rich

interested in probability theory and mirror symmetry

[rich @descentdatum]

@anisomorphism ye it becomes commutative algebra if u take the ideal corresponding to it, or algebraic geometry if u look at ideal sheaves on more general toric calabi yau's >:D

[rich @descentdatum]

anyone on here still

[rich @descentdatum]

@anisomorphism hello! how is it going

[rich @descentdatum]

classical fact i learned today: if M is a random Hermitian matrix w/ polynomial potential V and W(x) is the large N limit of tr(xI-M)/N then the density of the equilibrium measure is given by -[W(x+i0)-W(x-i0)]/(2 pi i) ( equilibrium measure is large N limit of empirical measure)

[rich @descentdatum]

@SpectralScheme Colimits in the category of groups suck 🤬

[rich @descentdatum]

@computer_dream damn, y'all got room for one more?

[rich @descentdatum]

@littmath @jerrrrryyy_ Yeah @jerrrrryyy_ is right, all you need is monotonicity of expectation.

[rich @descentdatum]

@SC_Griffith but more abstractly one can view \Omega as a 2-form with values in End(E)... idk, i always feel like the last one to the party with this stuff. Apparently on the algebra side these kinds of situations are called curved dg-algebras.

[rich @descentdatum]

@SC_Griffith In this case d^2 s_i = \sum_k \Omega_{ki} \otimes s_k where s_1,...,s_r is some kind of frame given by smooth sections of M \to E, and \Omega_{ki} are ordinary differential 2-forms which form the entries of the curvature \Omega when it's viewed as a matrix of 2-forms.

[rich @descentdatum]

@anton_hilado mannn, every time i read something you write it motivates me to go deeper down a rabbit hole. i started reading up on motives after seeing your mathoverflow question about anabelian geometry and motives.

[rich @descentdatum]

@AraValentini i'm so lost

[rich @descentdatum]

i've really been trying to get into physics ever since i saw this paper: https://t.co/Z16j0frfLY

[rich @descentdatum]

@_nilradical @grassmannian @SC_Griffith @convexcocompact ok go off

[rich @descentdatum]

taking another probability theory exam in 8 hours but this time it's grad level, measure theory gang

[rich @descentdatum]

Taking a stochastic processes final tomorrow and I feel like a complex mix between “as ready as I’ll ever be” or “about to take a fat L”

[rich @descentdatum]

@chlorophyllbich not the ideal response but you could try cigarillos

[rich @descentdatum]

I think these are all good questions that I don't really ask myself, mostly because my only goal right now is to learn more math. I don't see much overlap between the people who claim these questions have universal answers and the people interested in math. I could be wrong tho.

[rich @descentdatum]

Is math real? Is it discovered or invented in the confines of our mind? Why do some of us prioritize the pursuit of mathematical truth over other things in our lives?
Does math actually come from our desire to understand reality? It doesn't for me at least.

[rich @descentdatum]

@teagsy @MeHitchc0ck @littmath Indeed! Ironically a sequence of the form x_{n+1}=9^{x_n} produces very small numbers in Q_3.

[rich @descentdatum]

I feel like the end goal of a lot of the math I’m interested in is to understand certain field extensions.