The h Bar

FenderLesPaul

7:00 PM

just out of curiosity

is LQG more popular in Europe than it is in the US?

ACuriousMind

I don't think so

FenderLesPaul

ah okay

0celo7

@ACuriousMind read that as "mod tranny"

What are some spaces with nonvanishing second Stiefel-Whitney class?

Obliv

What does it mean to assign an element $u + v \in V$ to each pair of elements $u,v \in V$? Axler says "by an addition on V, we mean a function that assigns an element $u+v \in V$ to each pair of elements $u,v \in V$.

ex: an element of V is {1,2} and to assign {1,3} to that element doesn't make sense to me

0celo7

7:16 PM

> Hi Ryan,

I am attaching a two-page PDF with an argument to make timelike curves
smooth; organizing the details took a little more work than I expected.

Let me know if anything is unclear, or appears to be wrong.

@Slereah Wow, he actually did it

ACuriousMind

@Obliv He means that addition is a function $+ : V\times V\to V$. It assigns to a pair of vectors (e.g. (1,3) and (2,6)) their sum (here, (3,9)).

Slereah

Take that, Georges Ellis

Obliv

@Acuriousmind Oh I see, thanks. All of this notation really messes me up D:

Slereah

still good

John Rennie

@0celo7 Your definition of basic question appears to require having a research level knowledge of algebraic geometry and topology.

0celo7

7:20 PM

algebraic geometry?

Since when do you need algebraic geometry for GR oO

@JohnRennie One of my profs apparently answered my basic question, reading his email now...

Slereah

Do you know a good proof for the vectors of the inverse exp map are equivalent to the vectors of the geodesics

0celo7

But he's a mathematician, not a dirty physicist

Slereah

Gauss seems to be almost that

But

John Rennie

I can't understand your questions, and I can't understand algebraic geometry, therefore your questions = algebraic geometry :-)

Slereah

The vectors have to be "radial"

Whatever that means

0celo7

7:21 PM

@Slereah the tangent is parallel transported along the geodesic

@Slereah radial means that they are proportional to the radial vector :)

Slereah

What is the radial vector

0celo7

which is defined in terms of the distance function in the convex normal neighborhood

Slereah

Hm

0celo7

@Slereah do you have access to Jost or the AMS Lee book?

Slereah

Trying to think if that would be enough to show that the chronological future is an image of the tangent one

Probably ( ͡° ͜ʖ ͡°)

0celo7

7:24 PM

@Slereah get Jost's 6th edition riemannian geometry book

I've got my physical copy right here...

Slereah

Let me acquire it legally

It is acquired

0celo7

page 22

the radial vector is $\partial/\partial r$ whre $r$ is defined there

Slereah

Oh it's radial coordinates in Riemann normal coordinates

Hm

0celo7

Check Lee's Riemannian Manifolds book for a derivation of the Gauss lemma explicitly in terms of radial stuff.

I think other Lee's AMS book does it too...but I can't recall.

And I'm not getting up to grab it.

@JohnRennie Would it be kosher to email an author to ask if/when a second edition will be happening?

@Slereah Jesus. This proof is not easy.

Slereah

which

0celo7

7:34 PM

smoothing

Slereah

How close is it to the Penrose sketch

0celo7

not at all

I need some whiskey for this

What is up with these barbaric drinking laws in this country

@Slereah well

He does cheat a bit, he works in a chart on a compact set

and then measures angles or something

Qmechanic

@barrycarter : Well, there's this meta post.

Danu

So I'm writing an answer to that bountied res. rec. question about topology & geometry.

I'm torn about what kind of books to include...

Does a book on spin geometry qualify, or should I keep it more basic?

0celo7

7:50 PM

@Danu link?

Danu

@0celo7 To what?

The question is this one:

11

Q: Book covering differential geometry and topology required for physics and applications

I am a physics undergrad, and interested to learn Topology so far as it has use in Physics. Currently I am trying to study Topological solitons but bogged down by some topological concepts. I am not that interested for studying it for its own sake. Please could you mention the topics of Topology ...

0celo7

@Danu I know by "spin geometry" you mean THE Spin Geometry :P

And we all know you're gonna put Lee

Danu

@0celo7 I'm not, actually.

0celo7

are you sick?

DYING

Danu

Though I think it's a great book, it's definitely not what OP is looking for: I'll only include books that are specifically tailored for the physics community.

