The h Bar

Mike Miller

20:00

There are worries that the professor teaching differential geometry here next quarter is just going to teach Chern-Weil theory instead, since he does that for every course he teaches ever. I'm the TA and desperately hoping I don't just have to teach them differential geometry.

Danu

This happened to me :P

The course was "Riemannian geometry"

We just did two weeks of Riemannian geometry at the very end

0celo7

Lol

Danu

As a "trivial application" of Chern-Weil theory

0celo7

@Danu Squeezed in Hopf-Rinow and friends?

Danu

No.

0celo7

20:02

@Danu What "trivial application" did you do, then?

Danu

Super-basics.

0celo7

or link me your notes

Danu

Also Gauss-Bonnet and some small generalizations

Mike Miller

@Danu Well, uh, you probably wanted to learn that anyway, so...

Danu

@MikeMiller ...but now I didn't learn Riemannian geometry.

0celo7

20:04

what else do you need beyond what's covered in Carroll :P

Danu

lol

I don't need any of it.

I don't need any topology either

I want it.

0celo7

@Danu rly

how do you do FA without topology

Danu

@0celo7 Lol

How do you do QM without understanding Hilbert spaces?

0celo7

@Danu well you need operator topology and other things

Danu

Not really, unless you want to do research on that kind of stuff.

0celo7

20:05

@Danu According to ACM: not well

Danu

And that's a pretty small niche.

0celo7

@Danu It is my understanding that one needs some FA to do PDEs

Mike Miller

@0celo7 Not stuff that requires a significant amount of topology. Maybe the fact that compact unit ball implies finite dimensional.

Danu

FA won't hurt you but I'm alsot pretty sure I won't need it anytime soon.

Definitely not the advanced topology stuff.

0celo7

@MikeMiller oh

Danu

20:07

In any case, the things we're doing in my course are unrelated to FA.

Mike Miller

At least, elliptic PDE. I don't know much about non-elliptic PDE. That's scary.

0celo7

well I'm pretty sure I won't take anything beyond the standard two semester topology thingie

Danu

Your loss :)

But you'll be fine.

0celo7

well we certainly don't do surgery in intro topology

LMU is nuts...I'm putting it on my list for summer schools -- need to find out what kind of programs they have

(summer programs)

Danu

@0celo7 It's a graduate course I'm taking.

0celo7

20:11

@Danu yes, me too

Danu

Then I don't see why not!

0celo7

maybe in the second semester

Mike Miller

Surgery is not really a standard intro topology topic.

0celo7

@Danu if they follow Munkres closely, then they won't

Danu

But we didn't really do it in any real detail. We just gave some basic constructions

Mike Miller

20:12

You could cover it, but I'm not sure it's sexy enough to justify that when one could do more fun things.

Danu

I think surgery is pretty damn sexy.

(that came out wrong)

0celo7

no it didn't

Danu

okay.

0celo7

surgery is pretty damn sexy...open sets, maps...mmmm

...surgery things...

Danu

lol "open sets, maps"

surgery confirmed

0celo7

20:15

I know nothing about surgery :P

what would you have known about it in your first semester?

Mike Miller

is it possible to stop the feed item thing

Danu

@MikeMiller There will be a seminar on Lie groups next semester, and they're asking us to tell them what kind of topics we'd be interested in.

Do you have any cool suggestions?

I assume a lot of time will be spent on representations

0celo7

prove that $\mathrm{SO}(3)$ embeds in $\mathbb{R}^9$

Danu

But I'd like to do something less.. linear :P

0celo7

take detailed notes of that and post them here...

Danu

20:16

@0celo7 That doesn't really sound hard at all.

Mike Miller

I don't know a lot about representation theory. It would be work, but you could learn Morse theory and the proof that $\pi_2 G = 0$.

Danu

Maybe it is? idk

Slereah

@0celo7 $S^{2n}$ has no Lorentz metric

0celo7

@Danu well I could not do it

@Slereah I KNOW

I totally forgot that was a thing in HE

Slereah

WELL THEN SAY IT

0celo7

20:17

but how does one prove that statement

I think Hirsch has the proof...

Danu

@MikeMiller Our TA (who is close to the professor) said today, during the same announcement, that Morse theory is "probably too trivial"

0celo7

@Danu is Doner to trivial for your taste buds

Mike Miller

A Lorentz metric gives you a 1-dimensional subbundle of the tangent bundle. Prove using Euler classes that that's not possible for $S^{2n}$.

Danu

@0celo7 Yes.

Mike Miller

@Danu Did they give any suggested topics so I know what's not trivial?

0celo7

20:19

@MikeMiller Hawking-Ellis uses Poincare-Hopf

Danu

@MikeMiller Nothing concrete, just "Lie groups" or "Geometric group theory"

and sub-topics in those are up to us; or we can come up with other suggestions

0celo7

They show that you simply can't get a Lorentz metric because there's no line element.

