

mathematical universe and and and and

the real world, which I certainly do, uh

then it's just impossible to believe

that if there's something magical in the

little corner that there isn't something

vastly more magical uh actually going on

in in in in the real world. So, that

that was a belief, but it was only a

belief. And uh you know in various steps

uh we started uh seeing things uh uh

with the kind of character of the story

of the amplean but but quite different

in in um in uh in technical realization

uh emerge in the period after 2013. At

the same time um uh so so first even

purely within physics similar ideas

started emerging in in in cosmology. So

um and uh that uh that should

surprise you that that you know we're

we're it should it should seem at least

on the face of it surprising there's any

commonality between scattering

elementary particles and lying your back

and looking at the night sky and sort of

correlating what's happening here and

there and there don't on the face of it

seem to be similar problems. Of course,

technically they're they're very closely

related that they're they're both

computed in the same kind of uh you

know, quantum field theory formalism um

uh and in a it turns out in a very

precise sense that these sort of

correlations you observe in the sky and

cosmology swallow and contain the

formulas that give you uh scattering for

uh uh uh elementary particles. Um so

they end up being more closely related

than than than you might think. But

anyway, similar kinds of pictures,

similar sort of combinatorial geometric

pictures for what might be explaining um

uh uh cosmological correlations started

emerging in this intermediate period.

And finally um this is when uh it sort

of happened that my dominant

collaborators went from being

experimental theoretical physicists

experimental physicists theoretical

physicists to being mathematicians. And

um and that really blew me away. I mean

you know that um they're amazing group

of people uh brilliant um of course

think about things in totally different

ways than uh I do um and uh the most

fascinating thing to me was that um uh

uh we are not in one of these typical

situations either where the

mathematicians had figured everything

out already and then the physicists came

to use it as a tool which is maybe the

most common way this interaction looks

like or the the sort of interaction

where you know physicists know quantum

field theory string theory can predict

all sorts of things and mathematicians

have to come and figure out how to prove

it later where um uh well maybe

mathematicians care about the proving it

part but if you're a physicist you're

like I'd rather know how to make the the

the correct statements um but this is

not either one of those it's a it's a

bizarre situation where time and time

again um I mean I mentioned the story of

Pasikov and the positive Rasmanian right

when we needed it not 50 years before

you know like a few years before uh but

it just keeps happening over and over

again it's like we're running into the

same beast from different directions.

It's utterly bizarre that it's happening

roughly uh you know simultaneously. Um

and it means that when we talk to each

other, it's useful. You know, it's not

just uh interdisciplinary conversations

because it's cool to be

interdicciplinary. Far far from it. You

know, we're being sort of we're

individually experts in what we do, but

we're being dragged into some common

boundary because we're seeing the same

thing. Um and uh it's been incredibly

exciting working with like a large

number of different uh uh groups of uh

mathematicians. So um the answer to your

question I think just the the the

existence of the of this uh of this uh

of this project that's that's supposed

to bring together cosmology, particle

physics, mathematics in this uh you know

in this joint area where something

clearly is is happening um I think is

remarkable. You know, if you told a a

collider physicist 15 years ago that

grossmanians and cluster algebbras and

you know total positivity of matrices

with all positive determinants had

anything to do with anything, they would

think you're insane. You know that this

is not one of those, you know, it's not

one of those, you know, things between

math and physics where you kind of see,

yeah, probably they'll be related. It's

just insane that these things are

related. And if you told the

cominatorialists that what they're doing

playing around with like pictures of uh

permutations had anything to do with

what's going on when you collide

particles out there in nature or

accelerators or whatever, they would

also think you're you're insane. So um

so the fact that it's true is is

remarkable. And so I think the it's it's

it's just exciting uh to have more

systematic uh attitude about it. Having

said that, there are a couple of

specific things really specific sort of

dreams that that uh that at least I've

had that you know we even you dutifully

put in these proposals. We we are going

to do XYZW

which uh of course you know you have to

put something in a proposal but but when

you when you're doing research you go

wherever the hell the research takes you

but

>> but uh but a couple of the things just

hap just you know happened um uh much

earlier than I uh than I expected. Um,

one of the things that I've been looking

to do since 2017 is find a more I I I'd

mentioned back in 2017, we'd found some

very simple toy example of one of these

geometries that might be relevant for

cosmology, but we did not have a sort of

a complete picture of a geometry that

might be, you know, that might sort of

capture all possible processes uh

contributing to a uh to a cosmological

observable. um uh even in a toy model.

