Math General

[Anonymous No.8728665]

It's that time of the month again:
>what are you researching?
>what are you studying?
>any good problems?
>book recommendations?
>cool theorems?

To get the ball rolling I've been doing some categorical logic, namely reading about the Curry-Howard-Lambek correspondence, focusing on Lambek's side of work. Essentially we have an isomorphism of a certain sort of category (cartesian-closed categories), a limited version of intuitionist logic, and typed lambda calculus. Essentially you get a "proofs as types" relation from the Curry-Howard, but adding Lambek's work you get categories also!

Also been reviewing Milnor's topology from a diff. viewpoint before I head back into differential topology.

[Anonymous No.8728670]

This correspondence fascinates the shit out of me. Luckily I'm specializing in software verification, which has to do with types, logic etc.

[Anonymous No.8728674]

>any good problems?
the collatz conjecture is so fun to think about, yet not an inch of real progress can be made on any question related to it. the dynamical behaviour of maps of such simple maps on the natural numbers just turn out to be so strangely impenetrable

>book recommendations?
Kazimierz Kuratowski - Half Century of Polish Mathematics: Remembrances and Reflections

>cool theorems?
https://en.wikipedia.org/wiki/Zeta_function_universality

[Anonymous No.8728681]

>>8728665
>>what are you researching?

The same as always. I am researching whether or not I am actually a genius and not just "above average" so that I can know if I should stay in mathematics for a career and do great things, or if I should settle down and then get a masters in mathematical finance like the low IQ cuck I am.

Why is this so hard? Why is there no definitive genius test?

I do well in calculus, but then that could just be that calculus is my intelligence limit

I do well in analysis, but then it could just be that analysis is my intelligence limit

Fuck it all. But this semester I am taking number theory. I've heard that this field is brainlet-proof. To be good at number theory you HAVE to be a genius, right?

Right?

This time this will finally tell me if I am worth anything, right?

Does anyone know someone who was good at number theory but then later showed their brainletness?

[Anonymous No.8728683]

>>8728681
sounds like you're an undergrad who hasn't even attempted research yet

have you never applied for a summer research position with a professor?

[Anonymous No.8728694]

>>8728683
I have not done research because I am
RE
TAR
DED

Seriously. What are you supposed to research when you are just a sophomore? All I can research right now is if I am smart enough to do research in the future.

[Anonymous No.8728701]

>>8728694
i attempted a research project doing some time series analysis in the summer after my second year

it went terribly but it was still a worthwhile experience

does your school not have any list of professors with projects that they'll fund undergrads to spend a summer on?

[Anonymous No.8728704]

>>8728694
a) you are going about the decision the wrong way.
b) most schools offer undergraduate research programs, usually over the summer or sometimes during the semester.

I would suggest pursuing an undergraduate degree in mathematics, using your electives to do some finance stuff. If you do not choose to pursue pure mathematics at the end of your degree, you can always just apply for a masters in financial mathematics and get your secondary dream.

[Anonymous No.8728708]

Just went over the projective model structure on chain complexes with my advisor yesterday, he gave me a lot of good insight on the small object argument. finishing off this intro homotopy theory paper then moving onto more simplicial things in the summer.

Who else /homotopy theory/ here?

[Anonymous No.8728710]

>>8728701
>it went terribly but it was still a worthwhile experience

You could have spent that time reading books so maybe it wasn't that worthwhile.

>>8728701
>does your school not have any list of professors with projects that they'll fund undergrads to spend a summer on?

I don't know a list, but I do know that professors do research but they mostly act as advisors for senior students and then master students.

I've never heard of them working with someone who was below senior level and for good reason. Last year I got to talk with a senior student who was going to defend his senior thesis that day and the difference is huge. How am I supposed to even compete? He knows galois theory. I barely know what the definition of a field is.

>>8728704
I am already studying specifically mathematics. I don't care about studying finance stuff in undergrad. I want to use undergrad to find out if my IQ is high enough to be a mathematician. If I fail by the end I have masters degrees in this very university that will serve me as backup.

[Anonymous No.8728711]

>>8728710
well goodluck with that, m8

[Anonymous No.8728714]

>>8728708
Done a little HoTT and also some homotopy theory in algebraic but not too much beyond the usual texts for algebraic topology which focus much more on homology theory.

Got any good homotopy theory books?

[Anonymous No.8728720]

>>8728714
Hatchers book does basic higher homotopy groups and other early results pretty well. It's a bit harder to find good sources for the categorical approach to homotopy theory though, I'm reading "homotopy theories" by Dwyer and spalinksi, and so far it's been really helpful, but it will assume a bit of knowledge about categories and homological algebra (ext, tor, projective modules, etc...)

[Anonymous No.8728721]

>>8728710
>You could have spent that time reading books so maybe it wasn't that worthwhile.
there's a huge difference between reading a book and attempting to genuinely solve a research problem

i did another project the next summer that went considerably better

>I've never heard of them working with someone who was below senior level and for good reason. Last year I got to talk with a senior student who was going to defend his senior thesis that day and the difference is huge. How am I supposed to even compete? He knows galois theory. I barely know what the definition of a field is.
if you're american they have some sort of system for getting undergraduates into research (REUs)

it's hard to compete but you'll never succeed if you don't even try, i felt like a fool emailing every single professor in the department but the one who replied and gave me a chance made it worth it

[Anonymous No.8728756]

>>8728721
Out of curiosity, what was the research like?

[Anonymous No.8728773]

>>8728756
the first project was analyzing trends of the proton density in solar wind (learned some Matlab along the way, did a ton of organizing data)

the second project was studying the arithmetic properties of the zeros of certain functions related to elliptic curves (learned some Sage along the way)

not sure what specifics you're interested in but i was pretty out of my depths for both projects, it's more about getting the experience at that point rather than expecting publications

[Anonymous No.8728782]

>>8728756
Not the guy you asked, but I have a pretty great project where I got to do original research.

It was not trivial research, but it wasn't exactly at the forefront. The professor already established a result which guaranteed another one, and I and another student formalized this secondary result. It got published in an undergraduate journal and was my first research experience.

Another research project I did was less original, but it was proving a well-known theorem with new machinery. This one was also enjoyable for the paper writing aspect. Did not publish this one.

[Anonymous No.8728897]

>>8728681
>>8728694
Protip: you don't have to be a genius to be a mathematician.

[TobiasNoel !aMAj1CGlFM No.8728916]

>>8728897
But, you have to do mathematics in order to develop genius.

[Anonymous No.8728961]

>>8728665
>what are you researching?

Following my nose haphazardly. Reading list in pic attached. Not a student or smart enough to work in business so this is all just a hobby.

I'm also typesetting a small book on sets and proofs to learn LaTeX. Which... I really gotta say this.... Having just started using it, LaTeX is just absolutely fucking awesome. I'm sure this is just a honeymoon period, but after years of drawing equations by hand, and getting awful cramps and having to take breaks in between long passages of tedious writing, being able to type a couple lines of code (and copy and paste already written code) and then have any equation I want appear in perfect crisp detail at almost any size has kept me in an almost permanent state of joy and relief for the past couple days. It's just... awesome and I wish I had started using it sooner. ...That's all I have to say.

>>8728773
>analyzing trends of the proton density in solar wind
>studying the arithmetic properties of the zeros of certain functions related to elliptic curves

Do you have any background in physics? Would that have helped at all with what you were asked to do? How much direction were you given? Did you like who you were working with? Did you know what you were going to be doing before you started? Which one was more challenging or straightforward in what you needed to do, or is it difficult to compare because they presented different challenges? I know that's probably a lot of questions so no pressure to answer any, I'm just very curious about your experience.

[Anonymous No.8729795]

>>8728961
>Do you have any background in physics?
at that point i had taken a first year physics class and a second year E&M class

>Would that have helped at all with what you were asked to do?
not really, but i think the ideal person for the project would be someone with lots of knowledge about the sun (solar cycles...) and data analysis techniques, some knowledge of statistical methods

>How much direction were you given?
1st project not nearly enough, or I just wasn't asking the right questions (more likely)
2nd project it was always clear what needed to be done, it was just a matter of knowing enough mathematical theory to get through it

>Did you like who you were working with?
in both cases yes (both were genuine experts, one old, one young) so the limitations on both projects certainly came from my own lack of knowledge/experience

>Did you know what you were going to be doing before you started?
1st project was just listed as 'project in data analysis' and I got to pick between a couple different topics (I think one of the other one was ECG data or something like that)

I sort of accidentally got involved with the 2nd project after hearing someone give a lecture about it in a seminar and asking for references after, later he came and just asked me if I wanted to work on it with him over the summer

>Which one was more challenging or straightforward in what you needed to do, or is it difficult to compare because they presented different challenges?
The data analysis was far less straightforward (the nature of applied mathematics I guess, wide variety of tools) but the sort of 'ceiling' for the elliptic curves project was higher (nature of number theory...), the material you need to progress further ramps up in terms of prerequisites and depth quickly. There was a much more concrete goal for the elliptic curves than just 'play around with big data set'

[Anonymous No.8730845]

>what are you researching?
I've been developing a method to shrink categories. It allows one to use the properties of small categories "locally" in categories that need not be smal themselves, such as the Mitchell embedding theorem. No idea if this has already been done by someone, but I'm going to see a lecturer of mine next tuesday and see what she has to say about this.

