#representation theory

[miscellaneousmathematics]

[lipshits-continuous]

In my representation theory course this term we're moving onto representations of Lie Groups and I was wondering is there are results about how the homotopy groups/(co)homology groups of a Lie group affect what representations can exist of that Lie group?

[studywith-minmin-shelved]

[5/6/24] wow im back so soon? yes, it is to complain about matrix groups again. I may have girlbossed too far w my paper here but its too late to change. NEVER BACK DOWN NEVER WHATTTT (give up on my dreams and lie down)

I am GOING to finish this proof whether it kills me (I could never be a mathematician)

[coming-up-with-usernames-is-hard]

PhD Blog Week 2

I saw @positively-knotted doing this and thought it looked like a good idea, hopefully if we're both doing it we'll keep it up. I'm starting at week 2 so we have consistent numbering

Reading

Solitons, differential equations, infinite-dimensional algebras (Date, Jimbo and Miwa), Chap 4, started reading about the Fock representaiton of the bson and fermion algebras. Hoping for more of the infinite-dimensional algebras and less of the differential equations, which seems to be the case in this chapter

Bombay lectures (Kac and Raina), tried to read Chap 4 on the boson-fermion correspondence, had to go back and read the first 3 chapters just to get familiar with the notation

Courses

Lie theory, missed the lecture this week, but read through the notes, defined representations of a Lie algebra and classified irreps of sl2

No other courses started yet, next week I'll be taking conformal field theories and vertex operator algebras, and differential topology

Talks

Attended the integrable systems seminar about a generalisation of a class of differential equations, the slides were full of differential equations but I think I followed the key ideas

Started thinking about the example class I have to give, the Fock representation seems like a good thing to talk about, but I may have to explain some QFT

Reading Groups

Attended the Representaiton Theory and Complex Geometry (Chriss and Ginzburg) reading group, we started with a recap of Lie theory, which should be fine, but I'm sure I'll get lost as soon as we start discussing varieties. Despite that, I've agreed to give a talk about flag varieties, so I've got some reading to do

Starting a category theory reading group next week, and an infinity category reading group, which I plan to attend until I no longer know what's going on

Teaching

TA'd two first year classes, the first had almost 100 people, the second was almost empty, looks like no one wants to choose the Friday class

I'm looking forward to the first full week of courses and my first proper supervisor meeting

[homie-o-morphism]

Ok so given a group action (thought of as a functor G -> Set), we can construct it's action groupoid which has a nice covering map back to G. Well, Hopf algebras are kind of like groups internal to Vect(K). So given a groupoid G and a functor G->Vect(K), can we form a Hopf algebroid analgous to the action groupoid? From some initial investigation I think the answer is yes. The next question is what is the analogue of the covering map to G? Maybe a map of Hopf algebroids with codomain K(G)? But in what sense is it "covering"?

[dearmyloveleys]

Suho and Sieun being tied by the invisible string theory is so incredibly unspoken about. What do you mean they probably spent months to a year not acknowledging each other’s presence in the same classroom? What do you mean for months, Suho has been sleeping in the classroom until dawn and Sieun is the first to enter the classroom but they don’t interact? All the shared award ceremonies, PE lessons, chem lab practicals? It only takes one accident to set off everything between them.

[manichewitz]

straight men will write stories where two men choose each other over women over and over and again and the narrative will continuously emphasize the bond between the two men over all other emotional connections…and then get confused when queer people relate to that for some reason

[ihavea-natural-curiosity]

Viktors Disabilities, a Speculative Analysis

Ever since i first watched Arcane i have wanted to know (and i mean this in the nicest way possible,) what was wrong with Viktor. His disability was never explained beyond “he was born with a malformed leg”.

And so, i was left alone in the house with my thoughts today so i took it upon myself to figure it out, (and talk about his medical issues so i can ignore my own lmao) and i am releasing my thoughts upon yall!

