math.dartmouth.edu/~doyle/docs/gi/gi.pdf

darn i missed the jordan therapy hour

colorful

so excited to be back

Keep the colorful language to yourself, @Jordan

Your next suspension will be longer

no on answers questions on saturday nights

?

@JasperLoy

@MarianoSuárezAlvarez Here is the final version: math.stackexchange.com/questions/137876/…

Looks good, any mistakes?

'morning all

@AlexanderAmenta Any mistakes here?

I saw this problem and got hooked on it

let's have a look

i think it would take me too long to properly take in, since i haven't thought of this stuff in so long

Ah ook

i find it hard to get excited about these kind of results

hahahahahahahahahahahahha

though i am glad that they're around

@AlexanderAmenta I am not enjoying the analysis assignment

the results?

yeah, and the proofs

i haven't looked at the assignment yet, i should probably answer your question about it

but I think

them putting that $e^{-Lt}$ was just to worry some people

by the way the new algebra 2 assignment is out

It looks crazy

you're actually onto galois theory now right>?

yes

but the assignment has lots of stuff about galois groups

stuff not covered in class yet

And as usual jim is asking us to name all those crazy examples

but one of the problems is one biquadratic extensions

I tackled a problem on that in Dummit and Foote before the exam so it should be ok

what's a biquadratic extension again?

extension of $\Bbb{Q}$ of degree 4 I believe

oh right

yeah i remember doing those things

good fun

haaaaaaaa

It's actually a Galois extension with Galois group isomorphic to Z_2^2

:)

looking at the analysis assignment now - what's your question again?

ah well

@AlexYoucis Hey

@AlexYoucis so one that's made up of two quadratic extensions. sounds right to me

you remember the result I was discussing yesterday with mariano?

Hey man. You guys go to school together?

I have finished typing it: math.stackexchange.com/questions/137876/…

@AlexanderAmenta Yeah man. You do K-theory??

i've been dabbling

@AlexYoucis He's my tutor :D

Haha, very cool you guys.

@AlexYoucis Do you think that what I wrote sounds ok?

You know Rosenberg?

@AlexanderAmenta

not personally, though i went to a workshop recently that he gave

Cool, cool! He's a sweet dude

ah i see you're at maryland, so you know him?

We're not buds, but yeah, I know him. He's a very legit dude. We

're also lucky enough to have Larry Washington, as authors go.

(if you have heard of him..)

nice (i've heard of him but don't know much)

Where do you guys go?

i don't really 'do' K-theory, but i've used a bit over the last year

More algebraic or topological?

ANU

more topological

Forgive my ignorance, ANU?

australian national uni

forgive my forgetting people outside australia don't know ANU!

Wow, that's pretty cool man!

@AlexYoucis That's what we call it here.

Haha, it's cool, I don't think you would have known what UMD is

true

@BenjaminLim I looked at your proof--as far as I could tell, everything looked A-ok.

hahaha

@BenjaminLim - you wanted to know if T and L could be assumed fixed?

@AlexanderAmenta I assume you're a grad student, or risingsenior?

@AlexanderAmenta Yeah I suppose it should be

we have a 'honours year' here which i guess is senior? 4th year?

@AlexYoucis Did you see brett's comment?

yeah it makes no sense to not fix T and L

@AlexanderAmenta thanks. You know that $e^{-Lt}$ thingy

it just there to mess people up no?

@BenjaminLim Which one?

@AlexanderAmenta Right, right. That's cool dude.

The one where he's like, it looks ok to me, but you're using a lot of machinery bla bla bla...

Uh-huh. What about it?

I'm like

hahahahahahaha

@BenjaminLim it's not just to mess people up, it's actually important

Like that tensor product isomorphism

@BenjaminLim Haha, to be fair, he did put module theory as a tag--that kind of opens you up to module theoretic questions.

answers*

@AlexanderAmenta wait

In my proof of the completeness of that question

It was almost exactly the same as proving that $C[0,1]$ with the usual sup metric is complete

i don't think the exponential affects completeness

yeah

but why is it there?

for the remaining parts

@AlexanderAmenta So, any idea what you are going to do next year?

@AlexYoucis starting a PhD in august, at ANU and Paris 11 (half at each)

@AlexanderAmenta Which remaining parts? ah ok for the DE question??