And um and uh we ran into that object

back in December. So that was something

I mean I I had no idea how long it would

take to find it, but I certainly tried

for many years and failed. Uh and we via

a few happy accidents uh ran into it in

December. before that um something else

you know we're talking about in the

proposal uh which I equally thought

would take years and years uh uh to find

but happened very suddenly and very very

quickly is some sort of version some

friend some cousin of the empahedron uh

to to describe directly the sort of

gluons the particles and the strong

interactions in in the real world not in

toy toy models and um there were a

number of ideas that had been developing

with collaborators over the course of

the pandemic uh um that uh that had a

sort of another approach to thinking

about all of these questions involving a

different set related but rather

different set of uh mathematical and and

physical ideas. Um but again there were

very toy theories and I thought okay

after we get the toy theory settled

we'll start again you know have to more

work uh and uh it was again like uh

going through an open door. It turned

out to be much closer uh in a surprising

way much much closer to sort of connect

these uh uh these toy theories to really

realistic theories that uh that describe

actual parts of the real world than I

thought. So those are two things I'm

extremely excited about. I did not

expect to happen as quickly as they did.

Um, but uh there are several more things

that we promised. Uh, we'd like to

figure out I mean really our goal is to

try to describe all of nature from this

point of view. We're very far from doing

that. Uh, but uh, we're working on it.

>> All right. I think just building on on

that um, do you think beyond what you

just mentioned which tied some toy

models closer to theories of nature? Is

there something re um other than that

example you gave which um in recent

developments got you excited of pushing

further and further into the theories of

nature? Uh yeah, I mean uh there are

clues lying around for uh what might uh

uh what might push us further in that

direction. I would say that maybe the um

uh

the main

qualitative large open problem um is uh

how so uh so far the so that this this

point of view um is uh starts with very

primitive questions right you know so

the the for example if you're talking

about uh a scattering of uh elementary

particles what we're doing is we throw

some particles in from far away uh

they're they're moving uh in some

directions. They have some energy. They

have some momentum. So you specify the

uh you specify their momenta that tells

you Einstein tells you their energy. Um

so bunch of momenta you know little

threedimensional vectors saying the the

directions they're coming in abracadabra

something happens and then a bunch of

things are going out. So that's the data

of the problem you know. So um uh you

get a function literally a function it

depends on these three vectors the these

three vectors that specify the uh uh uh

the particles going in and the particles

going out. Um and the kind of normal

apparatus of physics a normal way we

think about these things is by thinking

about the trajectories of particles

moving in space and time interacting and

that of course has all of the all of

physics in it. Right? So particles are

moving in space and time to get close to

each other. So there's a notion of

distance and they get close to each

other. When they hit each other, there's

an interaction. Uh uh then they then

they they produce something else. They

decay and so on. So there's a there's a

sort of whole picture that involves all

the apparatus of uh of uh uh of of

modern physics to figure out what what

what the answer is. But you see all of

that apparatus lives kind of on the

inside of this uh uh scattering process

in the in the inside of the space time

and these particles are thought to be

moving and so on. The actual question is

not posed on the inside of the of the of

this uh uh region of space and time.

It's just a question about a bunch of

vectors going in and a bunch of vectors

going out. So that's the canvas. The

canvas in which we're trying to build a

mathematical universe. Uh an alternate

picture for what could be describing

this process. The canvas is just you

know you have seven particles involving

the scattering process. Seven

threedimensional vectors. That's that's

that's the space. So you have to figure

out what to do in this world of like a

bunch of uh vectors. Uh and it seems

like an empty and austere world where

there isn't much to do. Um but it turns

out with a very very few uh extra

assumptions there's just enough

structure in these spaces where

something kind of magical can happen.

But one of the most important uh uh

elements uh that has allowed this to

happen in the mathematics is that you

imagine that these these vectors are not

just uh handed to you sort of randomly.

Here are seven vectors but they're rand

they're handed to you in some order.

