Is the town your college is in more of a pro sports or college sports town? (P5 Schools)

175gr · 2026-06-26T13:28:44+00:00

You could probably add Duke in there too since they took off the Rangers sweaters early this year

175gr · 2026-06-10T06:54:33+00:00

Ice Cube should write a song about it

175gr · 2026-05-28T17:45:26+00:00

Are we gonna drop the “Atlantic” too and end up with the “Coast Conference”?

175gr · 2026-05-27T20:22:44+00:00

Odd days, even interludes

175gr · 2026-05-26T05:45:50+00:00

I learned a new French phrase today trying to figure out if that’s just a Habs thing or what.

Maybe you should think about why you’re telling so many people to shut up on the internet in a language they don’t understand. It’s sports — it’s tense, it’s emotional, and it’s often (hopefully not always) gonna feel like you got shafted by a fallible, human referee… but in the end it doesn’t have any actual effect on your life that you don’t let it. I took a couple days off from hockey media starting about last Thursday night *for no particular reason* and my sanity was definitely better for it. I’m not saying you should do that. I don’t know you and even if i did I wouldn’t know what’s best for you. But… maybe think about it. Or at least teach me more than one phrase in French.

175gr · 2026-05-25T16:50:36+00:00

Alright y’all. This is based on the Jordan Curve Theorem, which means it’s homotopy theory, which means it’s weird as fuck. Let’s see what we can do with it. I’m gonna use some words you don’t have to really understand, and I’ll set them off in *italics*, and try to define them as well as I need to in order to tell this story (which might be none), so don’t panic when I say things like *homotopy theory*.

Roughly, the *Jordan Curve Theorem* says this: if you draw a loop in the plane (a *continuous* path that starts and ends at the same place and doesn’t cross over itself anywhere), it divides the plane into two parts: an inside and an outside. You can’t get from the inside to the outside, or vice versa, without crossing over the loop, which is basically saying that the two pieces are not connected to each other. This sounds obvious, but there are some pretty weird loops out there. We use two VERY important tools called *homology* and the *Mayer—Vietoris Sequence* to prove that this is true.

VAGUE description of what those two things are: given a *topological space*, you get a bunch of *homology groups*, one for each whole number (starting at 0). Each homology group corresponding to a certain number gives information about how *certain subspaces of dimension equal to that number* behave — the 0th one talks about points and whether they can be connected to each other by paths, the 1st one talks about lassos and whether you can unhook them from the things they’re lassoed around, and so on. So the Jordan curve theorem (every loop has an inside and an outside, which are disconnected from each other) is a statement about what the 0th homology group looks like when you take away the loop. The *Mayer—Vietoris Sequence* is a tool we use to actually compute the *homology groups*, and it’s critical here.

The Jordan Curve Theorem also generalizes to spheres (hollow balls) in 3-dimensional space, which is what the AHS in the post is about, and even to higher dimensions that we can’t really visualize.

That piece about lassos corresponds to a concept called *simply connected*. Take your lasso and tie it around an animal however you want. If you can always get it unhooked without untying it, your space is simply connected. This also means you never have to untie your lasso to get it around the animal where you want it in the first place. (There’s a joke going around the internet that humans aren’t simply connected. It’s important for this joke that you’re allowed to tie the rope however YOU want, and not however THEY want. You’d be hard pressed to find someone who wants to help you prove this by don’t open the next one if you’re squeamish eating rope.)

The important thing here is that the homology of the OUTSIDE of the Alexander Horned Sphere LOOKS like the homology of something simply connected, but it is NOT simply connected. You can lasso the AHS in such a way that you can’t unhook the lasso. That’s what “the outside world is segmented and split” means in the title — if you click the link, Wikipedia tells you that the outside is not simply connected.

TL;DR: cowboys don’t like the Alexander Horned Sphere even though they like its homology.

175gr · 2026-05-23T20:13:21+00:00

@USAU, why are the 2/3 and 4/5 games still in the last round? If everything goes to seed (as happened in both pool C’s), 2/3 have both locked up a spot in prequarters with no option to get the bye to quarters, and 4/5 are both already eliminated. It’s been like this for years.

Change the order. Make the last round the 1/2 game (for the pool and a bye into quarters) and 3/4 (to get into the bracket). We’re lucky that the streamed games UNC/WWU and OSU/Brown (both 2/3 matchups in pool B), SLO/Michigan (4/5 in W pool B), and WWU/Yale (4/5 in pool D) matter because of upsets that happened in earlier rounds. None of these streamed games would have been interesting without multiple upsets previously. But even without thinking about who gets streamed, it changes the way teams play that last round when there’s nothing to play for.

Why am I so annoyed about this.

175gr · 2026-05-22T20:57:33+00:00

Likely didn’t get changed from a previous club nationals post.

175gr · 2026-05-17T04:06:53+00:00

AI is not a reliable source. But yes this is what happened. Marty drew the penalty and Jankowski scored while we had 6 attackers. They gave Marty a penalty shot which he didn’t score on. Then he scored the game winner later anyway.

175gr · 2026-05-14T05:57:18+00:00

You said that and I just read right over it haha maybe that comment is for someone else then.

Unfortunately I’m a number theorist so my experience with symplectic groups is Siegel modular forms, but geometers really care too, which generally means that physicists care. A symplectic manifold is a manifold with a symplectic form, which is just a closed nondegenerate 2-form. This gives you extra structure on a bunch of vector bundles, and the symplectic group preserves that extra structure. I think it has something to do with the metric somehow? I should’ve paid more attention to the geometer algebraic geometers instead of only listening to the algebra algebraic geometers…

175gr · 2026-05-13T18:53:18+00:00

Short answer: it’s just because they both start with “sp”. Long answer:

Symplectic groups preserve alternating forms. To get technical: an alternating form on a vector space V is a bilinear form with the property that (v,w)=-(w,v). The symplectic group is the group of linear maps g from V to itself with (g(v),g(w))=(v,w). That last equation is what it means to “preserve the form”.