Danu

they said Mathematical Gauge Theory was too hard :(

Slereah

More like gauche theory

0celo7

@MikeMiller in any case, "Prove using Euler classes" is too vague and beyond me

Mike Miller

20:20

@0celo7 Sure, that also sort of generalizes. On any manifold with $H^1(X;\Bbb Z/2)$ trivial, like the sphere, line bundles are trivial and have a nonvanishing section, so you just produced a nonvanishing section of $S^{2n}$.

Bad, as $\chi(S^{2n}) \neq 0$, as you said.

0celo7

@MikeMiller I believe you ;)

Mike Miller

Ok, I guess I won't bother.

0celo7

Huh?

Slereah

you damn dirty ape

0celo7

I think I understand what you're saying.

I just don't have the slightest clue how to prove it...

therefore I believe you

Slereah

20:22

the proof is in Steenrod, remember :V

0celo7

@MikeMiller you mean $S^{2n+1}$?

Mike Miller

No.

0celo7

@Slereah it's also in Hirsch

@MikeMiller but $S^{2n}$ does not have a nonvanishing section

Mike Miller

That's the whole point of what I said, yes.

0celo7

> so you just produced a nonvanishing section of $S^{2n}.$

Danu

20:24

sigh :P

0celo7

@Danu no reason to sigh my child

Danu

Getting a bit tired of this.

0celo7

huh?

Slereah

-1

Q: How do theoretical physicists work?

How do they spend their day? Looking out the window trying to think up something new? Learning new maths? Reading other people's papers? And how is their productivity measured beyond churning out papers?

discussion

Too bad it's closed

I would have liked to recount my days in the lab

Step 1 : write the relevant equations on paper

Step 2 : Go from there

Step 3 : Get stuck

0celo7

@Danu it's clear you have to tell me what you're getting tired of

Slereah

20:33

Step 4 : Look intently at the piece of paper

Step 5 : Take a new piece of paper, back to step 1

0celo7

seems like doing an exercise

great, 4chin is full of star wars spoilers

I know who dies

:(

Slereah

That is basically research

Also lots of bibliography

dmckee

20:59

@Slereah That step seem to be common to every interesting human endeavor.

0celo7

@dmckee also uninteresting ones

dmckee

Yeah, but those are uninteresting.

Slereah

Also quite a lot of research endeavours involve tracking down sign errors and factors of 1/2

0celo7

> Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something completely different.

yuggib

21:36

mathematicians $\simeq$ frenchmen

well, france is the country of mathematics

Qmechanic

@ACuriousMind : Ah, you are right. They are not using (4.3) to prove an off-shell symmetry. They assume that the off-shell symmetry has been established by other means. Then (4.3) becomes the corresponding on-shell conservation law.

Nick

Could someone please explain what that diagram is saying.

Maybe link to a video about the mechanism, perhaps.

HDE 226868

21:54

Does anyone know anything about the "bump" in the data at CERN that's made the news recently (e.g. nytimes.com/2015/12/16/science/…)?

I've only heard sensationalism, hype, cautious scientists, and champagne jokes so far.

vzn

@HDE226868 its a good summary at this pt, what more could you ask for? this also showed up in here

yesterday, by Slereah

http://resonaances.blogspot.fr/2015/12/a-new-boson-at-750-gev.html

HDE 226868

@vzn Cool article; thanks. cc @Slereah

Slereah

22:11

It's a somewhat exciting bump

Secret

https://i.sstatic.net/LSLyZ.jpg

@Qmechanic @Acuriousmind @HDE226868 @Slereah
Q1. The author said the internal conversion (laballed IC in that energy level diagram) is isoenergetic, which means there is no energy change in that transition

a. If we use what we have discussed earlier (with Acuriousmind, 0celo7, Slereah) that a state can be changed by a measurement (i.e. a suitable operator acting on the state which changes it), and energy does not necessary change in the process

how does the molecule knows it has to transit to a lower electronic state (but vibrationally excited) as after…

Secret

22:26

@Danu Can you help me on the above conceptual question on spectroscopy?

Secret

22:45

@ Skill Patrol I have reasons that the two are ignoring me. Ever since that unexpectedly violent reaction of them towards that integral space filler, I know something went very wrong

I cannot believe I accidentally robbed myself of access to GR because of a space filler

Secret

23:16

@ChrisWhite do you know spectroscopy?

kevin Tah N.

23:37

@secret . . . what is the question again?

@secret ok just read the question, took me a while to locate it lol

I was going to venture an answer to do with probability and iS in the path integral but let me just see what others come up with first

0537

@0celo7 Engineering can be rigorous.

ok well, kind of?

kevin Tah N.

@0537 lol

saw the paper

0537

looks really cool.

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