(disclaimer: yes i am aware that this arcane is a fantasy world that is not our world and the disorders/illnesses and treatments will not be the same but the issues he has have to be based off of something (especially with how detailed this show is and how many references are made throughout.) this is not me trying to say that he definitively has any of these conditions, i’m just comparing them to conditions that exist today and suggesting what Viktors disabilities may have been based off of.)

(disclaimer pt 2.: i have not played League of Legends, i do not intend to play League of Legends, i have only watched Arcane and i am only talking about Arcane and Arcane lore and what i have been able to figure out from watching Arcane and spinning it around in my brain like it’s in a microwave.)

Now, i think i’ll just start from the beginning, and go in order of development.

1. Viktors Leg

According to the wiki (and about every other site that talks about Viktor) he is said to have been “born with a malformed leg”, and said pretty much nothing else. Now, when Viktor is an adult, his leg appears to be very not-malformed, so, let’s start at the flashback.

Now, even in the flashback Viktors leg looks normal. It’s pointing forward, and looks totally fine. But as the clip goes on, and he gets up and starts moving, the problem becomes apparent. Here’s a clip:

Yall have probably already noticed what i’m talking about with this clip, but i want to illustrate it more because the clip moves so fast:

As Vikto moves faster, his foot shifts inwards! It shifts inwards pretty severely (i mean, he full on trips on it), and the only time in this entire clip where it is doing so. And that is because the other times he is around someone else. I think he is purposefully pointing his foot forward and in turn walking on the wrong part of his foot (balance issues), and more than likely causing himself pain 1. to appear less ‘crippled’ and more “normal” to other people, and 2. because clearly, his foot is pointing inwards to a degree that is impairing his ability to walk.

Now to me, (and i’m not a doctor so if any actual doctors want to call me on incorrect information please do so!) this looks like Femoral Anteversion, or a twisting of the femur that points the knees inward (it’s typically found in both legs but it can happen with just one)

Now this isn’t necessarily a terrible thing, ~10% of children are affected with Femoral Anteversion (or “pigeon toes”), and most of the time it resolves itself, unless it is super severe, at which point it requires surgery to fix it. Which, of course, Viktor did not have access to.

Now, his leg does appear to be normal as an adult, but the femoral anteversion thought is still plausible. There are 3 reasons i can think of for this one.

1. He got to Piltover and after a little bit Heimerdinger noticed how messed up his leg was and Viktor got the surgery to correct it as much as possible (it’s implied that Viktor was in Piltover for years, based on how he acts and the fact that he’s Heimerdingers assistant) (this thought doesn’t seem very plausible to me, i don’t remember seeing any surgery scars on his leg in the hexcore scene, but it is a possibility.)

2. He’s simply just still correcting his leg. The reason we wouldn’t see him mess up like we did in the flashback is that he’s about 24-25 in act one, and i’d say that 14-15 years is probably enough to get used to doing that sort of thing.

3. (Honestly this one seems to be the most plausible to me) His leg has (partially) corrected itself. Most children whose femoral anteversion fixed itself had normal gaits by age 8-10, but that’s an average age and those typically aren’t perfectly accurate to everyone (i have. very personal experience with that.) and it makes the most sense to me that his leg has mostly/partially corrected itself and he’s just also continuing to self-correct to avoid appearing any more disabled than he already does (he shows quite a bit of internalized ableism throughout the season, and his line about people not listening to him because he’s “just a poor cripple from the undercity” really drives it home for me, honestly.)

2. Viktors Deterioration

When we first truly see Viktor in act 1, he seems lively, and unless he’s actively walking, he’s not using his cane, not really (he hangs his cane on his arm to read a book with both hands (really great rep btw, we do in fact do that!), he leans it against a desk to pace in front of a chalkboard with Jayce, he puts it down somewhere to go help Jayce with the experiment, etc.).

I mean, look at his stance, he’s not really leaning on his cane for support, more likely he’s using it for balance, and as an assist to his bad leg, rather than an attempted replacement like we saw in the flashback.

