Mathematics - 2019-07-14 (page 2 of 3)

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5:00 PM

@ÉricoMeloSilva So think of a bundle $E \to X$, and $\mathcal{R} \subset J^r E$ be a differential relation in the $r$-jet bundle. Look at the fibers $F_x$ for each point $x \in X$ of $J^r E \to X$ (which are some Euclidean spaces), slice $\mathcal{R}$ by those fibers. It's ample if convex hull of $F_x \cap \mathcal{R}$ is all of $F_x$

Érico Melo Silva

aight cool

you have to do a little video for the NYU application

I think they ask you to explain your favoriate theorem

Balarka's video would be bonkers

@RyanUnger God forbid not Gromov student

I think some people from here actually did a few videos on advance shit a few years ago. Sanath Devalapurkar gave one on uh

(Gromov is at NYU)

higher categories

lol

It was actually pretty good

5:03 PM

lol what for his NYU video?

Érico Melo Silva

low key i think balarka would hate the stanford environs where eliashberg is at

there's some on YT and they're all super cringe

Nah it was some national silence talent stuff

idr

someone put the coffee cup and donut thing in the video

@ÉricoMeloSilva whats wrong with it

@RyanUnger Yeah I have heard of Murphy.

Érico Melo Silva

5:05 PM

stanford is dead

Erico Melo Nietschze

Érico Melo Silva

palo alto sucks

dude you care way too much about location

I do too

some places just suck

Érico Melo Silva

the silicon valley culture is awful

the food is good tho

5:06 PM

where are you living now Balarka

right now or in general

Érico Melo Silva

if i cared about location i would’ve stayed at chicago

i am in Bombay rn

at TIFR

@Eric oh btw I think the "short maps can be C^0 approximated by isometries" is one of Nash's key lemmas in his proof of isometric embedding.

(Operations research question and answer about square root bound)[https://or.stackexchange.com/q/678/671]

If only the variable bounds would agree with the numerators of the Dirichlet inverse of the Euler totient function expansion of the partial sums of the Möbius inverse of the Harmonic numbers, it would be the Riemann hypothesis. But they don't, unless there is some reason why only negative numbers in the variable bounds need to be considered in the linear programming problem.

Érico Melo Silva

@BalarkaSen americans are the nietzschian last man

5:09 PM

hahah

Érico Melo Silva

i unironically believe this to be true

also my trash raccoon big brained daddy zizek said it

@ÉricoMeloSilva what does this sentence mean

slavoj <3

Érico Melo Silva

that zizek has also said that americans are the last man of history

no, the trash raccoon big brained daddy bit

Érico Melo Silva

5:14 PM

zizek is famously called a trash raccoon as a meme (have u seen him) also he’s smart and i called him daddy bc its a bit idk don’t read into it lol

he has a “im eating every day from the trash can of ideology” line

and so on and so on

Érico Melo Silva

sniff

ok im ditching high school on the cv

some people keep it on there, dunno why

I got my GED at Trump university

no one needs to know that

lol there's a Trump university

it's defunct now

it was a real estate training school, I believe

Érico Melo Silva

5:19 PM

@BalarkaSen it was a scheme but like so is a lot of educational stuff in america

Tobias Kildetoft

You mean they learn about schemes in Trump University?

well there's been an outgrowth of scammy universities funded by industrialists in india as well

@Tobias separated schemes... separated by THE WALL

gottem

Érico Melo Silva

@BalarkaSen yeah u definitely have this worse than us

it’s extremely bad in brazil too

brazil also has legit cults running things

evangelism is powerful

the trashcan of globalization toppling over the poorer countries as usual

5:22 PM

nice Balarka

do you know of the prophet Alex Jones

he predicted this

LOL

Érico Melo Silva

@BalarkaSen good take

People make the mistake that globalization in India is a recent trend of rot, but it's sort of been there forever now that I think about it. I am in TIFR right now, which stands for "Tata Institute of Fundamental Research"... Tata was one of the major economic arms of Congress government

It's just that it's only recently started taking the bad switch

@BalarkaSen is TIFR a school or is it like IMPA, or even like IAS

I dunno what the differences are. It has a PhD program but mostly faculty doesn't have to teach and people visit frequently to collaborate/do research. So in that sense it's like IAS, you might say

It's held many many conferences during the revolution era of algebraic geometry

5:35 PM

they have undergrads?