Here's vector for particle one then

particle two particle three particle

four and so on. It seems like a

completely innocuous tiny thing but but

being handed in a particular order is

turns out in physics to be closely

related to the particles having uh what

we call color. So in the the the

strong interactions uh uh the particles

can be thought of as as having colors

and the way the colors flow from one

particle to the next is responsible for

this ordering. Um so all of the progress

at least all the progress that uh that

that this line of thinking that I've

been involved with um uh uh has been

centered around involves uh thinking

about particles with color. Now a lot of

particles in nature have color. Uh the

strong interactions there's a notion of

color. The weak interactions is a notion

of color. This notion of color is

ubiquitous. But some of the most

important things don't have color. You

know there's no notion of color

associated with photons. there's no

notion of color associated with gravity.

And so trying to understand how we have

a picture like this when you don't have

color and you don't have a notion of

sort of ordering um is a very deep and

basic one, you know. So um because it

seemed like it was the lifeline that let

something happen out of seemingly

nothing. And so we really have to go

back and and and and ask if there does

not seem to be anything, if there is no

no color, what could be the organizing

principle that lets us uh know what to

do next? that I think is the sort of

largest open problem. Um that's one I

mean we can we can we can say we'll

study it. We can say that we'll we'll

work on it. I've studied and worked on

it off and on for uh you know uh 10

years. Uh you never know what kind of uh

what uh set of accidents you'll uh uh

and uh happy coincidences will happen

along the way that might that might give

the key for where to go next. But there

is in this uh in this in this new set of

ideas um there is like a clue that uh

that that uh that at least at the level

of combinotaurics

um uh the world of gravity of uncolored

particles is sort of sitting there in

the structures that we're talking about.

That's very encouraging. So it's not uh

not only is it not absent, it's sort of

very much present. It's very much

present but in a very confusing way

right now in a way that we don't know

how to sort of turn into formulas that

physicists care about you know formulas

for scattering processes but they are

sitting there and so that's why I sort

of feel if we trump around in this

neighborhood for a while we might find

the right clue uh to let us make

progress but I think that's the sort of

biggest the most exciting question um uh

the biggest sort of potential obstacle

to the whole program and but one where

there's uh some possible clue for making

progress.

>> Sort of tying in also to something you

mentioned, I mean you've mentioned all

along the interview, you have definitely

been a key figure in pushing

interdisciplinary research between

mathematics and theoretical physics. Why

do you think this is important and how

could we make physicists and

mathematicians engage even more with

each other?

Well, um I I uh

I have a kind of maybe a funny attitude

towards interdisciplinarity which I've

maybe mentioned before. Um uh I've

always been personally suspicious of

interdicciplinary work. Um um uh I sort

of prefer to think of it as

cross-disciplinary than inter uh

interdisciplinary by which I mean um I'm

I'm suspicious. I mean I'm not I'm not

saying like actively hostile. I just I

literally mean

suspicious because I know many examples

of people who are sort of professional

interdisciplinarians which they mean

they permanently live at a boundary

between two fields

>> and um and then in almost all examples I

know when you like you know the fields A

and B uh when you ask people in field B

what they think of the work of this

person they say oh they're an expert in

A and when you ask the other way around

they say they're they're an expert in B.