But in act 2? Hoooo boy

Look at that, beyond just looking 10x sicker, look at his posture, his shoulders specifically. He is actively leaning on his crutch (because he needs a crutch now, the cane wasn’t enough), using it like a replacement. Now, over the course of the ~7 year time skip, Viktors condition has deteriorated enough that he 1. needs the braces 2. needs a crutch 3. can no longer even get up without his crutch, let alone take a single step!

i mean, even when he’s sitting down, he’s holding onto it, leaning on it. The way he uses his crutch, how skinny he’s gotten, how much more tired he seems, all of these things say some sort of newfound muscle weakness, but why?

And the braces. Let’s start with the leg brace, since it’s right there. How it’s built around the actual leg and knee looks a whole lot like a much cooler unloader knee brace, or a knee brace that redistributes weight away from the weakened knee. I have to wear one of those when my knee gets really bad in the winter, when it starts buckling randomly and just.. not working. Which makes sense for the muscle atrophy/weakness theory i have, because that leg was already weak to begin with, and his knee would have been all kinds of fucked up if he did spend basically his whole life misaligning it like i’m thinking he did. (and to support that theory even further, the way that the brace goes over his foot as well reminds me of the braces some children wear to attempt to correct their ‘pigeon toes’ (which have been proven not to work, btw)

Now, the back brace. I’m gonna be honest, this part took me the longest, it truly confused me.

When you look at it, it just looks like a thoracic back brace, with some extra support on the hips (once again, pointing to muscle weakness)

But the thing that really confused me?

The screws in his back.

It took me an embarrassingly long time to figure out what procedure this was referencing (Percutaneous Pedicle Screw Fixation (i’m like really sure that the screws aren’t showing in the real life surgery but the fact that they are makes sense with Arcanes style)), and an even more embarrassing amount of time to realize that the golden screws in his brace weren’t connected to him. (i am. very tired.)

But essentially, a Percutaneous Pedicle Screw Fixation is a less invasive spinal fusion procedure. Now a spinal fusion can be done for many, many reasons, but only one really fit.

Support, because of muscle weakness.

Every single thing that got added on to Viktor could be explained by muscle weakness, but there’s never any explained reason why he was so weak all of a sudden. His terminal illness is cited as a reason but that didn’t really make sense to me, all of these procedures, all of these mobility aids made perfectly to his measurements would’ve had to have been caused by something with a much slower onset than the illness would have given him.

And after literal hours of scouring, i have a theory.

Post-Polio Syndrome.

The timeline makes sense, Viktor would have most likely gotten sick before the flashback, when he was a child (a lot of children who get Polio fight it off without even knowing they have it). Viktor is estimated to be about 32 in act 2, and the average time between the initial Polio infection and Post-Polio Syndrome onset is about 20-40 years (inconsistent numbers).

Now some of the symptoms we have no way of knowing if they affect Viktor or not, but the main ones that caught my eye were muscle atrophy, chronic fatigue, and, you guessed it, muscle weakness.

Given where Viktor lived as a child, and how heavily polluted it was (remember that Viktor was in the undercity over 10 years before we saw it in act 1 with Vi and Powders childhood), it’s not too far of a stretch to say that he could have contracted an illness very similar to Polio as a child, and only really be feeling the affects of it now.

3. The Illness

I have 2 main theories for Viktors illness, the first one seems to be the most popular among the fandom: Tuberculosis.

If you’re unaware, Tuberculosis (TB) is a sickness that mainly affects the lungs, with the main symptom being coughing up blood. Now this is a really good theory imo, it fits pretty well, with some of the other symptoms being muscle atrophy, fatigue, malaise (general feeling of discomfort/unease with no discernible reason), loss of appetite, and severe unintentional weight loss. all of this sounds like our guy, no?

TB can take weeks to be symptomatic, so we probably just caught Viktor at the worst time ever lol with this theory.