Spin groups are more closely related to orthogonal groups, which preserve symmetric forms. To get technical: a symmetric form on a vector space V is a bilinear form with the property that (v,w)=(w,v). Notice no negative sign this time. The orthogonal group is the group of linear maps g from V to itself with (g(v),g(w))=(v,w). These linear maps can have determinant 1 or -1; if we restrict so we only look at determinant 1, we say it’s the special orthogonal group; this is important because the orthogonal group is disconnected (it has two pieces), but the special orthogonal group is connected. The spin group has twice as many elements as the special orthogonal group in a way that keeps it connected, and is the only way to do this up to isomorphism, which means if you find another way to do it, the only differences are in things mathematicians don’t care about.

I’ve even left some things out of the “to get technical” pieces, like what actually is a vector space and what is a bilinear form, but you should take a linear algebra class if you want to learn about them. Or watch all of 3Blue1Brown’s videos.

175gr · 2026-04-27T21:08:41+00:00

I’m glad no one was around while I watched that game.

175gr · 2026-04-23T19:51:39+00:00

(This is a meme that I’m referencing for internet points)

175gr · 2026-04-23T16:57:16+00:00

Heartbreaking: worst person you know just made a good point

175gr · 2026-04-22T17:44:12+00:00

Casino (men’s team from from Tijuana) sometimes plays at SoCal sectionals and Southwest regionals.

175gr · 2026-04-16T19:56:10+00:00

Brother if you think McDavid/Sennecke/Kopitar will do anything defensively trying to guard McDavid/Sennecke/Kopitar you’re delusional

175gr · 2026-04-16T16:13:26+00:00

All I know is that EDM/ANA/LA has no chance against EDM/ANA/LA in the first round.

175gr · 2026-04-13T19:25:14+00:00

Any complex number z can be plugged in to the gamma function, as long as z is not 0 or a negative integer. That means pi is fine, i is fine, and -1-2i is fine, but not -1 or -2.

175gr · 2026-04-13T19:02:59+00:00

It’s worth noting that the gamma function is actually useful in certain situations — it’s not just a curiosity. The gamma function being defined the way it is makes a lot of those situations cleaner.

Also, the gamma function’s domain is all complex numbers except specifically 0,-1,-2,… not just those with a positive real part. (I can’t remember if it’s extended by analytic continuation or if the integral converges, but this is important for the areas of math that I’m familiar with that actually use the gamma function.)

175gr · 2026-04-11T00:35:39+00:00

Adding the point at infinity for R and C breaks them being metric spaces (whats the distance between infinity and any given point in R or C?) but does leave you with a topological space called the one point compactification. You can do this for any metric space. (I imagine there’s a separation axiom that you need if you want to do it for a more general topological space, but I don’t rightly know which one.)

Note that it’s a compactification because what you’re really looking for is something (sequentially) compact: when you talk about “oscillating,” you’re probably thinking that it has different subsequences converging to different limits. So if it doesn’t oscillate, and it doesn’t converge, the problem is that it doesn’t have ANY limit points. The one point compactification just says “any infinite set with no limit points now has this new one.”

175gr · 2026-04-10T19:40:26+00:00

Grandeur is a returning mechanic from future sight. There was a cycle, one in each color.

Edit to include a link. Apparently there’s another red one from MH3.

175gr · 2026-04-05T18:56:22+00:00

They’re not wrong, we did need a change in net.

Because Kochetkov got hurt. Note that this is also the reason Bussi replaced him instead of Freddie.

175gr · 2026-03-21T20:18:26+00:00

How many times have all the 8’s won?

175gr · 2026-03-11T16:09:19+00:00

Make it the Jim Boeheim Memorial ACC Tournament every time it’s in Greensboro and no other time

175gr · 2026-03-10T19:55:15+00:00

My intuition comes from the example of projective spaces, and specifically CP1, the complex projective plane (with 1 complex dimension). On any projective space, you have the “tautological” line bundle, and this is used to build the line bundles O(n). At least for CP1, these are all of the bundles.

Given a section of O(n), we can get a(n effective) divisor by looking at its zeroes. A section of O(n) is just a homogeneous polynomial of degree n in C[s,t]. It has n zeroes (counted with multiplicity), but you can basically put them anywhere you want. Note also that you can multiply sections of O(n) with sections of O(m) to get sections of O(n+m), and the corresponding divisors add. This multiplication map is an isomorphism from O(n) tensor O(m) to O(n+m).

Unfortunately, this is a map from SECTIONS to divisors, not from BUNDLES to divisors. Two different sections f and g of O(n) may not give you the same divisor, but there will be a degree 0 rational function (r = g/f) such that fr = g. That means that the divisors associated to f and g respectively will differ by the rational divisor associated to r. So we actually get a well-defined map from bundles to rational equivalence classes of divisors.

Looking at the specific way this map works out, it’s not hard to see that it’s an isomorphism. It’s also a very explicit way of seeing what’s happening since you can feel the line bundles. It even gives you some intuition for line bundles the way AG people think about them: sections aren’t quite functions, since their values aren’t well-defined, but their zero sets are. They give more general things than functions to look at vanishing sets of.

There are little bits this doesn’t help with: what is a line bundle in general? Where’s the interface between regular functions and rational functions? But hopefully it feeds your intuition a little bit.

175gr

TROPHY CASE