I don't like that so much you know that

um uh I prefer cross-disciplinary

because it means uh it means that there

is someone who is you know science is

hard right you know we specialize for

good reasons um but um the the bad thing

about uh the worst thing about

specialization is not that you have to

sort of uh drill deep and know you know

one thing in order to make progress

that's all true that's life I mean you

know that's where where where we are in

the 21st century with our uh with the

way science works is if you do that so

much that you be sort of become blinded

to uh other things uh that are going on

elsewhere. You don't even sort of hear

about them. They don't sort of enter

your your your mind. Um and um uh but it

can happen, it does happen that the

exigencies of your own little thing that

you're working on, you know, force you

to a boundary, right? Um and it's even

more exciting when they force other

people on uh to the same boundary and

and you don't quite know why, but

something has dragged you there. uh

together. That's definitely been the

sense of this subject. That's why I

mentioned before, you know, it's not 15

years ago, it would have been insane to

think that that the cominatorics and

particle physics and geo have anything

to do with each other, but people were

dragged there uh together. Um once that

happens, I think it's extremely exciting

because because you're not just there

for the sake of being interdisiplinary,

you were dragged there for a reason and

you want to talk to each other because

they know something that that you need

and maybe vice vice versa. Um so um uh

uh I have to say my my interactions with

mathematicians have had none of the uh

sort of stereotypical flavor that you

sometimes hear interaction between

mathematicians and physicists have. Um

it has not been it has not remotely

revolved around the access of like you

know a physicist uh uh uh on the

frontier not caring at all about rigor

and the mathematicians caring about

rigor and dotting all the eyes and

crossing all the tees. Not remotely. I

mean it's not like that at all. Um of

course they care about rigor and proving

things more than we do. But it's a

sideshow that uh um much more

interestingly there's kind of a creative

tension between um trying to make

definitions and uh precise uh versus

not. I mean um uh as a physicist I'm

always a little nervous about making

definitions precise because I always

worry that we're trying to make things

precise too early uh and that if we just

wait a little bit longer we'll see what

the sort of correct structure is that we

should be talking about. So I don't want

to commit too early. Um uh and uh as a

physicist I also had the prejudice that

I was right you know uh but I've learned

on a number of occasions that my friends

on the other side were right that there

was sometimes this is a good time to

stop and try to say very be very precise

about what we're talking about um

because uh um once you do that and you

find something that works even in all

the degenerate cases then something

really good has happened. So that's

something that I have certainly learned

uh from uh uh interactions with my uh

mathematical friends. So even sort of

culturally that there was there are some

very useful parts in the way uh they are

thinking about things that uh that I've

definitely digested. I suspect that

they've picked up some things about the

way we go about doing things uh as well.

Um um but uh so it's been amazing. I

mean just uh and and and

not at all. Uh I've found sort of no

sort of cultural conflicts uh um even

the you know we don't understand each

other has been relatively minor. I mean

um of course that that they have a

different language uh and so on but

precisely because it's clear we're

seeing the same thing. Um it's uh it

doesn't take very long to say okay you

use these words we use this words but is

it about some matrix and does the matrix

look like this and do you do this thing

with it? It's like, yeah, yeah, that's

what it looks like. Okay, great. You

call it this. We say it uh uh this other

way, but it but it sort of quickly uh

settles down to something. Um um so uh

it's just been it's just been wonderful.

Um I I think the main thing um uh is to

just bring them mathematicians and

physicists uh who actually have common

interests uh into contact uh really

really more than anything it's into

physical contact and uh and talking at a

blackboard. Um uh uh one of the I think

this is one of the the kind of stupidest

things about uh the way um a lot of

academia is set up uh is uh is to make

informal interactions that last longer

than you know 5 hours or two days or a

week um difficult right uh and some of

these things just can't you know if

you've learned a subject in grad school

and you're talking to someone working in

an adjacent subject very adjacent

subject, you can maybe have a

conversation over lunch and then

something good can can happen. Um but uh

if if the if the fields are farther

apart than that, even a lunchtime

conversation is probably not enough for

more than superficial exchange of words

and ideas and so on. Um I found the sort

of biggest barrier to uh uh uh working

in this kind of field is um the kind of

two weeks, one week, two weeks,

sometimes a month it takes to learn

something. Um, and if you have to learn

it by reading someone's papers, forget

it. It's not going to take a month. It's

going to take six months, a year, God

knows, right? But, um, but you have to

get together in the same physical

location at a blackboard and talk for

uh, a day, two days, a week, however

long it takes until uh, there's actual

connection. Um, so it's it's a very

simple uh, piece of advice about how

this interaction can be improved, but I

think it's probably the most practical

one.

>> Yeah. So perhaps to wrap it up, um, if

something comes to mind, do you have a

favorite anecdote from your days in

doing research or your own studies that

comes to mind that you

>> Oh, there there are way way too many. I

mean, um, maybe maybe I'll say I'll say

some I mean, it's it's one it's one

example. It's one example of uh of many,

but I I'll I'll I'll maybe say this this

story because it's illustrative of uh a

number of the things that we're talking

about.