0celo7

7:52 PM

That's not the Danu I know ~~and love~~

Danu

It pains me, too ;)

0celo7

@Danu What about Straumann or O'Neil?

O'Neil is a math book that focuses on GR.

Obliv

to verify that $F^n$ is a vector space over F, do I just re-prove the properties associated with $F$ on $F^n$?

like associative, commutative, etc.

0celo7

What is $F^n$?

Slereah

Cartesian product I guess?

0celo7

7:54 PM

Oh, a field $n$ times?

Slereah

Prolly

David Z

@FenderLesPaul ooh, Berkeley is nice

Obliv

$F^n$ is a set {$(x_1,...,x_n): x_j \in F for j=(1,...,n)$} I think

0celo7

> I am not that interested for studying it for its own sake.

Damn physicists

@Danu I'm surprised you're not going on a rant that "math for physicists is always bad" or something :P

OP is definitely not interested in Lawson & Michelsohn.

Danu

@0celo7 Oh, I am, don't worry ;)

@0celo7 Yeah I'm omitting it

O'Neil will be in there, under the "specialized" section

0celo7

8:00 PM

@Danu My advisor is actually re-reading that book right now, one of his grad students is working on index theorem related stuff.

I see it on his desk every now and then.

FenderLesPaul

@DavidZ the location?

David Z

The town, as well as the university

FenderLesPaul

Ah ok

0celo7

@Danu You putting Carroll?

FenderLesPaul

yeah I've been told it's pretty artsy and stuff

0celo7

8:01 PM

Eww.

FenderLesPaul

I've been told UCSB looks like a beach resort

which means no work will get done yay! :)

David Z

At least UC Berkeley does have a great reputation for physics and many other subjects, but the town is also very scenic and there's a lot of interesting stuff to do

I've only seen pictures of Santa Barbara but that sounds about right

0celo7

@Danu Is it that specialized though? It's a standard intro to Riemannian geometry, but they also treat a lot of Lorentzian geometry.

FenderLesPaul

@DavidZ yeah @ChrisWhite mentioned Berkeley's pretty good for physics/astro

they have some funding issues though

as do most UC schools

David Z

Yeah, who doesn't

FenderLesPaul

8:03 PM

Donald Trump!

He should start a university

David Z

:-P

0celo7

@DavidZ My advisor goes from "I have no money!" to "we should buy another spectrometer" from week to week.

David Z

To be fair, these things are not entirely mutually exclusive

FenderLesPaul

@DavidZ did you spend time at Berkeley?

David Z

Yeah, I travel there sometimes for research. I have collaborators at Berkeley Lab.

FenderLesPaul

8:05 PM

cool beans

O.O

That's Berkeley :-P

Those turkeys make it so much better haha

I want to see if I can graffiti Jackson's office when I'm there

be a martyr for physics grad students everywhere

0celo7

does Jackson teach Jackson EM?

David Z

8:09 PM

Somehow I doubt you'd be the first to try

FenderLesPaul

Jackson is emeritus I think

but he still has an office there

@DavidZ have you visited UChicago?

Danu

@0celo7 No

David Z

Ah... no. I've been to Chicago but not to the university.

I have some friends there though.

Danu

@0celo7 It is specialized, since it's not really relevant for other topics than GR.

FenderLesPaul

@DavidZ Ah ok

just wondering how active UChicago is in the pheno world

0celo7

8:13 PM

@Danu Nothing besides GR uses Riemannian geometry?

Obliv

@0celo7 Should I try learning all of the algebraic structures before I continue with linear algebra? I kind of just spent 20 minutes voyaging through wikipedia clicking on things I don't know and realized that a field is a ring-like algebraic structure and a vector space is a module-like algebraic structure

Slereah

You use spherical geometry for like

astronomy

David Z

@FenderLesPaul They've got a couple big names there, but it's not exactly a "hub" these days, especially since Fermilab shut down the Tevatron

Slereah

And geodesy

Obliv

@0celo7 or are they too complicated to learn now?

0celo7

8:15 PM

@Obliv A field is a ring for which the group of units is the ring with zero removed.

FenderLesPaul

@DavidZ that's too bad

0celo7

Does Axler assume you know what a field is?

FenderLesPaul

what are the "hubs" these days?

at least in the US

0celo7

And a ring, etc.?

@FenderLesPaul wow xenophobe

Danu

@0celo7 Lorentzian---not that much, no

0celo7

8:16 PM

@Danu O'Neil treats Riemannian geometry as well.

