Lightnews — Scholar-powered news

godslayer @bitdizzy.bsky.social · 1h

Lesgo that's what i wanna see

1.1.2 Dyson–Schwinger equations
In Chapter 4 we study several properties of combinatorial Dyson–Schwinger equations. First,
we give some background (Section 4.1) on the physical significance of the equations, then we
get to work applying the results of Chapter 3 to solve these equations combinatorially. In the
past, solutions to certain Dyson–Schwinger equations have been found as certain generating
functions for rooted connected chord diagrams by Marie and Yeats [41] in a special case and
then Hihn and Yeats [31] in a more general one. The virtue of these expansions is that
3
while the number of chord diagrams of size n (and hence the number of degree n terms in
the expansion) grows superexponentially fast, the contribution of each diagram is relatively
“small” and easy to reason about or compute.

1

godslayer @bitdizzy.bsky.social · 1h

@consume.red joining and splitting they turned zhuang zhou into a combinatorial algebra

godslayer @bitdizzy.bsky.social · 1h

So like, one way to get to acquainted with the social topography of a field is to read a recent thesis in it (if there ain't recent ones everyone's dead RIP), and reference backwards through the results and problems considered important until you find a starting point you're comfortable with.

Abstract
Hopf algebras built from combinatorial objects have found application both within com-
binatorics and, following the work of Connes and Kreimer, in quantum field theory. Despite
the apparent gulf between these areas, the types of Hopf algebras that arise are very simi-
lar. We use Hopf algebra techniques to solve two problems, one coming from quantum field
theory and one from algebraic combinatorics.
(1) Dyson–Schwinger equations are a formulation of the equations of motion of quantum
field theory. From a mathematical perspective they are integro-differential equations
which have a recursive, tree-like structure. In some cases, these equations are known
to have solutions which can be written as combinatorial expansions over connected
chord diagrams. We give a new expansion in terms of rooted trees equipped with a
kind of decomposition we call a binary tubing. This is similar to the chord diagram
expansion, but holds in greater generality, including to systems of Dyson–Schwinger
equations and to Dyson–Schwinger equations in which insertion places are distinguished
by different variables in the Mellin transform. Moreover we prove these results as a
direct application of a purely Hopf-algebraic theorem characterizing maps from the
Connes–Kreimer Hopf algebra of rooted trees (and variants thereof) to the Hopf algebra
of univariate polynomials which arise from the universal property of the former.
(2) A pair of skew Ferrers shapes are said to be skew-equivalent if they admit the same
number of semistandard Young tableaux of each weight, or in other words if the skew
Schur functions they define are equal. McNamara and van Willigenburg conjectured
necessary and sufficient combinatorial conditions for this to happen but were unable to
prove either direction in complete generality. Using Hopf-algebraic techniques building
on a partial result of Yeats, we prove sufficiency.

1 3

godslayer @bitdizzy.bsky.social · 1h

This is so much easier with mathematics finding your way through physical and social sciences is so hard. you don't get forum beef in publications.

godslayer @bitdizzy.bsky.social · 1h

So like, one way to get to acquainted with the social topography of a field is to read a recent thesis in it (if there ain't recent ones everyone's dead RIP), and reference backwards through the results and problems considered important until you find a starting point you're comfortable with.

2 2

godslayer @bitdizzy.bsky.social · 1h

sickos yes!

1 3

godslayer @bitdizzy.bsky.social · 1h

looks fun to read :) www.math.uwaterloo.ca/~kayeats/stu...

www.math.uwaterloo.ca

1

godslayer @bitdizzy.bsky.social · 1h

learning quantum field theory

Some Applications of
Combinatorial Hopf Algebras
to
Integro-Differential Equations
and
Symmetric Function Identities
by
Nicholas Olson-Harris

1 4

godslayer @bitdizzy.bsky.social · 1h

siri can you explain how to sum over feynman diagrams with more concrete obects like hopf algebras and group characters thank you siri