>what are you studying?
Some algebraic topology and a bit of differential equations, and pointless topology on my own.

>any good problems?
Using the category of Hausdorff spaces and comtinuous maps, show that an arrow can be both an epimorphism and a monomorphism without being an isomorphism. (Hint: the inclusion [math]\mathbb{Q}\to\mathbb{R}[/math].

[Anonymous No.8730849]

>what are you researching?
I've been developing a method to shrink categories. It allows one to use the properties of small categories "locally" in categories that need not be smal themselves, such as the Mitchell embedding theorem. No idea if this has already been done by someone, but I'm going to see a lecturer of mine next tuesday and see what she has to say about this.

>what are you studying?
Some algebraic topology and a bit of differential equations, and pointless topology on my own.

>any good problems?
Using the category of Hausdorff spaces and comtinuous maps, show that an arrow can be both an epimorphism and a monomorphism without being an isomorphism. (Hint: the inclusion [math]\mathbb{Q} \to \mathbb{R}[/math].

[Anonymous No.8730850]

>>8730849
>I've been developing a method to shrink categories. It allows one to use the properties of small categories "locally" in categories that need not be smal themselves
could you elaborate on this a bit? sounds interesting

[Anonymous No.8730859]

>>8730850
Shit, I left out the most important thing. Until I've heard a pro opinion on this thing, and whether I should publish it or not, I'm gonna be a bit vague, but the basic idea is that I have a category C, and a certain type of subcategory C' of C, and these are ALWAYS equivalent. The "lesser" categories, as I have called them, are such that this C' is small. Clearly, small categories are lesser, but I have constructed several large lesser categories, too. I'm not completely sure if one can have a Grothendieck topology for any category, but this would allow one to take a (suitable) large category, get an equivalent small category, and topologize that one.

Sorry for being handwavy. This might be new, and I've seen the pic in which someone has posted on /sci/ how some quaternionic thing resembles the Lorenz attractor, and then this one guy has replied something like "Thanks for the free paper to publish".

[Anonymous No.8730860]

Possible brainlet question:

How does someone "do research"? How much math is needed to "do research"?

I am taking Algebra and Real Analysis next academic year, with a proofs class this summer. Did well in my lower division coursework which I finished up.

How do you even find research problems to work on? I'm just a pleb undergrad right now

[Anonymous No.8730868]

Why is every single fucker here obsessed with category theory

there are no analysts, no geometers, no topologists, there's never anything but category spergs on this board

[Anonymous No.8730941]

>>8730868
wit ct you do geometry and topology, not that 20 yo undergrad can know this

[H No.8730945]

>>8730859
>I'm not completely sure if one can have a Grothendieck topology for any category
Canonical topology.

[Anonymous No.8730960]

>>8730945
Yes, that is a topology that would be easily used anywhere, but one source says categories must be small, and the other that the can be whatever. For example, Johnstone defines (pre)sheaves for small categories in his book on topos theory.

[Anonymous No.8730965]

>>8730868
I'm more upset by the fact that all the category theorists are animufags.

[Anonymous No.8731799]

>>8730868
I am OP and I am a geometer.

There is nothing wrong with appreciating all parts of mathematics.

[Anonymous No.8731995]

>>8728665
>>what are you researching?
Nothing at the moment but I'm desperate to get into symbolic dynamics, specially after reading this paper:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC330698/pdf/nar00192-0217.pdf

The thing is that it seems like there is not much research going in right now ):

[Anonymous No.8732095]

>>8728681
I was good in number theory in undergrad.
Now I'm the brainlet of my algebraic geometry class in grad school.

[Anonymous No.8733264]

>>8728665
>mfw reading about quantum link invariants
>mfw the Verlinde formula for conformal field theories could be obtained as an operator link invariant on a ribbon category
>mfw there is a deep connection between conformal field theory and links on a 3-manifold despte them having seemingly no relation to each other
>mfw category theory does it again
I haven't been able to stop cumming since two days ago when I read about this.

[Anonymous No.8733337]

>>8732095
tfw you cant know whether you are a brainlet until it's too late and you have invested years and years

[Anonymous No.8733356]

>>8730868
I'm not even a mathematician rofl

[Anonymous No.8733687]

>>8733337
"brainlet" is the biggest meme ever and isn't actually a thing.

[Anonymous No.8733740]

>>8728897
>Protip: you don't have to be a genius to be a mathematician.
But I don't want to be a mediocre mathematician. I want to get a fields medal.

I wish I could know if I was fields medal material before it was too late.

>>8732095
Fugg. But maybe that has to do with the change of subject.

Are you still good at number theory? As in, grad level number theory? Algebraic Number Theory? Analytic Number Theory? Are you good at those?

I don't particularly care about geometry and even though I got an A in my last "geometry" class, I know that I am bad at it compared to algebra and analysis, so I don't care about it.

I just care about number theory my maaan.

[Anonymous No.8733754]

Not sure if this is the right place to post
I'm an electrical engineering student and I am "bad at math".
I want to learn calculus, differential equations and Laplace z and Fourier transforms.
Is there a diagnostic test available online to highlight my gaps in knowledge?

[Anonymous No.8733762]

>>8733740
>I wish I could know if I was fields medal material before it was too late.
>Fugg.
Yeah I can tell you right now, you are not Fields medal material. Enjoy your degree in software engineering.

[Anonymous No.8733769]

>>8733762
>Enjoy your degree in software engineering.
topkek I am already in pure mathematics motherfucker.

Also, it is just a meme holy shit this is 4chan.

[Anonymous No.8733971]

any canadians in? Advice for getting an NSERC?

[Anonymous No.8733975]

>>8733971
Be aboriginal, female, disabled, and top grades in your class.

If you are white male, just get A+ in everything and that should be decent enough, assuming you are good at writing the essays.

[Anonymous No.8733984]

>>8733971
which NSERC brainlet? i got one for both USRA and CGSM if you need tips

[Anonymous No.8734059]

how do you guys find managing studying math and having a social life? i never see my flatmates and they always go out without me, it's kinda depressing but at least they're around so im not too lonely.

[Anonymous No.8734092]

>>8733337
It's the journey that counts.

[Anonymous No.8734102]

>>8734059
Make friends who do math.

[Anonymous No.8734152]

>>8728704

>I would suggest pursuing an undergraduate degree in mathematics, using your electives to do some finance stuff. If you do not choose to pursue pure mathematics at the end of your degree, you can always just apply for a masters in financial mathematics and get your secondary dream.

I would really counsel against this advice.

Reading OP's statements I think the best place for him right now is outside of the mathematics ghetto. As a mathematician, he would be better served joining a research group in a field working on a real problem, biology, molecular bio, biochem, physics- nearly every project needs some mathematics.

One, it will broaden your horizons, two, you will exercise some respect for other branches of the sciences. Three, you will realize there is not nearly as much opportunity in mathematics as there is in real research fields, and four, you will be able to exercise and improve your socialization skills.

The messiness of real world data integration should be more than worth it form an experience standpoint alone.

I can't emphasize enough how important an undergrad research experience could be, especially if you are able to participate in publishing.

So take a shower, get a haircut, wear clean clothes, look people in the eyes, knock on doors and talk to profs and express some fucking human interest in life.

[Anonymous No.8734172]

>>8734152
Why would you counsel him to get outside math when math is what he wants to confirm talent in?

[Anonymous No.8734213]

Nice: any space can be made sober by taking the spectrum of its locale.

[Anonymous No.8734254]

>>8728665
>what are you reading ?
Topology book and some analysis. Undergrad level.
>what are you studying ?
Materials engineering.
>any good problems ?
Not that I'm aware off.
>book recommendations ?
Enclyclopedia of Mathematics seems pretty dope, even though I can't understand most of it.
>cool theorems ?
Bolzano-Weirstrass, either in the form that any bounded sequence (in R) has at least one convergent subsequence, or in the form that in any closed bounded interval [a, b] in R, any infinite subset X of that interval has at least one accumulation point in [a, b].

I don't know why, but I feel the two mean the exact same thing. Might try to do some work on it later that night.

Oh, and I'm doing a small presentation of the Riemann zeta function to my comrades engineers Monday. Don't know how far into the details I should go, they usually don't like maths :/

[Anonymous No.8734260]

>>8728916
Of course the namefag says something retarded.
There are geniuses who are not good at math.

[Anonymous No.8734272]

>>8733740
>I want to get a fields medal.
I want that to, but you gotta be realistic.

My plan right now is to finish my engineering degree and my master in applied physics, find a nice work in a laboratory of a university, get to know the professors, work there and study pure maths.

[Anonymous No.8734289]

>>8734272
what's the highest level math you'll take during eng?

[Anonymous No.8734313]

>>8734289
The highest I have taken. I don't do math anymore at this level, except on my own.
I've done a fair amount of calculus (culminating to Stokes theorem and other Green-Riemann stuff about surface integrals and line integrals), linear algebra (including a little bit with differential equations), and an introduction to Analysis (series, sums, complex transforms, a little bit of functional analysis, a little bit of Fourier analysis.)