My other theory is actually one my friend suggested to me, and that theory is COPD.

Chronic Obstructive Pulmonary Disease (COPD) is a progressive disease that is basically a terrible combination of chronic bronchitis and asthma that can be caused by exposure to pollution (Viktor grew up in the Undercity before Cassandra’s vent system, i mean the river he was playing on had an oil slick on it, i think it’s safe to say he was exposed to some pretty severe pollution as a child.)

This theory makes a lot of sense to me, because it’s said in the show that his illness was probably caused by the air where he grew up, which this would have been, while TB would not. (not 15-20 years later, at least) COPD, once it reaches stage 4 is very severe, any flare up of symptoms could be life threatening at that stage, and the symptoms? Fatigue, shortness of breath, coughing, weight loss, and less frequently, coughing blood.

Anyway, i guess that concludes my analysis/comparison? I’m gonna repeat that i’m not definitively saying that ‘he has this condition and this is why!’, i’m just analyzing and speculating on what different parts of his disability is based on in real life. So, let’s just all be nice, yeah? (also PLEASE feel free to use this as a reference point for modern aus and stuff!!)

i do genuinely think that Viktors disease progression and his deterioration is one of the best examples of chronic illness that i have seen in media, in my experience (both with my own issues and what i’ve seen in other people) and Viktor himself is one of the BEST representations of what it’s like to be young and disabled and the internalized ableism that comes with it (if anyone wants to hear about that i will happily yap your ear off about it!

Anyway, for real this time. Yap session over.

[edit: if you like this you should look in the reblogs there’s a couple of really good in-depth deep dives from others that build on this!!]

[bixels]

As cameras becomes more normalized (Sarah Bernhardt encouraging it, grifters on the rise, young artists using it), I wanna express how I will never turn to it because it fundamentally bores me to my core. There is no reason for me to want to use cameras because I will never want to give up my autonomy in creating art. I never want to become reliant on an inhuman object for expression, least of all if that object is created and controlled by manufacturing companies. I paint not because I want a painting but because I love the process of painting. So even in a future where everyone’s accepted it, I’m never gonna sway on this.

if i have to explain to you that using a camera to take a picture is not the same as using generative ai to generate an image then you are a fucking moron.

[commsroom]

still getting a grasp on this whole no gravity thing (by @jamisonrivv)

[dissonantpapersouls]

@disabled.daisy

I've noticed that abled people (NT's included) call "innovative" and "efficient" things lazy. If I can do things an easier way in a shorter amount of time while expending less energy, it's working smarter, not harder. Are they insecure because of their antiquated attitudes and lack of ingenuity? Why waste time, money and energy? They love menial unnecessary tasks that don't matter and when there's a faster/better way they think they're better than us for unnecessarily taking longer. Do they just want to feel better about their inadequacies by degrading and belittling others?

[miscellaneousmathematics]

[pep-the-artemis]

Colour blindness in Murder Drones

can we talk about how colour blindness is very common in Murder Drones.

In all the POV shots, the only character who see's colours is Doll while Uzi, N, and Kenzie Day are all colourblind (specifically cone monochromacy). We also know Alice isn't colourblind since she identified Nori's yellow eyes.

So when Uzi's eye(s) turn yellow or bleeds blood instead of oil; no one points it out because most characters wouldn't be able to tell.

Edit. if you look in the reblogs, I've done a lot more investigating and found N is colour blind but not Uzi. Check it out.

[applebuttercringe]

Asexual Viktor Controversy Explained (By an Asexual)

You may have heard of the new controversy tearing the Arcane community apart. To summarize: Christian Linke (Co-creator of Arcane) was asked in a german interview about Jayvik and responded that it is not canon by explaining that Viktor is intended to be Asexual. He then talked about the importance of Asexual representation.

This has sparked a number of reactions from Arcane fans, and especially Asexual Arcane fans. Most of the reactions are some mixture of the following points.