Slereah

Yeah I can't think of a single application of Lorentzian geometry that isn't either relativity or like

Wave equation more generally

0celo7

NOT LORENTZIAN

FenderLesPaul

@0celo7 >.>

0celo7

And yes, technically GR isn't Riemannian geometry.

But that wasn't what I was asking.

Obliv

@0celo7 I think as of right now he just ignored defining a field. He defined a vector space in terms of sets and relating to $R$ and $C$ without calling them fields.

Danu

8:17 PM

@0celo7 After all, it's a book on semi-Riemannian geometry.

0celo7

What other fields besides GR use pseudo-Riemannian geometry

Slereah

Basically the same I think

FenderLesPaul

anything that uses GR

:D

0celo7

@Danu Sigh...he treats stuff like Hopf-Rinow which is explicitly Riemannian.

Slereah

I don't think a lot of fields use mixed metrics

0celo7

8:18 PM

@Slereah holy shit

pseudo can mean Riemannian

stop being a goblin

Slereah

Well if you say "pseudo" odds are pretty good you don't mean "Riemannian"

FenderLesPaul

"goblin"

Slereah

shoo shoo GR goblin

FenderLesPaul

I thought Freeman Dyson was the GR goblin

he sure looks like one

0celo7

@Slereah Then replace it with plain Riemannian.

@FenderLesPaul what now

Slereah

8:19 PM

Well then a few things use riemannian geometry, yes

Jeez

I told you

Astronomy

Geodesy

FenderLesPaul

Condensed matter physics

ACuriousMind

"the full document is here: file:///C:/Users/Tor/Downloads/Snow_JChemEd1972.pdf"

Slereah

Yeah that too

ACuriousMind

::facepalm::

Slereah

Often objects that are like

Flat

0celo7

8:20 PM

@Obliv Ok.

Slereah

Are treated like 2D manifolds

For QM and such

FenderLesPaul

String theory

0celo7

@FenderLesPaul hmmmmm

David Z

@FenderLesPaul hm, good question. I think the field is pretty scattered, there aren't many places that really would qualify as hubs. If anything I'd have to say the national labs are likely candidates: Brookhaven, LBL (Berkeley), Los Alamos, Jefferson Lab. Some of the nearby universities get a bit of a boost from collaboration with the labs.

0celo7

Not Riemannian

That's complex geometry they use there

David Z

8:21 PM

random thing: karpathy.github.io/2015/05/21/rnn-effectiveness You get to see a neural network write nearly-compilable LaTeX

FenderLesPaul

same difference

SUGRA

ACuriousMind

@0celo7 Kähler manifolds are Riemannian.

0celo7

@ACuriousMind No shit.

FenderLesPaul

@DavidZ that sounds reasonable

I guess Stanford too?

because of SLAC

0celo7

I know what a Kahler manifold is

FenderLesPaul

8:22 PM

lies

0celo7

But reading a book on Riemannian geometry won't help you with Kahler manifolds

ACuriousMind

How would you know?

FenderLesPaul

@ACuriousMind mic drop

David Z

SLAC is like Fermilab, they used to be a big player but these days not so much since they've been surpassed by RHIC and the LHC. I don't think a lot of HEP phenomenology gets done at Stanford these days.

A lot of the prestigious universities like Stanford and the upper Ivy League have very theory-heavy physics departments. They prefer to focus on things like string theory rather than phenomenology.

0celo7

@ACuriousMind Uh, I read the parts in BBS and BLT on Kahler manifolds and it's not Riemannian geometry?

FenderLesPaul

8:25 PM

@DavidZ that does seem to be the trend

David Z

Oh, come to think of it: Columbia might be about as close to a hub in my field as we get in the US.

FenderLesPaul

pretty campus too

David Z

Columbia?

FenderLesPaul

yep

although I'm biased

David Z

I spent too many years calling it "Slumbia" to believe that :-P lol

FenderLesPaul

8:26 PM

since I grew up in NYC

ACuriousMind

@0celo7 That's a rather small sample size for deciding that what people do with Kähler manifolds is not Riemannian geometry, no?

FenderLesPaul

UChicago honestly has too many string theorists

string theory is so boring :P

0celo7

@ACuriousMind I was replying to a message on string theory!

David Z

@FenderLesPaul I wouldn't argue with you on that

0celo7

And I said knowing Riemannian geometry will not help you with the Kahler geometry they do there!