Nah

Érico Melo Silva

i mean globalization really is the economic continuation by different means of the last four hundred years of imperial/colonial governance in that the basic goal is to build on the same logic of either extraction or proliferation of markets, these things aren’t new exactly like u said @Balarka, they’ve assumed new forms bc the politics are different

did you just show up?

it sounds more like IMPA than IAS

@ÉricoMeloSilva Yeah that's true

@RyanUnger Well, I was invited

Tobias Kildetoft

@BalarkaSen I thought you were an undergrad

5:37 PM

fancy

so you ARE famous

yeah I am... meh no it's nothing fancy. I have been invited here twice before, I know a couple faculty members

Tobias Kildetoft

I decided not to go there some years ago since it would have had to be a full month, which was a bit much that near the end of my PhD, seeing as I mainly needed to focus on writing anyway

I could also have gone to CMI, but declined for the same reason

Balarka what's the big thing in India math-wise these days

You don't see too much GA or GR from there

@RyanUnger lol HEAPS of algebraic geometry i think

Mahan is the only one here who does actual topology

Tobias Kildetoft

Quite a bit of mathematical physics as far as I recall

5:41 PM

@TobiasKildetoft Oh yeah, you were at Uppsala?

Tobias Kildetoft

@BalarkaSen I was, but this was back when I did my PhD in Aarhus, and they had a big exchange thing going on with those two institutions

Ah yeah you told me

For some reason I thought it was Uppsala-CMI

the CMI's website is amazing

ironically or do you mean it looks good

ironically

very minimalistic

5:45 PM

huh i think it looks good

it's basically an interactive text file

LOL

that did make me crack up

maybe Balarka should go to like...University of Miami. It's chaos down there

Tobias Kildetoft

Who are the most famous Indian mathematicians (apart from Ramanujan)? I mainly know Verma and Harish-Chandra.

for some reason there's a good GR group there

@TobiasKildetoft Vafa

5:48 PM

@TobiasKildetoft There's Patodi

Atiyah-Singer-Patodi index theorem

Wickramasekra

Tobias Kildetoft

I was not aware that there was a third name on that theorem (or is it another theorem?)

Does Majul Bhargava count?

Manjul*

hi

@Tobias It's Atiyah-Singer with boundary term, I think

@Ryan would know

Tobias Kildetoft

5:49 PM

I see

it is

Like Gauss-Bonnet with boundary term

it's much harder because elliptic boundary conditions are super hard

Oh yeah Agarwal is pretty famous

AKS primality test

yeah

5:50 PM

Mahan Mitra, the mathematician monk

Lol

Oh, Varadhan is super famous

All of those 4 guys are

Varadarajan-Varadhan-Rao-Parthasarathy

all ISI alumni. They used to be called the fabulous four of ISI

lol

There really aren't a lot of Indians in GA/GR, huh

I think there's some Indian physicists working on GR

leaving

5:53 PM

I can name some mathematicians who aren't that famous but still well-known in circles

It seems like mathematicians from developing countries follow after the early big shots from those countries

Raghunathan, who basically gave the idea which opened up homogeneous dynamics

(I talked to him a few days ago)

Like do Carmo amassed a huge following for differential geoemtry in Brazil

Yau for geometric analysis in China

ya that's likely true. we got skewed sideways into algebraic geometry because of the French school influence

Mentioning Yau but not Chern will summon Ted

5:55 PM

there's a picture in the TIFR archives of Grothendieck walking in the lawn in front of the main building lol

There's a huge tradition of von Neumann algebras in Romania for this reason

There's lots of pseudodifferential stuff in Scandinavia due to Hormander

Oh yeah you might have heard of Narasimhan

advisor of Patodi

He has a book doesn't he

yeah

I recognize him from that

5:58 PM

I saw him briefly on a talk once but couldn't recognize until someone pointed out long after

Oh everyone knows Italians do analysis because of De Giorgi

Patodi's co-advisor was Ramanan who also has a huge tome of a book, "Global Calculus"

basically sheaf theory

Yeah I've seen that book

It's on my list of books to read when I retire lol

loool

(Italy is not a developing country)

5:59 PM

Ramanan's grandson is my friend and batchmate

@RyanUnger Italy did algebraic geometry until they got bamboozled by the French

they had to switch fields

most of it was wrong anyway

Italians are very good at analysis

maybe the switch was for the better :P

Alessandro Codenotti

Debatable

Who's De Giorgi by the way?

LOL @Alessandro

Érico Melo Silva

@AlessandroCodenotti a hot analysis daddy

Alessandro Codenotti

6:15 PM

The only famous Italian analysts I know are those with a big theorem named after them and contained in the undergrad syllabus

I can't tell if you're kidding

Alessandro Codenotti

I'm serious lol

Like Fubini, Tonelli, Dini, Ascoli and Arzelà I guess

Levi...