So um uh early on in uh uh in in this

story with uh uh with with Freddy Kazo

and my and my students where we're uh

understanding uh the connection uh

between uh

scattering amplitudes for gluons uh the

work of Andrew Hajes uh and uh some the

first stumbling into some connection

with the Gresmanian that kind of blew

our minds. Um actually the the mini uh

story there is that uh we didn't know

what a gross I didn't know what what a

grossman was but we had um we had uh

matrices we had these you know we had

these k byn matrices all over the place

that were sort of uh we were writing

them by putting an identity block in one

side and then some other uh things on

the other side and then uh you know we

could do linear transformations um on

these things we quickly realized

obviously there was some describing some

kind of k dimensional plane and and

dimensions so we knew all of those

things. I just didn't know the word

grossman, you know. And at some point as

we're discussing, uh, you know, Freddy

and I would would say to each other,

surely mathematicians know about like,

you know, planes and n dimensions. Yeah,

surely. Anyway, uh, Freddy was thumbming

through Griffith and Harris's algebraic

geometry book and he just found on some

page a picture of a k byn matrix with an

identity block and a bunch of like stars

and the other entries and he said, "Look

at this page." you know, he like he

emailed me, "Look at this page." I'm

like, "Holy we're like doing a

we're doing Griffith Harris," you know.

Uh anyway, um uh but the more the more

interesting story, so after all all of

this and we were talking to Pierre

Delene, who gave us hundred clues and

Sasha Grov pointed us in the right

direction. But then we finally ran into

the work of Alex Basikov who had been

doing we did not know anything about it.

We finally ran into the world work of

Alex Bosikov and I looked at his papers.

I couldn't make head or tail of them.

But you see um we had spent uh you know

6 months at this point starting with a

picture where we're gluing together

basic processes where three gluons meet

and for good reasons you know the the

the the the gluons two of them can be uh

uh negative circularly polarized one of

them positive circularly polarized or

the other way around. And so we're

representing the case where two are

negative one positive with a little

black vertex and the other one with a

little white vertex. And so we're

spending all day long gluing these black

and white vertices together to make

pictures that miraculously we found were

related to these k byn matrices and

gresmanians and all this stuff. So then

we found out that this posikov guy uh

also had these matrices and was saying

lots of interesting things about them

clearly seemed related somehow. So we

the whole crew of us uh drove up uh to

talk to him at uh uh MIT. So got to MIT

we met him for the first time. Wonderful

guy, amazing guy. still uh still great

great great great friends with them. Um

but it was very exciting. We spent the

whole morning, you know, we had our

matrices like, yeah, they look like my

my matrices and okay, we're clearly

saying the same thing. Mind-blowing.

Fantastic. But uh only about these

matrices and all these sort of algebraic

structures only about these matrices.

And then um then we went to lunch and

and uh uh in all the excitement, Alex is

like, you know, I'm a little surprised

though in my way of thinking about

things. there's some very important

pictures that go along with these uh

with these uh with these matrices. And

we're like, "Oh yeah, you know, what do

they look like?" He said, "They look

like this." And we drew like we drew one

of the pictures that's like literally on

our board like over and over and over

again for the past 3 months. Uh of

course interpreted in totally different

ways which we had been deliberately

hiding from him because you know we

thought that was that was the physics

part you know so we don't want to we

don't want to bore you with these

pictures but let's get to these matrices

and the aggressmanion. But that was

where it came from for him as well. And

then he pointed us back to his paper um

where he has this throwaway comment that

perhaps we can think about the little

black and white vertices as something to

do with finding diagrams. It's

completely insane thing that of course

ended up to be not quite fine diagram.

It ended up being totally true, right?

Um that sort of thing has happened a

number of times. It's a it's a it's a

great story because it it illustrates so

much this point that you run into the

same beast. But I'll never forget that

that uh one of the great things about

Alex um you know um the one the one uh

the one distinction I'll make amongst

mathematicians there are some

mathematicians when you ask for an

example they give you the tiniest most

trivial example right and then for me as

a physicist it's hard to understand

something from the dead simplest example

um you need to see maybe the second or

third most complicated examples before

you see something going on and uh Alex

bless his heart always starts with the

second or third most complicated example

to illustrate something. And so he

happened to draw a picture that was a

sort of pentagon box. Um, and it was

just shocked us that it was exactly the

pictures that we've been drawing for

such such a long time.