I lack training in formal topology, formal algebra (except the very basic stuff like bijections and maps), geometry (only ever touched that with physics classes), and, of course, "proving" stuff. Only the class in Analysis required us to prove stuff (namely, we had to prove Dirichlet theorem and the existence/convergeance of Fourier series in a project), the rest was just learning tools, combine them, apply them.

[Anonymous No.8734323]

>>8734313
you're going to wait until you already have an applied physics job 10 years from now to start? you can't be serious. if you want to learn math there's no excuse not to start right now

[Anonymous No.8734330]

>>8734323
I've started, reading topology books and other stuff on the side. >>8734254

I also did 2 courses in "applied" maths (Optimisation and Probabilities) where I got pretty good grades.

>you already have an applied physics job 10 years from now
Hopefully it'll be shorter. I'm graduating in 2-3 years, and the average period before finding a job is 2 months after graduation.

[Anonymous No.8734336]

>>8734330
oh in that case that's ok. books alone won't take you very far if you don't talk to someone to get a "big picture" kind of insight, so try to talk to a professor soonish

[Anonymous No.8734342]

>>8734336
I'm lucky on that front, dad is a math teacher with pretty good insights.

[Anonymous No.8734347]

>>8734342
Holy shit please be joking

[Anonymous No.8734353]

>>8734347
Why being smug ? He have a diploma more or less equivalent to a master in pure maths. He has the qualifications to teach in university if he wanted to.

And he can answer questions.

[Anonymous No.8734366]

@8734353
Confirmed bait. Nobody can be this stupid lmao.
No (You) for you.

[Anonymous No.8734381]

>>8734366
Illuminate me. I'm not referring to him as the ultimate reference, of course, and yes, I'll get in touch with other professors as well, but it's always nice to have somebody to help you figure out some stuff.

[Anonymous No.8734395]

>>8734213
Care to elaborate?

[Anonymous No.8734533]

Im the typical comp sci major in a calc class. Its going ok.

[Anonymous No.8734570]

Revising high school math because had shitty high school teacher that explained everything way to complicated.
23 years old now and it's easier to follow khan & basic math book.

[Anonymous No.8734611]

>>8734395
Take any topological space [math]X[/math], sober or not. You then have have the lattice [math]\Omega (X)[/math] of open subsets, giving you the frame of the space. Then, the locale [math]L(X)[/math] is the corresponding object in the category of locales, or the dual category of frames, and you now have a functor [math]L \colon \textbf{Top} \to \textbf{Loc}[/math]. For any locale, one can define a spectrum by considering its set of all completely prime filters, and equiping this with a suitable topology. Now, this gives rise to a functor [math]S \colon \textbf{Loc} \to \textbf{Top}[/math], and all the spectra themselves are sober spaces, so now the composite of these functors defines a sobrification [math]X \mapsto SL(X)[/math].

[Anonymous No.8734671]

>>8734611
Ok. A lot of these functors aren't clearly defined and I don't see how the sobrification relates to the original space. Anyways what this looks like is a space structure if the functor[math]L:\mathscr{T}\rightarrow \mathscr{S}[/math] is covariant, and it seems to be compatible with disjoint unions and associative/commutative on the nose as well. If we can endow this [math]L[/math]-space structure with a cobordism theory [math](M,L)[/math] then we can define a topological quantum field theory [math](\mathfrak{T}_K,\tau_K)[/math] on it where [math]K[/math] is a ring. Depending on what [math]L[/math] preserves this TQFT can probably tell us something about how locales affect the structure of the modules.

[Anonymous No.8734757]

>>8734671
Starting from the frame functor [math]\Omega[/math], we have, for any continuous map, [math]\Omega (f)(U) = f^{-1} U[/math] for all [math]U \in \Omega (X)[/math]. Since [math]\textbf{Loc} = \textbf{Frm}^{op}[/math], we set [math]L(X) = \Omega (X)[/math] and [math]L(f)=\Omega (f)_*[/math], where [math]\Omega (f)_*[/math] is the right Galois adjoint of the frame homomorphism [math]\Omega (f)[/math], namely [math]f \colon X \to Y \Rightarrow L(f)(U)=Y \setminus \overline{f[X \setminus U]}[/math] for all open sets [math]U[/math].

Then, the other functor. For any locale, say [math]M[/math] now that I was stupid enough to use L already LOL, define [math]S(M)=\{\text{all completely prime filters in } M\}, \{ \Sigma_a\ |\ a \in M\})[/math], where [math]\Sigma_a = \{ F\text{ a completely prime filter in } M\ |\ a \in F\}[/math]. That's the space. For the morphisms, set [math]S(f)(F)=(f^*)^{-1}F[/math], where [math]f^*[/math] is the left adjoint of [math]f[/math].

Does this clarify stuff? Both functors are covariant. No idea about those field theories, though.

[Anonymous No.8734780]

>>8734611
>>8734757
I fucking hate set theory

[Anonymous No.8734796]

>>8734757
>Does this clarify stuff?
No lmfao god forbid I actually find an application of Galois theory to physics.

[Anonymous No.8734805]

How do you guys come up with research questions? Just familiarity with your field?

[Anonymous No.8734824]

>>8734757
>>8734671
>>8734611

Friendly reminder that this is a math thread, not a fiction thread. We have a separate board for fiction discussions.

>>>/lit/

Feel free to continue your discussion there.

[Anonymous No.8734852]

>>8734824
t. engineer

[Anonymous No.8734862]

>>8734780
So do I sometimes. I don't like the fact that my glorious plans can be ruined by having a proper class where I'd like to see a set.

>>8734805
I was just doing my master's thesis and got a bit derailed, and then eventually I had accidentally redone what Quillen did (https://en.wikipedia.org/wiki/Q-construction)), and then went the other way around and will hopefully get to publish what I have or atleast put it on Arxiv.

>>8734796
Fug

>>8734824
Bully. Stop or be stopped.

[Anonymous No.8734880]

>>8734862
>I don't like the fact that my glorious plans can be ruined by having a proper class where I'd like to see a set.
What does it even mean ? You prove something on set(s) but if I give the set(s) a certain property it all falls apart ?

[Anonymous No.8734899]

>>8734880
Proving stuff, and using old results. Some require the "smallness" of sets, and then I need sets and still encounter classes, and this forces me to set some restrictions. It sucks when you lose generality like that. Nevertheless, I have been able to (give a method to) generalize several results that would be size queens.

[Anonymous No.8734908]

>>8734899
No need to use a gun on me, you psycho.
And I'm here, taking an hour to see that
(x, y) => (x + y, xy) is surjective but not injective.

(and the answer was so easy I cried in shame after)

[Anonymous No.8734914]

Before I go ahead and take a nap I'd just like to say that making category theory my bitch is an incredible turn on.

[Anonymous No.8734921]

>>8734908
I'm just beating the shit out of those classes. And don't worry. Sometimes the most concrete of problems are the hardest.

>>8734914
Physicists are always so physical.

[Anonymous No.8734935]

>>8734671
>A lot of these functors aren't clearly defined
yes they are
in classical math, a space is sober iff the space is T__0 + the irreducible closed subsets are the closures of a singleton

a topological space is sober iff the counit is an isomorphism ie the set of the space is the spectrum

[Anonymous No.8734952]

>>8734757
the complete prime filters are not good when you deal with locales
if you care about locales, the spectrum of X is LOC(1, X) with topology
{f^* such that f^*(u) = 1 for any open u}

also, on the logical side of the propositional theory, a topological space is sober when there is an isomorphism between the models of the theory and the points, instead of only having that points are models.

[Anonymous No.8734963]

>>8734757
the complete prime filters are not good when you deal with locales
if you care about locales, the spectrum of X is LOC(1, X) with topology
{ {f^* such that f^*(u) = 1} for any open u}

also, on the logical side of the propositional theory, a topological space is sober when there is an isomorphism between the models of the theory and the points, instead of only having that points are models.

[Anonymous No.8734974]

>>8734963
I only started reading about these things today, so I'm just a beginner. The sobrification thing was pretty cool, though, and I decided to share it. What do you mean by LOC(1, X)?

[Anonymous No.8734993]

>>8734974
>LOC(1, X)?
the arrows of the category Loc of locales and locale arrows, from the initial locale to X

it is natural to build this, rather than the classical way of Y∖closure[f[X∖U]]

so you go
Top->Loc
X->ΩX
f->f^*

Loc->TOp
L -> [Loc ( 1 ,X), { {f^* such that f^*(u) = 1} for any open u} ]
g-> composition

[Anonymous No.8734997]

>>8734993
>f->f^*
must be f-> (f^*) formally reversed

[Anonymous No.8735002]

>>8734999
>>8734000

[Anonymous No.8735059]

>>8734993
Right. That makes sense, as it makes points generalized elements. Thanks for sharing this. I'll let it digest for a while so that it becomes more intuitive.

[Anonymous No.8735127]

>>8734921
I am woke and ready to go.

[Anonymous No.8735133]

>>8735127
Welcome back.