@AlexanderAmenta Wow, very cool stuff. Any idea what you want to do work in?

@BenjaminLim the exponential in the metric allows your functions to 'blow up' sub-exponentially at T, in some sense

huhuhuh??

@BenjaminLim have a think about the unit ball around the zero function in this metric

ok

@AlexYoucis i'll be working in harmonic analysis, essentially

@AlexanderAmenta I'm just worried that my proof was wrong

because it was almost carbon copy for the one on the completeness of $C[0,1]$ in the usual metric

@AlexYoucis things to do with differential operators and geometry

@AlexanderAmenta Applied or pure?

@AlexYoucis pure, though i suppose this kind of harmonic analysis can be application-motivated

@AlexanderAmenta I have done very little harmonic analysis, mostly related to rep theory, but from what I've seen, it's very neat stuff.

@BenjaminLim i don't think the completeness proof would be any different, since you're dealing with functions on [0,T] rather than [0,T)...

@AlexYoucis i haven't done much either to be honest, but what i've seen is the real-variable stuff in applications to functional analysis

@AlexanderAmenta Very nice man. I have to be honest though, I was never a huge analysis guy.

@AlexYoucis You should be around here more often

@AlexYoucis neither was I!!

There are not many people here that wanna talk about commutative algebra

@BenjaminLim That seems strange. There are a lot of (alg) geometers on here.

@AlexanderAmenta what changed?

not on chat

@AlexYoucis i started seeing 'geometry' as one big field rather than lots of smaller fields, and realised that pretty much everything that applies to it is interesting

@BenjaminLim I, can see that. What are you taking next term?

@AlexYoucis Looks like algebraic topology, algebraic number theory

@AlexYoucis in particular i started seeing analysis as something which impacted more than just analysis

and perhaps some more commutative algebra/smooth manifolds

@AlexanderAmenta You're probably right. I noticed that in CA there is like 3 million definitions

@AlexanderAmenta I don't think I am ever going to be an analyst, but I know exactly what you mean. I am taking a course on Riemann surfaces next term that is going to mix algebra and analysis and it's amazing to me how cool analysis can be when applied to geometry--e.g. Dolbeault cohomology.

@AlexYoucis that's exactly the sort of thing i'm talking about

which can put a lot of people off

(stuff like Dolbeaut cohomology, Hodge theory, Index theory...)

@BenjaminLim Those are all good courses. Have you had regular topology (e.g. Hatcher first chapter, covering spaces and the fundamental group)?

@AlexYoucis My topology is self taught.

@AlexanderAmenta Yes, yes! Complex (analytic) geometry makes me very happy!

hatcher is not regular topology that is already AT

@AlexYoucis I need to use it for commutative algebra

@AlexYoucis @BenjaminLim at ANU our algtop course starts from fundamental group/covering spaces

@BenjaminLim Yes, true. But before you start getting into more advanced algebraic topology it helps to know covering spaces and the basics of the fundamental group first.

@AlexanderAmenta Oh? Is it an undergraduate algebraic topology?

@AlexYoucis Well our algebraic topology course starts exactly from the basics

It is an undergrad course

@BenjaminLim Any reason you are so interested in comm. alg?

@AlexYoucis yeah, we don't have a dedicated 'first topology course', but we do a few weeks in our 'analysis 2' which is enough preparation for our algtop

Just got hooked on it

@AlexanderAmenta Oh, well that makes more sense then. I was assuming it was the graduate course.

@BenjaminLim Eisenbud?

@AlexYoucis No i'm using atiyah macdonald now

@AlexYoucis we tend not to have dedicated graduate courses in australia, it's a bit strange. our algtop is considered to be a 3rd/4th year course

which is pretty silly

@BenjaminLim That's a good (classic) book. I'm doing the exercises when I'm bored now. I would definitely take a look at Eisenbud, Matsumoro, and Reid though if you are really interested.

