@user2103480 did you write this?

no, our prof

Incredible handwriting

I wish my handwriting was as clear

I wish my prof's writtings were so neat lol

To be honest

I had like 3 or 4 profs with handrwitten notes and all those were page upon page without any corrections

and mostly very readable

superhuman abilities

The worst in in exercises sessions, where the prof draws arrows in every direction

I can't write 5 words without erasing anything

@BalarkaSen this would erase all spatial relations though

dunno what that means

I had some profs who were able to write on a chalkboard and it looked it was printed

damnit i cant remember the example

@BalarkaSen no distance. Also the quotienting should only work if we take half open cubes, meh. Else it's not a partition

I don't care to evaluate that

Do you have PDE question? I can try to answer

this reads like jargon to me. doesnt seem relevant to what the point of ensembles is

And why do we have a density with respect to R^6N with this sigma algebra? The density is constant on the microstates so one might just as well just call this the countable sum that it is

Wait nah that doesnt make sense

@user131585 asking a specific question is probably a better approach than to ask someone to make a public statement of their personal evaluation of their abilities.

@robjohn Before you go back to The Mean Square, after Thanksgiving, can I have a slice of your pi?? ;D

Do you know an ODE which models heat flow?

lol

That's one of the very first interesting examples of PDE, back to Laplace. In fact, it's almost the canonical example of a certain type of PDE. There is a way to talk about it as an ODE in Hilbert space --- one common technique in the study of PDE is to turn them into ODEs in infinite-dimensional spaces --- but I do not know any way to talk about such thing in the context of finite-dimensional ODE.

But also, I am a pure mathematician. The only person I have to convince that I'm doing useful work is the NSF, and they are suckers. So I just work on what is interesting to me. The techniques which have traditionally evolved to study PDE, and their value in problems of geometric origin, are interesting to me. So even if it turns out there is some ODE which gives a reasonable approximation to the behavior of heat flow (doubt it!) I can just work on what seems fun. ;)

@BalarkaSen what is the point

the point is you model the big system as iid copies of smaller systems

thats what an ensemble is. its a buzzword for iid copies lol

here you model the whole system of N particles as iid copies of each particle

each particle inhibits h^3N amount of stuff in your phase space by quantum whatever

and then the whole system is a tensor product of these

don't the particles move?

Do they move from microstate to microstate in time?

"More generally, if V and V' are complex (not necessarily compact or Kâhler) manifolds of equal dimensions and their even Betti numbers are flnite and equal then every proper surjective holomorphic map f: V — > V' is finite-to-one and when deg f = 1 the map is injective"

@BalarkaSen wtf?

@user2103480 yeah but at any instant of time if you freeze the particle is in one of those h^3N volume little cubes

and all those cubes are indistinguishable

@MikeMiller pretty cool

I think it depends on the problem. For some problems you can model them using ODEs. Sometimes you can't.

i guess follows from some factorization maybe

An ODE in Hilbert space is a great way to work with a very specific type of PDE (most do not take that form). And even then, that's VERY different than working with ODE in the traditional sense; it is, for instance, not at all computationally tractable

the only proper surjective holomorphic maps between equidim manifolds i can think of which are not finite are blowdowns

but the betti gets flipped

whats degree between noncompact things

It's a proper map

@user131585 I think I'd put it more succinctly like this. Real-world phenomena can behave in many, many different ways. Anyone who says that their one favorite tool can solve all those problems is either deluding you or yourself, and is definitely selling something. ;)

ok, well, i'll admit it's harder than that to get funding nowadays

@MikeMiller wow

but the point is that the people in charge are other pure mathematicians

this is Bharali-Biswas

i know both of these people

complete nutcases

No, it is Gromov

Oh

They just wrote down a proof

amazing

Thesis problem: Find a sentence in Gromov that nobody has explained before, then explain it

Yeah

actually

Bharali-Biswas uses resolution of singularities

lmao

some factorization man has to be, you write it as some blowup blowdowns

I dunno, what is your field?

Do you have an advisor to talk to?

I am a topologist so I'm definitely not knowledgeable about what's useful to modeling fluid dynamics or whatever lol

@user131585 You aren't hijacking anything. I just don't have answers. :)

Maybe you will I dunno

$(\alpha - z)/(1 - \overline{\alpha} z)$ is a hyperbolic reflection of the disk right?

involution, fixes a semicircle's worth of points at least at a glance

@MikeMiller I think that Stein and students may have used pseudodifferential operators to study the heat equation in somewhat geometric approaches. I know they started it years ago, but I don't know how far they have gone.

@BalarkaSen It should fix a circle's worth of points.

Inside the disk

Sorry

But yeah I agree

@anakhro remember our talk about lecturers cramming too many topics into once course?

german efficiency

it is indeed efficient to state a dozen results without proof, but I guess that's my life now

well, why prove it when its obvious

Hello everyone. In my intro analysis class, the professor has 3 and 1/2 weeks to teach differentiation, integration and sequences of functions (if enough time). Will it be feasible?

well, depends on how much of that time they actually have to teach

Ideas 💡?

@Thorgott Obvious tends to mean 'it had been proved'. Many geometrically evident results are difficult to prove.