[Anonymous No.8735136]

how many layers of abstraction are you on right now

[Anonymous No.8735138]

If you want to do compelling math use a computer with a massive gay men GPU and generate some pretty fractal

[Anonymous No.8735139]

>>8735136
So many I don't even know what I'm talking about my dude

I just circlejerk with an anime avatar

[Anonymous No.8735143]

>>8734935
The fuck you on about? I know what a sober space is you fuckwit.
>>8735133
Put down the gun boy.

[Anonymous No.8735150]

>>8735136
like,, maybe 5, or 6 right now. my dude

>>8735143
You first.

[Anonymous No.8735155]

>>8734796
>god forbid I actually find an application of Galois theory to physics.

It already has applications via Langlands

[Anonymous No.8735161]

How many of you can/can't program?

What would you program if you were really good at programming?

[Anonymous No.8735164]

>>8735136
I am using category theory to study knot/link theory to study gauge theory to study AdS/CFT to study strongly correlated fermions. So I guess 4.
>>8735150
Are you resisting arrest?

[Anonymous No.8735167]

>>8735161
I can't, but I would probably program some program to make hyperbolic tesselations.

>>8735164
A.C.A.B.

[Anonymous No.8735176]

>>8735161
I know Mathematica, Maple, C++, Python, FORTRAN, and I'm currently learning Golang. I've made SCFT, Lanczos-type calculations, DMRG, QMC simulations, odeint, and dozens of other root finding algorithms.
>>8735167
You're being very naughty right now.

[Anonymous No.8735184]

>>8735161
I'm reasonably competent with a few languages. Probably could not hack it in a professional programming position but I can function on small-scale projects.

Unless you go to a place that lets you jack off in 100% theory all day (most don't) and you are only interested in doing that (you shouldn't be) you'll end up learning at least some R or Matlab or something and some C out of necessity.

I'd like to learn how trading algorithms work but my knowledge of finance is weak and I'm too lazy to improve it right now.

[Anonymous No.8735189]

>>8735176
Don't hurt me!

[Anonymous No.8735192]

>spend an hour working on a problem
>no progress
>google for assistance
>there's a typo which makes it incorrect
>stated correctly, said problem is trivial

[Anonymous No.8735193]

>>8735189

Anime pleb can't even hit her own brain...

[Anonymous No.8735204]

>>8735189
As long as you understand

[Anonymous No.8735227]

>>8735193
Well, I don't think your shot hit your brain either...

>>8735204
I will, eventually.

[Anonymous No.8735287]

how do yall like geometry just taking my first class now it happens my professor is lame doesn't teach us and gave us a book that tells you to define everything yourself

[Anonymous No.8735357]

>>8735287
Geometry is only good if it's combined with analysis and topology.

[Anonymous No.8735454]

>>8735357
how come

[Anonymous No.8735709]

>>8735454
Because I said so, cunt

[neil No.8735785]

>>8733984
USRA

[neil No.8735788]

>>8734366
>@
what the fuck

[Anonymous No.8735984]

>>8735785
honestly just apply to as many of them as possible, they're hard to get even if you're a third or fourth year student. apply to ones that aren't at your school if you have the option of mobility (i had a friend who traveled to Western to do a USRA). email as many of the professors beforehand as possible and sell yourself

[Anonymous No.8736400]

How is everyone doing today?

[Anonymous No.8736453]

>>8736400
bathing in the blood of brainlets

[Anonymous No.8736480]

>>8728916
>who is michael faraday

[Anonymous No.8736504]

>>8736400
Pretty good. Trying to familiarize myself with Heyting algebras in order to properly understand what I'm reading, since the lattice of open subsets is always a complete one.

>>8736453
How much blood did you take? This must be the reason behind the headache I had when I woke up.

[Anonymous No.8736510]

I'm formalizing ZFC in Agda. I'm trying to prove induction. Using constuctivist logic is a bit hard (I didn't knew how much I loved you, principle of the excluded middle).

[Anonymous No.8736517]

>>8736510
You don't realize how much you love things before you lose them :^)

[Anonymous No.8736518]

>>8735161
MATLAB, Python, R, Agda, Haskell, Prolog.

Want to learn Coq and Idris

[Anonymous No.8736748]

>>8735161
I've done a fair bit of CS courses before switching majors.
I can program in Matlab/Scilab, a bit in Python and in Java.

[Anonymous No.8736749]

What's /math/'s opinion on quantum computing?

[Anonymous No.8736754]

>>8736510
>suc

>>8736400
Have some plans for the week-end. Monday I'm doing a small presentation on the Zeta function (nothing too detailed, just explaining it to my fellow engineers) and I need to flesh out the details.

Also I'm reading a pretty good book on Topology

[Anonymous No.8736784]

cedric villani's acting debut

https://vimeo.com/205778279

has he lost his mind bros? will he be ok?

[Anonymous No.8736795]

>>8736784
He's always been a bit special. But very good and knows how to teach.

I'm reading his book on Lesbegue integral, available online. It's pretty good. I don't understand everything, but it's not as opaque as some other books I've read.

[Anonymous No.8736822]

>>8736784
What the fuck

[Anonymous No.8736831]

>>8736754
what book

[Anonymous No.8736834]

>>8736784
Kek, that's probably how you guys will end up, if your theorems are used at all.

[Anonymous No.8736839]

>>8736831
Analysis Course, Tome II : topology, Gustave Choquet

[Anonymous No.8737067]

Bump
https://arxiv.org/abs/1506.05805

[Anonymous No.8737127]

>>8735164
>I am using category theory to study knot/link theory to study gauge theory to study AdS/CFT to study strongly correlated fermions

Teach me your ways.

>>8736510
>not enjoying exclusively proving things by cases

[Anonymous No.8737298]

Anyone has some nice diagrams about topology of func. analysis like the table OP provided?

[Anonymous No.8737301]

>>8737298
*or

[Anonymous No.8737392]

>>8737127
I'm currently at a colloquium right now. I'll draw you up a diagram of how those relate together when I get back.
xoxo

[Anonymous No.8737407]

>>8735139
You do realize using avatars is forbidden on 4chan right?

Get banned you fucking degenerate

[Anonymous No.8737613]

what the hell is the deal with descriptive set theoru? i cant think about Baire space i start to get sick ;_;

[Anonymous No.8737680]

Question:

If [math]\mathcal{A}[/math] is an abelian category and [math]\mathcal{A} \to {\mathcal{C}_\tau }[/math] is a stack, can we make [math]C{h^ \bullet }\left( \mathcal{A} \right)[/math] into a stack?

[Anonymous No.8737807]

>>8737127
>>8737392
I'm back. Enjoy this cancer meme.

[Anonymous No.8738463]

Bump.

[Anonymous No.8738469]

Who else /academic forced to have their e-mail put up on the department website/? How do I avoid crackpot emails from Russians?

[Anonymous No.8738665]

>>8728665
cs student doing research in computational topology

[Anonymous No.8738699]

>>8728665
>It's that time of the month
...you're on your period?

[Anonymous No.8738968]

>>8738699
ya how did you guess???

[Anonymous No.8739023]

>what are you reasearching
Minimal framework in which one does not have a general theory of PDEs

>good problems
Is pi^( pi^( pi^( pi^(pi))))) an integer ?

>cool theorems
Jordan curve.

Or this : "any non-empty compact, convex, smooth set of R3 contains at least one point"

[Anonymous No.8739125]

>>8739023
"any non empty set contains at least one point?"

what?

[Anonymous No.8739130]

>>8739023
>"any non-empty compact, convex, smooth set of R3 contains at least one point"
>non-empty
>at least one point

Wut

[Anonymous No.8739219]

I know /sci/ isn't here to help get my home work done, but I have a very specific problem I need help with.

What filter mask can further exaggerate the shown peak? Any other means of sharpening this signal?
It's in image processing...

[Anonymous No.8739233]

>>8739219
>dumb retard engineer can't even read

[Anonymous No.8739308]

>>8739233
thx for the constructive hint.

[Anonymous No.8739332]

>>8739023
>cool theorems

[Anonymous No.8739357]

in the future I'm going to work with camera data that is streamed into a computational unit in time and I want to model the whole framework with a mental picture of some object and arrows between them.

What are good ways to capture values a type X that vary in time? (And time is, in most cases, descrete for me)
I think I remember MacLane in his Sheaves book using, I think, somehting like Hom(N,-) and the image Hom(N, X) being composed of indexed X's that represent X at different time steps.
But this might not provide all the things I want. It might be that I'm interested in stochastical processes from a category theory perspective - is there something on this?

[Anonymous No.8739835]

Anyone have a reference to a proof of the strong Whitney embedding/immersion theorems, preferably starting from the weak forms?

[Anonymous No.8739875]

>tfw p-adic Hodge theory is too complicated

[Anonymous No.8739929]

>>8739875
ITT: wtf am I looking at

[Anonymous No.8739933]

I'm an engineer looking to make his way to Spivak, as a first goal, and I'm currently reading Euler's Elements of Algebra.

210 pages in and it's a much easier read than I was expecting, pretty fun, too. I'm supplementing this with Gelfand's Algebra, and after I'm done, I'll move on to the other Gelfand books, along with Chrystal's Higher Algebra.