@AlexYoucis I'm looking at miles reid too

@AlexanderAmenta Interesting... That is slightly strange. Here most of the "advanced" undergrduates just take all graduate courses.

it is less dry than AM

@BenjaminLim Good man! It's definitely not "perfect" (e.g. no tensor products, for example!) but still a good read (almost as good as his alg. geo book)

yeah

But man

@BenjaminLim Also, I highly reccomend these notes by Pete L. Clark math.uga.edu/~pete/integral.pdf

pete is a great expositor

@AlexYoucis our 4th year courses are sometimes like a first graduate course - but typically the advanced students will take reading courses on top of the usual courses, and these can definitely be at 'graduate level'

@AlexYoucis I don't know if doing AM now is considered "graduate leve"

@AlexYoucis AM is super dense man

@AlexanderAmenta Hmm, I see. I have done a hell of a lot of reading courses (I'm doing one right now!) but they are discouraged over taking graduate courses.

@AlexYoucis Yeah sometimes I look at those

@BenjaminLim it wouldn't be

@BenjaminLim I wouldn't consider A&M graduate level--advanced undegraduate.

yeah

@AlexYoucis i'm finishing up a complex geometry reading course at the moment

@AlexanderAmenta Oh, you lucky dog! Using who?

@AlexYoucis then possibly no more coursework ever! finally

@AlexYoucis The analysis course that I'm doing now is really putting me off analysis

@AlexYoucis Wells and some of Kodaira and Kuranishi's deformation theory material

It's like a massive caesar + nicoise + whatever salad mix

@BenjaminLim I wouldn't be put off by analysis. Analysis is actually very nice. Especially several complex variables and functional. I would try it a little more. Life doesn't end after baby Rudin.

@AlexanderAmenta Is Wells Differential Analysis on Complex Manifolds?

@AlexYoucis as his analysis tutor i've told him to stop focusing on the class and lended him Rudins's functional analysis

@AlexYoucis yep, not a bad book

@AlexanderAmenta Yeah? I was thinking about getting it. Have you ever used Forster?

@AlexYoucis never heard of it, i'll look it up

@AlexYoucis I'm not doing a Jordan here but I'm really put off by all this random DE's and fractal stuff thrown in

@BenjaminLim the DEs are put in as an 'application', the fractal is because you're at ANU

@AlexanderAmenta The ultimate goal is this amazon.com/Complex-Geometry-An-Introduction-Universitext/dp/…

@BenjaminLim I hate fractal stuff (no offense if there any fractalists on here). Seriously, take a look at something like the Gelfand-Naimark theorem.

@AlexYoucis ok I shall

I'm the kind of guy if I want to do something I want to do it "properly"

@AlexYoucis looks quite good, i appreciate the supersymmetry and algebraic approach to deformations

I don't wanna get started on the massive crisis on math education at our uni

btw

@BenjaminLim Me too--trust me. It makes learning hard.

@BenjaminLim it's an australia-wide crisis really

@AlexanderAmenta Which book? Huybrechts or Forster?

huybrechts

@AlexanderAmenta Yeah we talked about this.

forster looks pretty nice too

@AlexanderAmenta Yes, it definitely looks very neat. Next term I'll be doing a very analysis/differential geoemtry/PDE focused course though--it'll be refreshing. I've been doing nothing but group cohomology and "avanced" Galois theory all year.

@AlexanderAmenta *on Riemann surfaces.

@AlexYoucis take a look at hodge theory if you get the chance, it's a very nice application of PDE to geometry

@BenjaminLim how was Reich?

@AlexanderAmenta Here's the book we'll be using. I'm curious to hear your opinion on it mathnt.mat.jhu.edu/zelditch/Teaching/F09RS/DrorRS.pdf

@AlexanderAmenta Going there tonight

@AlexanderAmenta I can't come to your tute tomorrow

my bus is 12 from sydney

@BenjaminLim ah i thought it was yesterday

by the time i'm back it's in the afternoon

I was not getting much out of the tutes anyway

I'd rather talk to you one on one

@BenjaminLim no problem - i can't give the attendance mark though

no worries

I don't really care about that

good

i agree with your removed comment

yeah

wth man

Ok I should go now

And get started on the algebra 2 stuff

enjoy

ok

bye all!!