3

godslayer @bitdizzy.bsky.social · 1h

it's also just a really good post that's a valid answer too

1

godslayer @bitdizzy.bsky.social · 2h

What if there should only be a polynomial amount of feynman diagrams as you extend out the perturbative expansion it'd be so funny if nature said "exponential combinatorics is fake and gay (derogatory)" :^)

3

Reposted by godslayer

Helen @homotoptheory.bsky.social · 2h

dril tweet: the wise man bowed his head solemnly and spoke: "theres actually zero difference between good & bad things. you imbecile. you fucking moron"

1 1 10

godslayer @bitdizzy.bsky.social · 2h

reading this like a koan namo guanshiyin pusa

1 1

godslayer @bitdizzy.bsky.social · 2h

yeag cognition disease etc.

1 1

godslayer @bitdizzy.bsky.social · 2h

makes perfect sense actually like those are two different Modes and it takes a lot of energy to switch modes

1 5

Reposted by godslayer

Helen @homotoptheory.bsky.social · 2h

gonna tell my kids this was ultrafinitism

godslayer @bitdizzy.bsky.social · 2h

it is insane how much theory fits into 300 characters

1 8

godslayer @bitdizzy.bsky.social · 2h

Long Mathematician (Topology)

Long line (topology) - Wikipedia

en.m.wikipedia.org

2

godslayer @bitdizzy.bsky.social · 2h

it is insane how much theory fits into 300 characters

10

godslayer @bitdizzy.bsky.social · 2h

Well, for starters, the holocaust ended immediately for gay people in East Germany instead of being forced to finish their nazi sentences into the 50s

1 2

godslayer @bitdizzy.bsky.social · 2h

RULE FIVE OF SALTY THOT— NEVER TRUST A BITCH WITH A THEORY OF EVERYTHING

1 24

Reposted by godslayer

🏳️‍⚧️ mixie 🏴‍☠️ @mixiekitten.goodgirls.onl · 1d

only need $80 more! thank you too everyone who has helped so far

cashapp: $maidenmeow

🏳️‍⚧️ mixie 🏴‍☠️ @mixiekitten.goodgirls.onl · 9d

unfortunately I am still having to ask for donations. I know everyone is stretched thing right now, but if I could at least get $200 in the next two weeks to catch up on my phone bill, that would help me so much. i think i'm close to getting a job, finally. thank you all ❤️

gofund.me/dd2ab73c

Donate to Help Mixie Afford Bills and Stay Afloat, organized by Mixie Meow

I'm moving across the country to be with my girlfriend, and I have bills and things… Mixie Meow needs your support for Help Mixie Afford Bills and Stay Afloat

gofund.me

4 4

godslayer @bitdizzy.bsky.social · 4h

a cartoon of a man with blonde hair and a blue and orange shirt

Alt: goku thumbs up

media.tenor.com

godslayer @bitdizzy.bsky.social · 4h

evidence of map game time travelers in the historical record

Reposted by godslayer

[LVL 35]Alsvid Wotansdottir🔵 @alsvid.bsky.social · 4h

Can we get Darling boosted?

Darling 🤍 @ohhdarling.bsky.social · 9h

Please send $10 for food..

cash.app/$KymSlade

Pay me on Cash App

Instantly exchange money for free on Cash App

cash.app

2 3

Reposted by godslayer

axolotl lovely / fka frog k ⚧️🏴‍☠️ @vaporlight.bsky.social · 23h

imo the final boss of "weird historical vicissitudes that defy pop history" is that the effective end of any indigenous rule in India on any scale independent of the BEIC/Raj & the princely system was an ally of Napoleon Bonaparte whose country had fairly mature military rocketry

2 2 22

Reposted by godslayer

Paul Eric Scannell @pauleric70.bsky.social · 18h

Twitter BANNED the creator of this ad because it moves voters 7 pts toward Dems.

Voters are DISGUSTED by Trump’s gestapo kidnapping US citizens in Portland and Chicago.

SPREAD THIS EVERYWHERE

2 130 220