[Anonymous No.8739939]

>>8739933
engineering student, rather

i'm just tired of getting through all my math classes by rote memorization, like with Calc 2 series

it feels like cheating

[Anonymous No.8739940]

>>8739929
It's a magic trick, I think.

[Anonymous No.8739959]

>>8735161
I can't, but if I could, I'd try to program a natural language parser and try to see how to build a speech processor

[Anonymous No.8739963]

>>8739940
They're called Kirby moves, and they preserve the results of surgery on [math]S^3[/math].
And no I don't know how they work.

[Anonymous No.8739978]

>>8739219
Have you tried weighing it exponentially?

[Anonymous No.8739994]

>Math general thread
>Quickly devolves into a bunch category theory autists posting anime
Every fucking time. At least I can feel identified with the deppressed anons in here, but aside from that it's only engineers and cathegorists who have no interest in anything else besides circlejerking their love for anime and immensely abstract maths.

>inb4 brainlet get out of my general REEEE
No need to be rude with the mentally impaired.

[Anonymous No.8740010]

>>8739994
Pick up a book for once and join the discussion instead of autistically shouting by the sidelines.

[Anonymous No.8740021]

>>8728665
>any good problems?
This one was suggested by some dude I know:
Is there a noncommutative division ring R such that each left polynomial of degree n (ie. expression of the form a_nX^n + ... + a_0 with a_n <>0) has at most n roots ?
>book recommendations?
Algebras of Linear Transformations by Farenick
>cool theorems?
If m<>n and K is a field, then GLm(K) is not isomorphic to GLn(K) (there's an easy way to do it in characteristic <> 2, but it is surprisingly tricky in characteristic 2).

If f is in GLn(Fp), then f can be seen as a permutation of [math]\mathbb F_p^n[/math] and its signature is [math]\varepsilon(f) = \left \dfrac{\det f}{p}\right)[/math]

[Anonymous No.8740096]

>good problems

[Anonymous No.8740115]

>>8739994
>general thread devolves into attention-deprived faggots using it to pretend they have friends
who woulda thought

Nobody except these people even has any use for a "math general".
The whole board is science and _math_, the only thing a general accomplishes is creating a circlejerk for you to belong to. It's like going to /vp/ and making a "pokemon games general".

[Anonymous No.8740118]

>>8740010

I'm a fucking undergrad (the retarded kind), what do you expect me to add to the discussion?

[Anonymous No.8740120]

>>8740096
>physics

[Anonymous No.8740127]

>>8740115
Actually it's one of the few places on this board where actual difficult math is discussed. Otherwise it's all:
>300k starting
>baby rudin or spivak?
>CS or math?
>brainlets! :^)
>how can we improve the mathematics curriculum???
>etc.

I have frequently gotten help from math generals on where to go research wise, as well as had my interest piqued by people discussing their research in the math general threads. I get that majority of sci does not benefit from people discussing mathematics, but perhaps you should go wahwahwah elsewhere?

[Anonymous No.8740135]

>>8740120
Math is a branch of physics where the experiments are cheap.

[Anonymous No.8740814]

bump

[Anonymous No.8740856]

>>8740814
Thanks anon

[Anonymous No.8740861]

Need your guys help for the final question. Can only get it 29.

[Anonymous No.8740918]

>>8728665
>research
nothing
>studying
nothing
>problems
politics
>books
probability/Groethendieck
>cool thms
a few lemmas but no
if you know your stuff history is good
Muslims invented hospital cleanliness

[Anonymous No.8740952]

>>8737807
L.S, I would know this autism anywhere.
This is a good meme actually to explain it.
>t.your friend H

[Anonymous No.8741299]

>>8739978
no. good hint. thx.

[Anonymous No.8741329]

>>8737680
wow /sci/ can't even answer a simple question

[Anonymous No.8741339]

>>8738469
does your department not use an image of your e-mail?

[Anonymous No.8741342]

>>8741339
unfortunately not

[Anonymous No.8741380]

Is /math/ pro (axiom of) choice ?

[Anonymous No.8741382]

>>8741380
>mfw mathematicians think its reasonable AT ALL for every infinite dimensional vector space to have a basis

[Anonymous No.8741396]

>>8741382
>mfw there's mathematicians who think it's reasonable AT ALL for there to exist a partition of [math]\mathbb{R}[/math] whose cardinality is bigger than [math]\mathbb{R}[/math] itself.

[Anonymous No.8741401]

>>8728665
To the people in this thread: is it a good idea to write a math book? I'm in the process of writing a book about how to use combinatorics for programming. I also think I'd like to write a book about complex analysis and ways to use it for 3d graphics. Not trying to get rich I just want it on my list of achievements

[Anonymous No.8741403]

>>8728665
I'm creating a database program

[Anonymous No.8741413]

>>8741396
>mfw there's mathematicians who think it's reasonable AT ALL for [math]\mathbb{N}[/math] to have the same cardinality as a strict subset of [math]\mathbb{N}[/math] itself.

[Anonymous No.8741417]

>>8741396
>there is an infinite number of infinite
I'm starting to understand Wildberger's obessesion

[Anonymous No.8741420]

>>8741417
This is precisely the reason why Kronecker called Cantor the 'corrupter of youth'

Denounce infinity or you'll end up dying in a sanatorium like Mr. Infinity

[Anonymous No.8741460]

>>8741401
People here are mostly undergrads/grads/postdocs. You might be better off asking in math.stackexchange/academia.stackexchange/ r/math. There's usually more proffessors in there who could give you good advice.

[Anonymous No.8741520]

I posted this in its own thread but it was deleted. I'm hoping that someone could give me good advice, unlike the one I'd get in /adv/.

I have the option to get a double master's degree from Spain and France through PAU university. For the moment, I'd like to be a researcher (either geometry or numerical methods), but I may end up in industry, that's why I'm considering taking the opportunity to do one of their applied maths master's in conjunction with the one from my current uni, and then try to get a PhD in those topics.

Is it a good idea? Is PAU good? I don't want a shitty meme degree, I'd rather just stay here for that.

Also, I've heard that I could do the double master's, and then do a PhD with two directors (one from PAU {or maybe anywhere in France, I'm not sure}, the other from here) and get a "double PhD" of sorts. Is that true?

[Anonymous No.8741531]

>>8741520
>Les équipes de recherche, sont en majorité associées à de grands organismes, (CNRS, INRA, INRIA) ou de grandes entreprises (TOTAL).

You're fine. CNRS is pretty much the highest scientific institution there is. Though they are mostly in physics, as well the INRA and INRIA.

[Anonymous No.8741925]

How much did you party in undergrad

[Anonymous No.8742018]

>>8741413
>mfw there are people who invent their own definition of cardinality and get mad when others use a different one

[Anonymous No.8742036]

Can I a general question?

I'm a third year math student and I have realised that I really don't give a shit about math in general. I just like solving problems. I actually hate learning new math. It's so tedious.

Is this normal or am I just weird?

[Anonymous No.8742055]

>>8742036
You're just an idiot. It's ok though you can switch majors to engineering or something.

[Anonymous No.8742136]

>>8742055

If I'm an idiot so is the whole class cause I'm easily top 5% according to grades.

[Anonymous No.8742146]

>>8742136
Nice unwarranted brag.

[Anonymous No.8742154]

>>8742146

Why did you call me an idiot? It was completely unwarranted.

There are many guys who get good grades doing stuff they don't particularly give a shit about. Heck I bet most of the top of the class is like that.

Also I said, I liked doing math. I just loath the learning of it. It's tedious.

[Anonymous No.8742203]

a simple HoTT related paper was just uploaded:


https://arxiv.org/pdf/1703.03007.pdf


>>8741568
too quiet?

[Anonymous No.8742209]

>>8742154
You like what you understand, which is a small tiny fraction of what's out there. You don't like math, you like being the king of your minuscule infinitesimal domain of knowledge. You sound like the typical high school autist who'd never accept his intellect being challenged. "Tedious" my ass, you've never even begun to learn. Eat shit, child.

[Anonymous No.8742215]

>>8742209
That's rude but I agree. Even I feel like a retard most of the time I do math, I try to learn new stuff.

[Anonymous No.8742275]

>>8742154
>Why did you call me an idiot?
Excusatio non petita, acusatio manifesta.

[Anonymous No.8742563]

>>8741925
Not at all. People are scary.

>>8742203
I have HoTT on my computer. Does it provide anything interesting for someone interested in homotopy or is it more for logicians?

[Anonymous No.8742575]

>>8742563
Well just take a look, mate.

It's basic, but it pulls up syntactic/semantic categories (Ctx, the category of context).

[Anonymous No.8742712]

>>8742575
Maybe I should when I have time. It sounds interesting, but people call it a meme, and it makes me so uncertain.

[Anonymous No.8742794]

>>8742712
I lost track of which anime guy I talk to.
What isn't a meme?
I personally don't think HoTT can take off (because there are too few relevant things it could prove within the next 10 years and I don't see that many uses for typey equality in programming, given how cumbersome it is to write down those long types), but I'm sure there are type theories with simpler equality and simpler semantics that people should learn and study and develope.