Reasons people don't like it:

It's just to invalidate Jayvik: A lot of people are angry because Christian Linke is well known for not liking Jayvik, and so some people believe he only said Viktor was Asexual in order to try and get rid of Jayvik. Thus creating the impression that the only purpose of making Viktor Asexual was to invalidate an mlm relationship. Or that Christian Linke only did it because he is homophobic.

It wasn't in the show: The claim that this was always the intention for Viktors character is brought into doubt when you consider that this obscure interview is the only time Viktor has ever been said to be Asexual. Several of the other writers, animators, and artists who worked on Arcane have said Jayvik is canon. Which creates the impression that this was not an intentional choice that was discussed thoroughly in the writers room and interwoven into the story, but rather a last minute addition by Christian Linke after the fact. Kind of like J.K. Rowling making Dumbeldore gay or Hermione black in a tweet, just added for attention and representation points. Asexual people deserve purposeful depictions.

It plays into Asexual stereotypes: A common and very damaging stereotype about Asexual people is that they are emotionless, lonely, or inhuman. With so many people believing romance is what makes us human, or that it is unnatural to not experience sexuality and therefore it is bad. Often lack of romantic or sexual desire is equated to lack of any kind of love or emotional coldness. Viktors story is largely about him being isolated and lonely for most of his life, being abandonned by his only close relationships, and eventually ridding himself of all emotions. He is shown to hate human emotion and actively tries to rid himself of his own humanity. It isn't hard to see how Viktor being the only Asexual representation in the show could reinforce harmful stereotypes about Asexual people. He has a whole monologue where he disavows human passion. This is really what bothers me about Viktor's Asexuality confirmation. If this really was intentional, they were playing into stereotypes. The only asexual character being made into an inhuman villain who's motivation is hatred for emotion and gets their via rejection of love is pretty rough.

It plays into stereotypes about Disabled people: This I know the least about, so I will just summarize what I have seen. Disabled people are often portrayed as sexless as a result of their perceived "undesirableness". This creates a steretype of equating disabledness to uglyness to asexuality. This is damaging as it perpetuated many stereotypes. It is used to infantalize both disabled and asexual people. It also treats asexuality like a symptom of a disorder. Good resources to learn more:

Christian Linke doesn't seem to understand Asexuality: Christian Linke calls Viktor Asexual. But it seems that the terminology he meant to use is Asexual/Aromantic. He seems to say that Jayvik CAN'T be canon becasue Viktor is asexual, but asexual doesn't mean aromantic. He can be Ace and Gay. Thus how him being asexual doesn't invalidate Jayvik. If he really did intend for Asexual Viktor to be canon this whole time, he probably should have done more research about the nature of Asexuality.

Creating controversy: Considering the all consuming power house that Jayvik has become in the Arcane fandom, it should have been expected that the co-creator rebuffing it would not be taken well. This whole thing has sparked a lot of discourse and caused for both Jayvik shippers to be inundated with comments of people calling them acephobic for shipping Jayvik, and Asexual Viktor enjoyers being shouted down. A lot of asexual fans are annoyed by the communities violently negative response to Asexual Viktor. Overall it feels like this whole thing has just thrown everyone under the bus.

Reasons people did like it:

Asexual Representation!: Asexual people are some of the least represented of the Queer community. They are also some of the most misunderstood by popular culture. A show as popular as Arcane having a canon Asexual charachter is a huge win, especially one as beloved by the community as Viktor. Despite the sometimes stereotypicalness of his story, many Asexual people deeply connect with Viktor and headcanoning him as Aro/Ace has been popular since Season 1.

Reading Jayvik as a deeply loving platonic relationship is very touching for Asexual people especially. One of the most prevalent stereotypes about Aro/Ace people is that their lives are lonely or meaningless because they don't experience sexual/romantic love. This is of course wrong, and deeply Amatonormative. Arcane depicting a deeply close, world endingly loving platonic relationship between two men is great and sorely needed. For this reason many Asexual people love this development as it shows a fulfilling, important, loving relationship that is sex free. Breaking one of the biggest stereotypes about Asexual people and the very nature of love. In this way Platonic Jayvik is just as groundbreaking a story as Romantic Jayvik.