Jeez, what did I do to piss you off?

ACuriousMind

8:27 PM

@0celo7 Same comment applies. Rather small sample size to apply it to all of string theory

0celo7

Ok, fuck it.

You win.

ACuriousMind

@0celo7 Huh? I'm not "pissed off"

0celo7

@ACuriousMind Yeah you are.

I ask a math question and you ignore it.

Then I make a remark about something irrelevant and you attack me.

Later.

FenderLesPaul

You sound hurt

@DavidZ do you know any of the pheno people at Cornell?

David Z

@0celo7 you're overreacting

@FenderLesPaul no, I don't think so

FenderLesPaul

8:32 PM

Aw

0celo7

@DavidZ Hahahahahahaha. Coming from you :'D

ACuriousMind

@0celo7 I didn't "attack" you, I happened to think that Fender's remark that string theory uses Riemannian geometry was correct and wanted to see why you brushed that off so easily.

FenderLesPaul

Yeah!

0celo7

10 mins ago, by ACuriousMind

How would you know?

FenderLesPaul

@ACuriousMind's got my back

0celo7

8:33 PM

Read: "You're too stupid to know anything about that."

FenderLesPaul

:D

0celo7

10 mins ago, by FenderLesPaul

@ACuriousMind mic drop

Clear agreement.

FenderLesPaul

Hey don't drag me into this

I'm an external observer

ACuriousMind

@0celo7 No, read: "How do you know that?" If I meant it insultingly it would have been "How would you know?"

0celo7

I read those the same way.

FenderLesPaul

8:35 PM

can we not have this conversation?

It's silly

this sounds like one of those fights couples have when they're bored

0celo7

I stand by my statement, perhaps with a modification though. The Riemannian geometry in O'Neil does not help with Kahler geometry.

ACuriousMind

@FenderLesPaul As opposed to the totally non-silly stuff that usually happens here? ;P

FenderLesPaul

@ACuriousMind heyyy

that stuff isn't silly!

it's quality

does anyone here like George Ezra?

Slereah

I don't like anyone

FenderLesPaul

=O

who hurt you @Slereah

ACuriousMind

8:37 PM

@FenderLesPaul Well, there is such a thing as high quality silliness

Slereah

It was LIFE

ACuriousMind

And who's George Ezra?

@Slereah Please show me exactly on this doll where life hurt you

Slereah

@ACuriousMind Right on my heart :,(

David Z

I approve of high-quality silliness

FenderLesPaul

@ACuriousMind he's a British singer-songwriter

he has a really sweet voice

let me link some of his stuff

Budapest George Ezra Lyrics

►

George Ezra - Listen to the Man

►

0celo7

8:39 PM

@FenderLesPaul No, he's terrible.

Can't even speak properly.

I thought he had some condition when I first listened to Budapest.

FenderLesPaul

K

ACuriousMind

@FenderLesPaul Not my kind of music

FenderLesPaul

:(

Slereah

So many feels

FenderLesPaul

now I'm too scared to show you my cover of it

0celo7

8:44 PM

@ACuriousMind Ok, maybe you weren't attacking me. Maybe you're like Danu and don't realize it. But that doesn't explain FLP's comment.

@Slereah Well, this proof makes no sense.

Danu

0

A: Book covering differential geometry and topology required for physics and applications

The first thing that must be said is that the question is not really specific enough: Applications to what exactly are you looking for? To me, a book on algebraic geometry and mirror symmetry, and how it relates to mirror symmetry as physicists know it, is very relevant and interesting. However, ...

@0celo7 ^

I think I should get upboats for effort alone (also note that it's CW)

0celo7

> Fecko - Differential Geometry and Lie Groups for Physicists

ACuriousMind

"upboats"?

0celo7

@Danu Have you read every book on that list?

Danu

Plus my answer is a lot more extensive than anything else that has showed up or probably will show up.

@0celo7 Nothing.

@ACuriousMind Yush

0celo7

8:55 PM

@Danu Sorry, what?

Danu

@0celo7 I haven't read any of it.

user54412

@0celo7 Almost all my humanities profs had masters degrees at least in math/science...

0celo7

@Danu It's absolutely terrible.

user54412

at least the philosophers did -- never spent much time doing literature or history

Danu

@0celo7 You're entitled to your opinion :)

0celo7

8:56 PM

@Danu I know you would not like it either, dude.