%%%%%%%%

Today I came up with this formula that I hadn't known before

[math] \prod_{k=a}^{b-1}\dfrac{B+k}{A+k} = \prod_{k=A}^{B-1}\dfrac{b+k}{a+k} [/math]

Product[(A + k)/(B + k), {k, a, b - 1}] // Simplify

Corollaries are

[math] \prod_{k=a}^{b-1}\left(1+\dfrac{1}{A+k}\right) = \dfrac{b+A}{a+A} [/math]

[math] \prod_{k=a}^{b-1}\left(1+\dfrac{1}{k}\right) = \dfrac{b}{a} [/math]

[math] \prod_{k=1}^{b-1}\left(1+\dfrac{1}{k}\right) = b [/math]

[Anonymous No.8742822]

>>8742794
I'm the guy studying pointless topology. I was just thinking about the little thing that the frames are complete Heyting algebras, but Heyting algebras are related to intuitionistic logic. Basically, I'm curious about how close to intuitionistic logic HoTT is, as then I would know whether it could be used to develop some sort of pointless homotopy (assuming that hasn't already been formulated).

[Anonymous No.8742850]

>>8742794
>[eqn]\prod_{k=a}^{b-1}\dfrac{B+k}{A+k} = \prod_{k=A}^{B-1}\dfrac{b+k}{a+k}[/eqn]

That seems nice, but it sounds like something already known.

[Anonymous No.8742863]

>>8742822
>pointless topology.
In the literal or metaphorical sense ? Pointless as in without points, or without objective ?

[Anonymous No.8742880]

>>8742863
Without points. It allows the generalization space -> locale. This is done by considering the lattice of open sets of a topological space, calling this a frame, and taking the corresponding object in the category of locales that is the dual category of frames. I haven't had time to proceed this weekend, but so far it has seemed quite cool.

[Anonymous No.8742883]

>>8742880
Well, it do seems more interesting than just metric spaces, but metric spaces are a tad more useful

[Anonymous No.8742910]

>>8742883
>more interesting than just metric spaces
Yes and
>metric spaces are a tad more useful
maybe. Although, one could possibly get some properties for general topological spaces using the pointless approach, and this would then be applicable to metric spaces. Therefore, it could be seen the way that this is more useful than metric spaces, as this would yield more applications. A matter of perspective. If one wants to do something concrete quickly, then the metric spaces are a lot more useful, though.

[Anonymous No.8742911]

>>8742822
Martin Löf type theory MLTT serves as an intuitionistc logic and HoTT is MLTT with more rules about how to treat the type/proposion of equality of two terms. So it's more rules added to the constructive framework and thus restricts semantics. ("intuitionistic" and "constructive" is close but I'm sure some people can point out minor differences.)
HoTT, viewed as theory of homotopies, is certainly without points in the sense that you don't deal with sets of many elements at all. A circle S^1 for example is not modeled as an uncountable number of points. In that sense it's somewhat pointless.

[Anonymous No.8742914]

>>8742911
I will definitely try it out then. Thanks!

[Anonymous No.8742918]

>>8742910
>If one wants to do something concrete quickly
Well I'm an engineer so
But it seems interesting enough. I don't really like working with sets and other extremely abstract stuff though, I prefer dumb entry-level analysis.

One problem I liked was to show the sum of [math]\frac{1}{n}[/math] converges if you take out all natural numbers containing a nine. It was fun to prove it, albeit easy since it was railroaded.

[Anonymous No.8742928]

>>8742914
gl
I made some reading notes on it , defining basic concepts and comparing them, here
(S^1 is given as an example too)
https://axiomsofchoice.org/babbys_first_hott

[Anonymous No.8742939]

>>8742928
Is that you Anon ? Goddammit. Shave and get a better lightning

[Anonymous No.8742951]

>>8742939
Don't mean to be rude, though, that's an impressive work. You're a phD in maths or physics ?

[Anonymous No.8742958]

>>8742939
Okay, but consider this:

[math] \prod_{p\in P} \dfrac{p^4+1}{p^4-1} = \dfrac{7}{6} [/math]

where [math] P [/math] denotes the set of all prime numbers.

[Anonymous No.8742964]

>HoTT

[Anonymous No.8742966]

>>8742918
Then it is better for you to concentrate on the metric spaces. The general case most likely won't be of much help, unless you were some computer engineer working with a lot of data and somehow tried to topologize that.

>>8742928
Thanks man! I put the link in my faves.

>>8742939
I think he looks nice without shaving.

[Anonymous No.8742968]

>>8742958
Can you proof it ?

[Anonymous No.8743020]

>>8742968
You need to play with Euler products a bit till you show this expansion
https://en.wikipedia.org/wiki/Liouville_function#Series
and then you pick values for the Riemann function ratio were you just end up with rationals like 7/6. I'm not a fan of number theory, but I sort of collect computational shortcuts on that website.

[Anonymous No.8743127]

Finished a copy-editing project for now.

[Anonymous No.8743174]

>be at AdS/CFT colloquium
>ask the speaker some questions afterwards
>mention TQFT
>"oh like Chern-Simons?"
>I said no
>hfw I mention category theory

[Anonymous No.8743236]

>>8743174
but Chern-Simons is highly relevant also to the category theoretical approaches, no?

Also, for non-anime speakers you'd have to explain that face. The post implies she's no happy, but the image.. doesn't look so bad

[Anonymous No.8743273]

>>8743236
Chern-Simons theory is a TQFT in the sense that it encodes purely topological data on the manifold, with no dynamics to speak of. Analysis of Chern-Simons theory can be done by just appealing to algebraic topology or differential geometry.
Categorical TQFT is defined as a functor from the category of cobordisms to the tensor product of K-modules equipped with a homomorphism that maps every cobordism gluing to a module homomorphism. The reason I brought up TQFT in this sense was that the AdS/CFT correspondence (as explained by the speaker) seemed to be a correspondence between cobordisms in AdS spacetime and tensor products of Hilbert spaces in a CFT. I saw the connection and asked her if she thought this categorical construction would be able to solve the AdS [math]\rightarrow[/math] dS problem. Of course the response was the typical "sorry I'm not an expert in this please go away" look.
Also please read the filename.

[Anonymous No.8743290]

>>8743127
Are you publishing his handwritten notes or something?

>>8743174
T R I G G E R E D

[Anonymous No.8743301]

>>8743273
if I had a nickel for every time I've read a
>dude categories can totally solve this problem I barely understand
post on this board I'd be able to buy at least a couple coffees by now

[Anonymous No.8743308]

>>8743301
>T R I G G E R E D

[Anonymous No.8743331]

>>8743290

No, I just wanted to collect his professional writings in one place, for myself. I now have a nice binder of the stuff. I'm not presently inclined to drill down to the level of later correspondence.

One big thing is missing: the doctoral dissertation "Boundary Functions" itself, in its entirety. An early fragment can be found online, but it isn't the whole thing. Worldcat gives the following existent print copies throughout the East; One Full Internet to an anon who can locate same and upload:

http://www.worldcat.org/title/boundary-functions/oclc/34519173&referer=brief_results

Apparently the original on deposit with Ann Arbor has gone missing, and all that they have is a microfilm that they don't care to disseminate, for obvious reasons (notoreity, and it's apparently genuinely not very impactful mathematics). I imagine that it's more of an embarassement for them that they won't(?) destroy, out of general academic principles, but would rather not popularize, again for the same obvious reasons.

Also, I imagine that it's "personal" for the institution in the sense that one of Kaczynski's victims was at Michigan.

[Anonymous No.8743347]

>>8743301
Memes on a memesite.

>>8743331
Okay. It's nice that you had the energy to do so nevertheless.

[Anonymous No.8743361]

>>8743273
You can't use TQFT for a geometric problem. You can restrict the functor to cobordisms w/ metric, and maintain geometric data, but then it is just a regular QFT.

[Anonymous No.8743367]

>>8743361
Source? Are you saying geometric objects don't have global topolgical properties?

[Anonymous No.8743385]

>>8743367
Geometric objects have global topological properties, but it is not enough to work purely topologically.

[Anonymous No.8743391]

>>8743385
>have topological object that you can "work purely topologically" with
><endow metric
>suddenly it's no longer a topological object that you can "work purely topologically with"
Also we don't need to work purely topologically with it. I just need to know what sets the happens to the modules/vector spaces when I endow the [math]\mathfrak{A}[/math]-spaces with a metric.
You still haven't provided a source btw.

[Anonymous No.8743412]

>>8743391
>You still haven't provided a source btw.
its obvious from the definition of a TQFT

[Anonymous No.8743419]

>>8743412
Sure it is, that's why you can't elaborate right?
Also you do know TQFTs work with manifolds right? I just need an invariant volume/area form on it to calculate the von Neumann entropy on the Hilbert space side of the correspondence.
Fucking children on this board ffs.

[Anonymous No.8743426]

>>8743419
You'd make all the children here much happier if you fucked off somewhere else

[Anonymous No.8743429]

>>8743426
Why would I want to make the children happy? Kids are fucking retarded

[Anonymous No.8743455]

>>8743419
>Also you do know TQFTs work with manifolds right?

