/sci/ - Science & Math

>>15854228
>he doesn't know about the Yukariposter
Anon, I ...

>>15503116
>he give any kind of practical use
He mentioned some applications to stuff in quantum optics and OOE dynamics like we had mentioned. However, he did not present anything beyond "oh look there's non-unitarity here".
I was also discussing with him about applications to Tomita-Takesaki theory or superconductivity, but I guess that didn't make it into his thesis. It's unfortunate really.

>>15163257
No matter how hard I or any manager tries there's still a lot of luck in this. That free kick outside the box never happened in testing. Also /aesco/ should be done with the Yukari model by next friday

Poll's closed, the team will be updated accordingly

>>15073336
>>15073551
Yukariposter is a very special kind of shitposter, don't even try to lump him in with the rest of us.

Bumperooni.
https://eudml.org/doc/164885

>>11397661
>induction
>beautiful
Oh honey...
>>11397782
That's the case for me with Ueno. Barely understood any of the alg-geo Kodaira-Spencer stuff in Chapter 1 but the affine Lie stuff in Chapter 2 was smooth sailing. Felt like passing a kidney stone.
>>11400848
Yeah.

>>11310028
Fun anal (OA and *-rep theory, PDE/optimization), topology (alg and diff), geo (anal and diff), alg (Lie and affine Lie and rep theory).
You can pick up a mathematician at the shelter and he'll teach you all that stuff.

>>10231040
I've taught modulo arithmetic to 4th graders with clocks. That list itself probably isn't doable but things can certainly be sped up compared to the standard curriculum.

>>10117862
Hypergeometric functions are solutions to the conformal blocks of a conformal field theory with the affine Lie algebra [math]\mathfrak_\mathbb{C}{sl}(2)[/math] on the Riemann sphere (complex projective line) [math]\mathbb{A}^1_\mathbb{C}[/math]. The coupled ODE they satisfy are the Knizhnik–Zamolodchikov equations, which is a necessary condition on the conformal blocks in the highest-weight Verma modules [math]V_\mu[/math] satisfying the quantum Clebsch-Gordan gauge condition for the existence of a singular (cyclic vacuum) vector.

>>10114324
>integrable polarization
A polarization is a Lagrangian subbundle [math]P\subset TM[/math] of the tangent bundle such that [math][P,P]\subset P[/math], where orthogonality is defined in terms of the symplectic form. Define [math]D = P \cap P^\perp \cap TM[/math] and [math]E = P \oplus P^\perp \cap TM[/math], [math]P[/math] is integrable if
1.[math][E,E] \subset E[/math],
2. [math]M/D \rightarrow M/E[/math] is a submersion of smooth manifolds.
When [math]P[/math] is integrable, you're able to "polarize" out coordinates in [math]P^\perp[/math] on [math]M/E[/math]. For instance, holomorphic quantization is achieved by taking the integrable Kahler polarization [math]P[/math] that polarizes out vector fields [math]X = X_i \partial_{p_i}[/math] after prequantization. This makes [math]P[/math]-wavefunctions holomorphic and momentum independent.
>leaves of a foliation
A foliation is a family of diffeomorphisms [math]\varphi_i:U_n \rightarrow U_m[/math] between opens sets in Euclidean spaces such that [math]\varphi_i^{-1}(U_m) \cong U^{n-m}[/math] for each [math]1 \leq i \leq n-m[/math], and each preimage intersect transversally with each other. A leaf is a (n-m)-dimensional subset of [math]\varphi_i^{-1}(U_m)[/math].
It can be seen that an integrable polarization gives a foliation [math]\varphi_i: (x,y)\mapsto (x,y_1,\dots,\hat{y}_i,y_n)[/math] of [math]M[/math], which you can think of as "integrating out" the set of coordinates [math]y[/math] on each local chart of [math]M[/math]. If [math]P[/math] is integrable and if [math]X_H[/math] is a Hamiltonian vector field compatible with it, then trajectories of [math]X_H[/math] lies within leaves [math]\varphi_i^{-1}(U_m)[/math] of the foliation given by [math]P[/math]. This is a purely differential geometric understanding of the fact that "trajectories stay in the level sets of constant energy for time-independent systems".

>representations of semisimple affine Lie groups on Verma modules
>automorphic forms of nodal points on Riemann surfaces and modular curves
>??? (aka geometric Langlands)
>AdS/CFT
>mfw

>>10029118
Kodaira-Spencer gravity.
>>10031157
Mapping class group.
>>10031722
What's confusing you exactly?
>>10036647
Pretty sure I'm doing a PhD at the same place you're at anon. The math building is fucking gorgeous
>>10038527
I'd just have one single question that I focus on, then
>exposition
>strategies
>significance
>applications and implications
That's what I did for NSERC.

>physics grad students
Fun, interesting and outgoing but level-headed, perfect for having a drink with. They're also often multi-talented and can make conversations outside of physics.
Some of them are pretty handsome and decently hung too.
>math grad students
Nice and nerdy but plain; very passionate about their research but less outgoing and well-rounded than physics grad students. Average looks but great inquisitive personalities.
>engineer grad students
Very extroverted and assertive (almost invasive), almost never talks about their research; they're only interesting and decent people if they already were those ASIDE from them being engineers.

Also there are subclasses of physics grad students:
>high energy
Shy and milquetoast.
>cosmology
Big personalities but not very interesting.
>hard cond-mat
Absolute Chads.
>soft cond-mat
Cute and bubbly as fuck.
>experimental
Either a stoner or a virgin.

>>9842787
I personally also play violin, and have given a few solo concerts in the orchestra at the place I'm at now.
Also a few colleagues of mine has this annual whiskey brewing gathering where we all bring our own brewing material and make flavored alcohol. I get shitfaced and flirt with all of my colleagues. It's great.
>>9842788
It's less about what you learn, but more about concurrence of research in NA. The things you learn should also be globally uniform, given the field.
>If I should self-study the whole master program what's the point in enrolling in one and not staying in my place
Because NA masters programs are much more than just learning. It involves active research. Besides, the courses you take can fill in the gaps in the knowledge you've gained from self-studying, and without doing at least some minimal groundwork you can't hit the ground running (though I now understand that it is not necessary to hit the ground running in EU). Again, inefficient system.
>how can they judge if you suit or do not suit to work with them
This is my point, that the NA system does this through your applications, self statements and rec letters, then they immerse you directly in research. Again, the EU system is just inefficient. If you can't do anything about it then I can't help you.