Levi was a good guy

Levi continuity is my favorite theorem from probability-2

Ennio de Giorgi

Ennio De Giorgi (8 February 1928 – 25 October 1996) was an Italian mathematician, member of the House of Giorgi, who worked on partial differential equations and the foundations of mathematics. == Mathematical work == He solved Bernstein's problem about minimal surfaces. He solved the 19th Hilbert problem on the regularity of solutions of elliptic partial differential equations. == Quotes == "If you can't prove your theorem, keep shifting parts of the conclusion to the assumptions, until you can" == Selected publications == === Articles === ==== Scientific papers ==== De Giorgi, ...

very short wiki page

sad

Alessandro Codenotti

6:19 PM

Levi? I know Levi-Civita

"If you can't prove your theorem, keep shifting parts of the conclusion to the assumptions, until you can"

7

Beppo Levi

Oh my Levi isn't Levi it's Levy

French guy

sad

Alessandro Codenotti

Oh, of course, I actually know him

Levi's monotone convergence theorem

Suffice it to say it's not possible to talk about PDE in 2019 for very long without running into De Giorgi

he was a hugely influential figure

Alessandro Codenotti

6:21 PM

Oh, Caccioppoli as well

Ok maybe I know a few

de Giorgi developed the theory of Caccioppoli sets

all of calculus of variations goes back to him

Alessandro Codenotti

@RyanUnger my ignorance of PDEs is really showing now

de giorgi showed that H^1 solutions of elliptic equations with bounded measurable coefficients are Holder

part of the De Giorgi-Nash-Moser theorem

Alessandro Codenotti

I don't know what H^1 means

doesn't really matter

C^1 in a measure theoretic sense

6:24 PM

H^1 = L^{1, 1}, Sobolev

No, Balarka

Oh

L^{1, 2} I meant

$W^{1,2}$

this L is something topologists use

Alessandro Codenotti

Oh ok I know what that is

Mike explained it to me a while ago

@AlessandroCodenotti what is the "de" doing instead of "di"?

Alessandro Codenotti

6:29 PM

The same

@AlessandroCodenotti I think every Italian analyst alive can trace their roots back to De Giorgi

foreigners learned Italian to read his early papers

the Italian and French schools merged and formed Figalli

Manolis Lyviakis

Consider a loop on a circle why the same loop but running it backwards are not homotopic?

If $\gamma$ has homotopic to $\gamma^{-1}$, then $\gamma^2$ would be homotopic to identity loop. This is not true but requires a proof.

Easiest proof is to lift to the universal cover $\Bbb R$ and compare endpoints. See any textbook like Munkres or Hatcher.

Manolis Lyviakis

munkres does not provide proofs on why curves are not homotopic

provides intuition though

He definitely has a proof of why $\pi_1(S^1) \cong \Bbb Z$ :)

Manolis Lyviakis

6:40 PM

but i didnt come across a proof of the style " there does not exist a homotopy function between .."

yes ofc you can prove that

Homotopic loops on the base of a covering space lifts to homotopic paths on the total space of the covering space. In particular, the lifted paths must have the same endpoints.

Manolis Lyviakis

but doesnt require to prove what im asking

oh ok

$\gamma$ and $\gamma^{-1}$ lifted to $\Bbb R$ have different endpoints; first is the unit-time curve from $0$ to $1$, and second is the unit-time curve from $0$ to $-1$.

Manolis Lyviakis

thats correct

So in particular they are never homotopic.

Manolis Lyviakis

6:41 PM

that way u can see why a 2 round loop on the circle is not homotopic to a one round loop

cause of the helix covering space

Yes.

Exactly

Manolis Lyviakis

and the same for the inverse

thanks

i remember the lemma on munkres

about the endpoints

so thats pretty usefull to prove things are not hmotopic

@BalarkaSen hi

Yup. It takes a little time digest what's actually happening in that lemma, which is exactly what we discussed.

Hi @Leaky

Manolis Lyviakis

ok but what about something not so obv

how to prove that the continuity breaks between a loop that surrounds a hole and another that doesnt

obv they aint homotopic

6:45 PM

@BalarkaSen it's very tiring

when every protest evolves into a conflict

literally every protest ends in a conflict between the protestors and the police

there have been 5 protests this month

Manolis Lyviakis

but a formal proof requires that you prove there doesnt exist a continuous homotopy . How do you actually write down that the continuity breaks.

1/7, 6/7, 7/7, 13/7, 14/7

Manolis Lyviakis

leaky where do you live?

Hong Kong

@LeakyNun What's the current state of affairs

6:47 PM

the government isn't doing anything

the citizens keep protesting

the police keep arresting and beating up and scaring people

we're in an impasse

Ugh, that sucks.

looping and looping

Manolis Lyviakis

here in greece we changed to a right winged goverment and the police is already more violent

and both sides are getting angrier at each other

Manolis Lyviakis

breaking protests

6:48 PM

both sides = protestors and police

2 mins ago, by Leaky Nun

and both sides are getting angrier at each other

and this is the scariest thing

who knows if it will evolve into a war

I guess it's already a war

and I guess both sides are getting angrier at the governemnt

the protesters keep insisting that the police is abusing their power

the police keep insisting that the protesters are rioters who should be heavily punished by force

@BalarkaSen is etale morphism like covering map?

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