Danu

@ChrisWhite The philosophers of science are all failed physicists :D

@0celo7 I believe you!

0celo7

@Danu Then why would you recommend it?

Danu

@0celo7 I'm not recommending it. I'm just providing a list of options.

Based on everything I'm aware of.

user54412

@Danu when philosophers of science succeed, we call them "scientists"

0celo7

@Danu Why not HE and BEE?

Danu

8:58 PM

@0celo7 Meh

Already had 2 GR books.

0celo7

BEE is not a GR book, it's a Lorentzian geometry book ;)

Danu

I don't even know what that is.

0celo7

...you don't know what Lorentzian geometry is?

Or what BEE is?

Danu

...

0celo7

16 secs ago, by Danu

...

Ah, of course.

The three dots, so very informative.

I know exactly what you meant now.

Danu

9:00 PM

You should

0celo7

Well I don't!

With you I never know!

skill patrol

@ChrisWhite did you take any advanced logic?

x-x

lol I've never seen an active conversation in chat before.

Danu

I think that, within logic, there is a very wide and perhaps not so deep branching going on

0celo7

@Danu Hmm?

@Danu In case you were talking about BEE, then see amazon.com/Lorentzian-Geometry-Edition-Chapman-Mathematics/dp/…

Danu

9:04 PM

@0celo7 Do you know any "hard" logic? Like, concepts that'd take several years to be able to understand

user54412

@skillpatrol depends what you mean by "advanced"

skill patrol

Past second year

0celo7

@Danu I have no clue what you're talking about.

Danu

Oh yeah, I could've included that BEE book. Seems nice.

Feel free to add it to my answer if you like.

@ACuriousMind how is transistor going?

I'm about to complete the second run

0celo7

@Danu Well, it's not really a "physics" book. A lot of what they do is explicitly for mathematical purposes.

One of the goals is "how much Riemannian geometry can we actually import into Lorentzian geometry"

@Danu So why no HE?

@Danu Oh shit, Naber is a two volume thing??

+1 for alerting me to that!

skill patrol

9:09 PM

@Danu now that is "hard."

ACuriousMind

@Danu Didn't play much since we last talked about it

@Danu I think the "hard" logic is usually just called set theory.

skill patrol

Perhaps advanced set theory.

0celo7

@Danu I still can't get the difference between a contrapositive and a contradiction proof.

Slereah

Set theory isn't logic tho

0celo7

Is that hard enough?

Slereah

9:12 PM

Hard logic would be like

Proof of completeness and such, I guess?

Proving that a logical system is complete and coherent isn't easy

user54412

@skillpatrol Still not sure what that means. I took this math/CS class and... I'm not sure any other. My philosophy exposure to logic was tangential.

ACuriousMind

@Slereah I was thinking of stuff like forcing

Slereah

yeah stuff like that

skill patrol

I meant what ACM was thinking of in his link @ChrisWhite

0celo7

> I personally think it's terrible because it doesn't explain anything properly, but I guess it's good to learn buzzwords.

@Danu ;)

@Danu Currently reading a book written by an experimentalist. I'm going to have nightmares from this...

Hand...wave...too...strong

@Danu Have you read Naber's second book?

Danu

9:45 PM

@ACuriousMind That's not really logic.

Mathematics (and hence set theory) is just an application of second order logic AFAIK

ACuriousMind

33 mins ago, by ACuriousMind

@Slereah I was thinking of stuff like forcing

Danu

@0celo7 Nope

@ACuriousMind I guess

Wouldn't call that set theory, though.

0celo7

@Danu What have you read?

Danu

Nothing, like I said.

ACuriousMind

@Danu The article starts with "In the mathematical discipline of set theory" ;P

0celo7

9:47 PM

@Danu Oh, you mean you haven't read any of the books on the list?

Danu

Yup

0celo7

@Danu ...why did you make a list of books when you have zero experience with any of them?

ACuriousMind

For ~~the bounty~~ glory!

Danu

Not for the bounty, honestly

Just because I know I have some ideas about these books, and nobody else is going to write such an exhaustive answer.

0celo7

@Danu :/

You literally cannot vouch for any of the books

Can't retract my +1, damn.

Danu

9:53 PM

Oh, I can vouch for some of them

I can vouch for Isham being ok-ish if you're not interested in rigor

I can vouch for Deligne et al.

0celo7

When I looked at those two books they seemed insane

Danu

The book by Nash seems so interesting

Floer homology the dream

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