But just topologically, hence the name. It is useless in a gravitational theory.

[Anonymous No.8743472]

>>8728681

>masters in mathematical finance

commoditized degree, you are better off heading straight to wall street (t. thats what i did after some consideration of the option)

[Anonymous No.8743623]

>>8734272
Where do people come up with this shit? Christ almighty.

[Anonymous No.8743668]

>>8743455
So you're saying that I can't add new definitions and constraints to a TQFT (such as what a volume form must map to) in order to study AdS/CFT?
What?

[Anonymous No.8743705]

>>8743668
You can but then it is no longer a TQFT.

[Anonymous No.8743707]

>>8743705
I think you misunderstood me anon. What I meant was that I would likely be able to solve the AdS/dS problem for AdS/CFT using TQFT, not that TQFT will solvsolve whatever structure I end up with may not be a TQFT but that's my starting point.

[Anonymous No.8744268]

>>8736510
>(I didn't knew how much I loved you, principle of the excluded middle).
what a brainlet

[Anonymous No.8744276]

>>8736504
>Pretty good. Trying to familiarize myself with Heyting algebras in order to properly understand what I'm reading, since the lattice of open subsets is always a complete one.
read this

Townsend_2006_On the parallel between the suplattice and preframe approaches to locale theory

Townsend_1996_Preframe techniques in constructive locale theory.pdf


Simmons_2006_The basics of frame theory.pdf [callsical work]

Masuret_2009_Closure and Compactness in Frames.pdf


Marsden_2010_Comparing intuitionistic quantum logics From orthomodular lattices to frames.pdf


Battilotti, Sambin_2006_Pretopologies and a uniform presentation of sup-lattices, quantales and frames.pdf

[Anonymous No.8744277]

Is maths essentially the religion? Noone have proven the existence of R, Q, C, N, but we still apply them to real live.

[Anonymous No.8744281]

>>8743273
>she
DROPPED

[Anonymous No.8744291]

>>8744277
>Noone have proven the existence of R, Q, C, N,
Holy fuck never post anything this retarded ever again
The existence of N is an axiom and if you disagree then obviously math is not for you
Constructing Q and C are trivial
Constructing R is far less trivial but you can still do it

[Anonymous No.8744294]

>>8744291
> The existence of N is an axiom and if you disagree then obviously math is not for you
> The existence of God is an axiom and if you disagree then obviously life is not for you

[Anonymous No.8744300]

>>8741520
>PAU
what is this ?

[Anonymous No.8744305]

>>8744294
hey faggot
ever seen God?
Yeah that's what I thought

hey faggot
ever counted to ten?
yeah that's what I thought

[Anonymous No.8744310]

>>8744305
You can count to very big nubmers. But it has it limits. Even if you count everything observed by humanity, it will still end at some point. But naturals somehow dont end.

[Anonymous No.8744311]

>>8744305
this is what is believed by 20 yo rationalists who claim to be empiricists

[Anonymous No.8744315]

>>8744310
naturals don't end because if you can conceive of a number I can always conceive of a bigger one

>>8744311
if you say so, buddy. but I'm not an empiricist. That doesn't mean the sky wizard from your ancient book of desert goatfucker fables is real, though.

[Anonymous No.8744316]

>>8744310
you dont have to count everything

you can just count the same object over and over again

[Anonymous No.8744317]

>>8744276
Thanks, I will!

[Anonymous No.8744320]

>>8744316
But in a Set objects should be different. Or you can say that N ={0}
>>8744315
> Naturals dont end up because they are defined such that they dont end up.
> God exist by definition.

[Anonymous No.8744327]

>>8744320
>But in a Set objects should be different. Or you can say that N ={0}
the atomic makeup of any object changes over time, so each time you count it it's different

[Anonymous No.8744330]

>>8744327
You will need an infinite amount of time to count it.

[Anonymous No.8744332]

>>8744330
>You will need an infinite amount of time to count it.
so?

[Anonymous No.8744335]

>>8744330
What I mean is that you havent proved that something with a property "infinte" exist.

[Anonymous No.8744338]

>>8744330
>>8744332
and actually you don't, just count the first object after 1/1^2 seconds, the second object after 1/2^2 seconds, the third object after 1/3^2 objects and so on and so forth

then you will have counted all of them before pi^2/6 seconds have elapsed

[Anonymous No.8744340]

>>8744332
You cannot just divide time by infinitely small parts because
>>8744335

[Anonymous No.8744342]

>>8744340
1/n^2 is always a finite number

[Anonymous No.8744344]

>>8744320
naturals don't end because the sum of any two numbers in N is also in N
So the elements of N get arbitrarily large; there is no largest element

There are numbers in N larger than the number of particles in the universe
There are numbers in N larger than the total number of ways you could arrange the particles in the universe
And yet there isn't a number in N small enough to express the number of contributions you will make to mathematics

[Anonymous No.8744348]

>>8744342
At some point you can just run out of larger "n"s.

[Anonymous No.8744350]

>>8744348
>At some point you can just run out of larger "n"s.
proof?

[Anonymous No.8744357]

>>8744350
This is essentially to disprove that N exists. I cannot do it, because I started with it in the first place.
>>8744344
Made me think.

[Anonymous No.8744362]

>>8744357
like i said, count the nth object 1/n^2 seconds after the last object you counted

then you will have counted them all by pi^2/6 seconds

(this is a finite amount of time)

[Anonymous No.8744363]

>>8744344
Sum of 2 naturals may not exist. If it exist "by definition" it is not a proof.

[Anonymous No.8744369]

>>8744362
This almost convinced me, I am juat interested how will you divide time in a piece shorter than Plancks time.

[Anonymous No.8744371]

>>8744357
of course you can't disprove the existence of N if you start with it; that's why I said the existence of N is an axiom. I'm not going to prove it. You're not going to prove it. Nobody needs to prove it. You can demonstrate it.
>>8744362
This only works if you can count multiple objects per planck second

[Anonymous No.8744372]

>>8744371
>>8744369
planck seconds only limit how fast light can travel, not how fast thought can travel, you brainlets

[Anonymous No.8744376]

>>8744372
> thought
Why not soul?

[Anonymous No.8744377]

>>8744372
if your neurons can fire faster than a planck second then we truly are brainlets in your midst, ascended one

[Anonymous No.8744381]

>>8744371
> of cod the existence of God is an axiom. I'm not going to prove it. You're not going to prove it. Nobody needs to prove it. You can demonstrate it.

[Anonymous No.8744385]

>>8744381
I eagerly await your proof that God exists
I'm even more enthusiastic if it involves you necking yourself and then reporting back to me

[Anonymous No.8744384]

>>8744381
where have you ever seen an axiomatic treatment of god?

[Anonymous No.8744391]

Gödel's incompleteness theorems say that
a) any consistent axiomatic system (i.e. set of axioms) encoding arithmetic will not be able to prove certain arithmetic results;
b) the consistency of the axioms cannot be proved within the system.

Can we avoid these pitfalls if we just take a proper class of axioms, instead of only a set of axioms?

[Anonymous No.8744406]

>>8744391
You forgot that the set of axioms must be semi-decidable for the theorem to hold. You can get a consistent and complete theory with an undecidable set of axioms, it's just not very useful

[Anonymous No.8744408]

>>8744391
You can avoid the pitfalls if you have two separate classes of axioms that are capable of proving things about the other class

Like arithmetic and meta-arithmetic

[Anonymous No.8744787]

>>8744300
It's a French university. I think its complete name is "Université de PAU et des Pays de L'Adour".

And holy fuck did you guys take the God bait. Also, how do you guys study from textbooks? Do you just read them because you'll remember everything? Take notes? Make diagrams? Capture the main ideas in bullet points? Something else entirely?

[Anonymous No.8744864]

>>8730849
You may want to look into derived categories/twisted completions and stability conditions. In mirror symmetry we have some examples of complicated categories that are generated by very simple subcategories.

[Anonymous No.8744869]

>>8744391
You also need that the axioms are recursively enumerable for Godel's incompleteness.
See https://en.wikipedia.org/wiki/True_arithmetic

[Anonymous No.8745048]

>>8744864
I will. It seems that the stuff I had had already been done, though, but thanks for the tip nevertheless! It's nice to learn new stuff.

[Anonymous No.8745072]

>>8744369
>This almost convinced me, I am juat interested how will you divide time in a piece shorter than Plancks time.
Hardest I've kek'd all week.

[Anonymous No.8745080]

>>8745048
Read ch.4 &5 of this book https://www.amazon.com/Dirichlet-Branes-Symmetry-Mathematics-Monographs/dp/0821838482/ for a good introduction

[Anonymous No.8745085]

Is mathematics of any use in chemistry ?

[Anonymous No.8745099]

>>8745085
https://en.wikipedia.org/wiki/Space_group

[Anonymous No.8745110]

I'm studying various graph theory topics to help me develop efficient algorithms for parallel computing. Specifically, I'm trying to develop better methods for simulating chemistry.

So far, I found a way to identify atoms and molecules as integers.

First, assign prime integers to the 118 atoms. H=2, He=3, ... Uuo=647. these are our "atomic primes".