Doesn't invalidate Jayvik: Asexuality is a spectrum, and it is distinct from being Aromantic. Asexual people can experience occasional sexual attraction, or be sex neutral and still have sex for the benefit of a partner. Viktor being Asexual doesn't disqualify him from being gay, or being in a romantic/sexual relationship with Jayce. It doesn't stop Jayvik from existing in the way Christian Linke seems to think it does.

Final Thought: I'm Asexual. I.... like the idea. However the execution leaves a lot to be desired. The foundation is their but this is still a deeply flawed piece of representation (if we even consider it representation at all). It feels like the kind of idea that we will see written so much better on AO3. I look forward to seeing that.

In terms of Jayvik, I don't think it is Acephobic to continue to ship Jayvik/write Jayvik Smut. the canonicity of this is dubious anyways and considering how wide spread and loved Jayvik is it would be ridiculous to demand people stop writing about them, or delete their hundred thousand word fanfictions/fancomics just because of an interview. People are deeply invested in Jayvik, it would suck to take that away. Keep doing what you are doing. I fully stand by the idea that Jayvik is left purposely open to interpretation. I love Platonic and Romantic Jayvik.

Fuck it. Trans/Genderfluid/Asexual/Gay Viktor. Thats what I believe.

(Please don't harass any of the people who's tweets were included)

[jammatown919]

The Netflix Family YouTube account just released a "Ben and Gia's best moments" video and it made me realize something.

The comparison of Bengia to Yasammy didn't start in season three. The very first mention of Ben's girlfriend, way back in season one, was part of Ben's response to Sammy's concerns about Yaz not answering her phone. Sammy is worried and fretting, while Ben claims that he would not be in his relationship in the same situation. The next time we hear about Ben's girlfriend, Ben is alluding to his own relationship struggles to comfort Yaz about the argument she just had with Sammy.

While the comparisons of them in season three, Bengia being happy while Yasammy is struggling, didn't feel great to me, I do think I understand the reason now to be comparing these couples in any capacity. For the most part, I think it's to make Ben a better-equipped support for Yaz and Sammy.

He knows what it's like to be in a long-distance relationship where communication with his partner is probably not as frequent as either of them would like. He understands that aspect of their struggles better than anyone else. I do think Brooklynn is going to be a useful perspective as well, but Brooklynn's relationship with Kenji was ruined by the mistakes that were made. We also need the perspective of someone who has figured out how to maintain a healthy relationship. Both of them are going to be important for Yaz and Sammy to take notes from.

Especially in season one, Ben brings up his relationship in support of Yasammy. He tells Yaz he gets it, he knows how hard relationships can be, but "it'll work out, you and Sammy have a good thing going". While it's less explicit while he's talking to Sammy, there is still some semblance of "I've been in your shoes". He doesn't necessarily say it, but there's an air of telling her she doesn't need to fret so much about Yaz, and considering that her fretting and coddling was one of the primary things that drove Yaz to leave Texas, that is an important thing for her to hear.

In season three, we get to see a lot of Ben and Gia being happy and not a lot of Yaz and Sammy being happy. But I think there will be a payoff to that. We now know 100% that Ben is in a real, healthy relationship and have a better understanding of his position and how it can be used to advise others. He's always been the OG Yasammy supporter, after all.

We probably won't see Gia again next season, but her influence could be really good for the Yasammy reconciliation because of how it allows Ben to offer his perspective.

[hyog-blog]

Fangs of Fortune - ep. 15

Another one of those precious moments of Bai Jiu cosplaying his Ge. That lil' serious face he's making makes Zhao Yuanzhou smile, ahah :D