@AlexYoucis there's some pretty interesting stuff in that text, looks good

@AlexYoucis though i only browsed the contents so i can't say anything for the exposition

The only thing that makes me sort of upset, is that he doesn't use any sheaf language.

too bad. complex geometry is a perfect place to start using it

Yeah, I know. In the course I am doing this term we are doing sheaf cohomology and I was looking forward to getting my hands a little more dirty with it.

you could always try to work some in

Yeah, I will. Every do any alg. number theory?

a little, we have a course on it, but they have to teach a lot of commutative algebra first (since we don't have a CA course)

so it was a bit unsatisfying

Hmm, that's unfortunate.

it put me off alg number theory (but that was my own fault, i didn't study very hard that semester)

I guess that's an advantage to having a lot of grad courses.

I really like it--especially applying group cohomology.

What's the thing you're weak in?

we definitely hadn't learned group cohomology! too bad

Do you guys not have a hom alg course?

i hadn't really built up the 'intuition' for what the algebra was doing with respect to the number theory

and i was getting caught up in CA technicalities

we don't have hom alg, we touch on it in algtop

Ah, I can definitely see how that can make it sucky. Which book did you guys use?

also our number theory course is pretty weak, so i wasn't used to proving things by splitting into cases depending on what the prime was modulo 4 or 8...

Learning hom alg and category theory are the two things that make so much more math make sense.

mostly milne's notes

i agree there - my category theory is pretty good

Are they bad?

(learned it myself though)

Same! Besides what was taught in hom alg.

actually they're pretty good.. my performance in the course was entirely my own fault

Ah, we all have courses like that. You seem pretty advanced man. Are you a typical undergrad at your university?

i've since reconciled with comm alg

i don't think so - there are others who are pretty advanced, but i kind of stayed outside the 'system' for most of my undergrad

i didn't pay much attention to coursework but spent a lot of time studying things on my own

Yeah man, same. I transferred here this year with a friend who's coming here for grad school--I hang out mostly with the grad students.

Same, same.

i did/do the same thing (transferring and hanging out with older students, though not always grad students)

Haha, it's like you're the Australian me, or I'm the American you.

possibly. which year is junior year?

Third.

sounds about right then

Just out of curiosity, anything you didn't learn in undergrad, but regret?

so with the american system, is it true that you have to do lots of non-math courses? or am i exaggerating?

hmm i'll have to think about that

haha.........yes. Matthew Emerton was talking about this--school in Australia.

i don't regret missing anything, i can always pick it up in the future

For example, I am a senior next year and I still have to take an upper level literature course, Econ 300, Python, and something else.

dang

We have TONS of gen. eds. It's terrible.

i did nothing but math courses from 2nd year onwards (exception being one semester of chinese in 4th year, because i felt like it)

I would say we probably have to take more gen. ed.s than major specific courses.

I hate you so much right now...haha

this is why we don't have graduate coursework

I am currently taking history of the medieval world and Econ 201, bleh.

actually i do regret not doing slightly less math courses

Why?

it's easy to study math outside of a class

at least once you know what's there and where to look

Yeah, grass is always greener, right?

well, i'd rather do no general stuff than have to do lots of it

but it would have been better to do just a bit more

eg. learning a language throughout undergrad, just one course per semester

Right, I can see that.

and doing 4 difficult math courses per semester can be a bit of a stretch, particularly if they're mostly disjoint

I agree though, learning math is easy. In fact, do you ever feel like the only impediment is time? If you had infinite time you could learn everything.

i guess so, time and having other people around

it's hard to learn something when nobody else around is doing it

I could also see that. Try doing three difficult math courses and two gen. ed.s though, then we'll talk :P

good point

Sure, I agree with that. Math is a communal thing.

i was pretty lucky since all the reading courses i chose ended up relating to each other

and i had no idea in advance that that would happen

Haha, that is pretty lucky. Like what, for example?

a list of my reading/seminar courses:

clifford algebras and dirac operators, modular forms, pseudodifferential operators and index theory, spectral sequences (for characteristic classes), basic algebraic geometry, complex geometry

so in modular forms i learned about riemann surfaces and continued that thread through algebraic/complex geometry

You lucky bastard! That's pretty cool stuff!

yeah i was pretty lucky

For me it's been: group cohomology, representation theory of finite groups, hom alg, manifold theory, representation theory of lie groups

i'm sure you've got equally good opportunities at maryland though

Yes, but only starting this year--I was at a different school before that.

i'd always wanted to do some group cohomology but never got around to it

true, but it's not too late!