Second, assign composite integers to molecules. The composite integer assigned to a molecule should be equal to the product of the molecule's set of atomic primes.

Ex:
Hydrogen = 2
Oxygen = 19
Water = 76 = 2*2*19 = HHO = H2O

I think something in graph theory could help me find a way to represent molecule geometry as multidimensional arrays.

[Anonymous No.8745172]

>>8745110
Except that product is degenerate, isn't it ? I'm pretty sure there are numbers that have two prime numbers decompositions. You would have ambiguity between two molecules.

[Anonymous No.8745180]

>>8745080
How much algebraic geometry should I know to understand that book?

[Anonymous No.8745232]

>>8745180
For chapters 4&5, just the basics on projective varieties over C should be enough. I think chapter 8 involves formal schemes, but that is just for the actual proof of HMS for elliptic curves.

[Anonymous No.8745234]

>>8745172

Our good friend, the Fundamental Theorem of Arithmetic, proves there is only 1 set of prime factors for any composite number.

If my explanation seems incorrect, I may have explained it poorly.

If two molecules share a similar identity, they will have a the same composite identity and atomic-primes. Finding a way to represent a molecule's geometry using matrices will help me differentiate molecules beyond their atom composition.

[Anonymous No.8745253]

>>8745232
That's not too much work, then. Thanks. I'll get that book.

[Anonymous No.8745263]

>>8745234
Well, I learned something new today.

[Anonymous No.8746694]

>>8744787
Les places au CNRS dependent de la spécialité. ex= math-phy c'est 1 nouvelle place par an, au niveau mondial.
Ce qui compte c'est la thèse : le sujet + le superviseur disponible pédagogue, la fac et ses conf, puis le jury.
Quoiqu'il arrive, pour le CRNS, il faut être dans les plus jeunes, à compétence equivalente avec les autres candidats. [idem pour rentrer au M2 de Ulm soit en math soit physique théo]
après la thèse, les gens enchainent des postdocs jusqu'à ce qu'ils trouvent un poste d'enseigneant chercheur dans une fac, ou bien un poste de chercheur au CNRS.

tu veux faire des math pure ? tu veux faire quel M2 ? quelles sont tes notes ?

[Anonymous No.8746718]

>>8745110
what about molecules with different chiral forms?

[Anonymous No.8746721]

>Physics major 4.0 GPA
>PhD atm
>Dark matter
My thesis is heavily based on Einstein theorems. Im almost finished with it. Almost 400 pages. Supernervous
>Book recomendations:
-The flat earth & genesis (myfav)
and of Mein kampf

[Anonymous No.8746723]

>>8746721
>haha le trole xdd

[Anonymous No.8746800]

Any UNSW fags here. Help me with MATH2111 please

[Anonymous No.8746814]

>>8746694
Pas l'espagnol.

Et merde, il est temps de mettre mes rêves et mes espoirs au placard.

[Anonymous No.8746831]

>>8746814
Tu peux faire 2 m2, mais fait les en mm temps, au lieu de l'un après l'autre. Les anglo saxons ne se préoccupent pas trop de l'âge des candidats, on peut être en thèse à 30 ans avec eux, donc c'est permis de prendre son temps, si les 2 m2 sont complémentaires et que les notes suivent.

[Anonymous No.8746836]

Le compromis c'est faire un m2+l3 en mm temps
ou une thèse+l3 en mm temps

[Anonymous No.8746837]

>>8746831
Je ne pense pas que ce soit possible. La je suis en L3 d'études d'ingé dans une école ni trop réputée, ni trop nulle. Je pense faire un master optique et nanotechnologies en double-diplôme.
Après ça, sans doute une thèse en physique expérimentale puisque de la physique théorique ou bien des maths ça risque d'être tendu.

Autrement dit, adieu le CNRS.

[Anonymous No.8746852]

>>8746837
si tu veux faire phy-theo, fini ta l3 puis regarde la l3/magistere de phy-theo d'orsay.
Cette l3 est bien pour ceux qui viennent de prepas sans vouoir être ingé. Après, tu fait le m1 à orsay, puis le m2 dans une ENS, puis these dans une ENS ou X ou CEA [uniquement pour les cordes...] ou ailleurs.
Il y a pleins de M2 de physique à orsay, mais pas de théorique.
Puisque Orsay a de bons labos de physique théorique et experientale, tu feras de bons stages sans trop chercher ailleurs.
Pendant la l3 ou le m1 de physique, tu peux mm tenter la l3 de math d'orsay [surtout si tu viens de MP], ou t'inscrire à la l3 de math de l'upmc, par correspondance.

Il y a mm des centraliens qui y viennent en cours du soir de la l3 pour apprendre la MQ, l'optique et les TPs et se penser scientifiques.

Prepare au moins un dossier de candidature pour la prochaine rentrée de la L3 de physique d'orsay.

[Anonymous No.8746855]

J'avais déjà fais un message sur orsay d'ailleurs
https://boards.fireden.net/sci/thread/7772003/#7773486

[Anonymous No.8746890]

>>8746852
>[surtout si tu viens de MP]
J'ai fait prépa intégrée :^) :^(

[Anonymous No.8747606]

>>8746694
Answering in English because I'd rather be clear and not fuck up.

> tu veux faire des math pure ? tu veux faire quel M2 ?
That's what I'd like, yes, but I'm not sure if that's really what I want, and I'm probably not cut for it, so I'm considering doing the "Parcours mathématiques, modélisation et simulation" master that PAU offers and then try to have someone take me as their PhD student in geometry despite my masters being specialized in something else (numerical methods would work too). The masters is essentially a backup.

> quelles sont tes notes?
I have an average of ~8.5 that I might be able to take to a ~9. That's considered high in here, but this place is a shithole, so it's probably shit elsewhere.

I also still don't fully understand how the coordination will work because here undergrad is 4 years long, while your licence is 2 years, and I'm not sure I can take advantage of that and have 6 years worth of education.

[Anonymous No.8747647]

>>8741380
I'm still not sold on it. Every time you use it, it just feels like handwaving.

[Anonymous No.8747712]

2nd year math major physics minor pleb here
>researching
Working on an internship at plane manufacturer
>studying
Calculus to no end
>reading
Everyday Calculus by Fernandez
(Recommend me books if anyone has any good ones)
>theorems
Working on an idea about how the Big Bang should have caused the Universe to spin

[Anonymous No.8747722]

>>8741380
I don't like it but math without the axiom of choice looks so stupid that I'd easily rather just live with an odd axiom with some odd implications

[Anonymous No.8747819]

>>8747647
It has never felt like that. Have you tried to do algebra without Zorn's lemma?

[Anonymous No.8747880]

>>8747647
>it just feels like handwaving
Fucking undergrads

[Anonymous No.8747886]

>>8738699
Math is done best while on your period. The hormones make you more creative.

[Anonymous No.8747889]

>>8741380
You can get by without it most of the time, but I still make a point of using it whenever I can to spite the smug undergrads I TA

[Anonymous No.8747917]

I'll soon have my masters degree and I still feel like a brainlet reading most of the posts ITT. How long did you study those highly advanced topics?

[Anonymous No.8748076]

h-hello everyone

https://www.youtube.com/watch?v=mwcNETa0KFI

am i just a brainlet or this guy went ahead of the lecture(he talks about ant(G) or something )

coming from linear algebra i find this lecture pretty hard to follow

[Anonymous No.8748113]

>>8748076
Why are you watching group theory lectures when you obviously don't have the foundation for it?

[Anonymous No.8748134]

>>8747917
Algebra and topology since spring 2015, categories since late December of the same year, I guess.

[Anonymous No.8748137]

>>8748113
You don't need any prereqs for algebra.

[Anonymous No.8748142]

>>8748137
Except for the concept of proof

[Anonymous No.8748144]

>>8748113

he said if you come from linear algebra its enough, what is the foundation for group theory?

p-please dont be mad at me

[Anonymous No.8748149]

>>8748142
That's trivial.

[Anonymous No.8748159]

>>8748144
>what is the foundation for group theory
Abstract thought + notion of proof.
The symbol is Aut which stands for automorphism group btw.

[Anonymous No.8748164]

>>8748144
You should have seen the definition of a group in lin alg already, as it is needed for the definition of a field and consequently a vector space.

[Anonymous No.8748172]

>>8748159

i took discrete math, and i know my way around proofs (took real analysis)

is that not enough :( where else do they teach homos and autos then? never heard them used anywhere.

>>8748164

maybe i went to a brainlet uni but my LA does cover up to vector spaces but they never deal with the very basic foundation of them....or i took the engineer's class

but there's another class called "Algebraic Structures" where we do learn about groups and stuff

[Anonymous No.8748192]

--------> >>8748188 <--------

[Anonymous No.8748302]

>>8748172
That's because you learn them in this course dummy.

[Anonymous No.8749421]

>>8747606
Il faut faire des maths si tu veux faire des maths pures, donc inscris toi au cours par correspondance de l3 de math de l'upmc

[Anonymous No.8749623]

>>8728665
test

[Anonymous No.8749896]

[; test ;] $ test $

[Anonymous No.8749897]

[; {2} over {4} ;]

[; {int from {2} to {infinity} {x^2}} ;]