Yeah! Next year I think I'm going to take: riemann surfaces, homotopy theory, complex analytic geometry, and p-adic representation theory

i started doing the reading courses in 3rd year (i'm technically in first semester of 5th year now)

sounds pretty good, and you can definitely get some running threads going through those courses

Ah, I see man. That index theory course sounds badass. Care to tell me something about it?

i'll try

how much do you about the atiyah-singer index theorem (if anything)?

I know it's statement (very roughly) and that it proves Riemann-Roch and Gauss-Bonnet

Are indexes what I think they are? Like in Morse theory?

ok that's a good start

i haven't done morse theory so i don't know

(go on)

the setup of atiyah-singer is that you have a differential operator on a vector bundle over a manifold

for example the d-bar operator on the dolbeaut complex over a complex manifold

Mhmm

and you have the 'analytic index' index(D) = dim ker D - dim coker D (where D is the operator in question)

which in general isn't defined, since dim ker D and dim coker D could be infinite

but if D is elliptic (whatever that is) then it's a Fredholm operator, meaning that dim ker D and dim coker D are both finite (which is good for us)

so i should've said that the setup is an elliptic differential operator on a vector bundle etc

(d-bar being elliptic)

the point of atiyah-singer is that this analytic quantity ind(D) can be written in terms of topological information

Oh, so an equation like analysis=topology--like Gauss-Bonnet!

yep

taking certain differential operators gives you certain expressions

such as Gauss-Bonnet

That is very cool stuff man. How difficult is the set-up to learn that stuff?

so the original atiyah-singer proof (at least the original one that was published) requires 'pseudodifferential operators', which generalise differential operators

the setup is pretty tricky i think

What kinds of math are needed?

it seems easier now that i've done it, but looking back i was finding it pretty hard

hmm

the main 'new' thing would be pseudodifferential operators

Do Australian people say "maths"?

you definitely need vector bundles and some basic k-theory (thom isomorphism, bott periodicity)

we do say maths, but i don't like that, so i say math unless i lapse and say maths

since it deals with manifolds there's a little differential geometry in there

of course you have to be comfortable with what a manifold IS, but you also need things like tubular neighbourhoods of submanifolds

Well dude, basic k-theory isn't something common to know. I know the basics of algebraic K-theory (like in Rosenberg's book) but no topological.

of course, but it's not advanced k-theory

True, true.

topological k-theory shouldn't be any harder to get started with than algebraic k-theory

I guess I'm just more, historically, an algebra guy. And you're a what-- a geometry guy?

i was historically algebra and topology

i try to do a bit of everything these days]

Cool. Well dude, I have to head out. It was extremely nice talking to you, I feel I learned a lot!

likewise, it's good to know i have an american counterpart

Haha, if you ever come to UMD we'll have to have a duel I guess.

excellent, see you on chat again some time

Yeah man, see ya.

I want to search for questions involving the expression $n^n$, but it seems that the search box is disregarding the ^ symbol. It finds all the questions involving $n$, which is not useful. Is there any way to get what I want?

uniquation.com does what I want.

@JonasTeuwen que?

Isn't conformal-maps too localised?

Ah, you're right, it shouldn't be restricted to just domains in $\Bbb C$. I shouldn't have jumped the gun! (At least the WP article is linked...)

There, I fixed it. All better now.

: )

I saw the suggested edit and then decided to leave the decision to someone else.

Is complex-analysis too general?

What? Wait, were you saying the tag was too specific to actually be a tag, or were you saying the wiki excerpt was too localized for specifying complex numbers?

I was thinking about the former but I'm not saying anything, I'm just wondering.

Those who downvote without leaving comments are .........

I don't think that thread you were downvoted in was on the main page at the time of the vote. If you feel like it, perhaps you should keep some documentation of the times you are downvoted and (roughly) when the threads they're in are on the main page. If they don't match up at all it would be, in my opinion, mediocre evidence of a downvote stalker.

@anon You're right. I also keep track of a person who I think is downvoting.

Who might that be?

(And, his vote count has increased...)

This one... @anon

What's the history behind this?

And this one was involved in a voting irregularity, and was suspended for quite some time.

Interesting. Anything personal between you two or just a generic fit for the profile of annoying voter?

@anon He wrote a completely useless answer not answering even one part of OP's question and I left a comment and downvoted the post. Subsequently more followed and he deleted the post.