Mathematics

7:00 PM

Very cool, @Tobias. If we ever end up in the same corner of the earth, we can play :)

Yeah, I think they are looking into making the automatic mahjong tables do the same, but those are too expensive for most local clubs to afford

Shobhit

@TedShifrin i cant think of such a function, example?

Ted Shifrin

@Silent: Do you have any thoughts?

Tobias Kildetoft

And affording enough for an actual tournament would probably require the game to be more popular outside of China and Japan than it currently is

Shobhit

does anyone play seep? (card game)

Ted Shifrin

7:01 PM

Have you ever played the game Carcassonne, @Tobias? It's quite cool, somewhat mathematical. There's even an iPad app for it.

(I also happen to love the town in France after which it's named.)

Tobias Kildetoft

@TedShifrin I have played it a few times. I like it as a game to play with people who don't regularly play board games, since it is fairly simple and not too deep strategically (so people don't end up spending too much time trying to optimize their play)

I have considered getting it myself, since it is also of an appropriate level of difficulty to play with my daughter without having to alter the rules to make them easier

Ted Shifrin

I find it sufficiently challenging myself :)

DogAteMy!!

Ted!!!

sup chat

heya ERic

7:06 PM

how's it going

Ted Shifrin

Eric, if you're interested, there's someone asking a bunch of minimal surfaces questions (based on Minicozzi/Colding's book) on main.

Antonios-Alexandros Robotis

what's going on

Ted Shifrin

heya Antonios

Anyone left in the algebra course?

Antonios-Alexandros Robotis

seems she did end up curving the exam, or at least so I've been told.

some had already dropped though, I think.

Ted Shifrin

Still it would be nice if people learned something ...

Antonios-Alexandros Robotis

7:09 PM

yeah, exactly.

Semiclassical

Hmmmm

Tobias Kildetoft

That reminds me. Got the preliminary plan for re-exams today. 6 people eligible for the algebra re-exam. Should not be too tough to grade those, though it feels like a shame to have to make an entire exam set just for 6 people

Akiva Weinberger

@LeakyNun ?

Semiclassical

I’m trying to put together what I thought I figured out, but now I don’t trust it. Bummer

Ted Shifrin

@Tobias: I've written several qualifying exams just for one student over the years.

Akiva Weinberger

7:10 PM

@LeakyNun How does origami make the fact that the torus quotiented by a meridian and parallel is a sphere obvious?

Ted Shifrin

@Semiclassic: Have you found an error in the write-up?

Tobias Kildetoft

@TedShifrin How long are those?

Ted Shifrin

3 hour written exams, Tobias.

Semiclassical

An error in my use of a certain bound

Akiva Weinberger

Oh, you mean like viewing the torus as a square with opposite sides identified? @LeakyNun

Tobias Kildetoft

7:10 PM

ok, so about the same (this is a 4 hour exam)

Semiclassical

The premise was stronger than I realized.

Ted Shifrin

Aha.

Eric Silva

@TedShifrin ill check it out

Leaky Nun

@AkivaWeinberger right, and then the quotient basically identifies the boundary of the square

Akiva Weinberger

Don't make premises you can't keep

Leaky Nun

7:11 PM

so you get a sphere

Akiva Weinberger

Right, I see

Ted Shifrin

DogAteMy: With talk like that, Demonark will materialize.

Semiclassical

The context was that I wanted to find a bound on $\text{tr}(U^\top U S)$ in terms of the Frobenius norm of U and the eigenvalues of S

But the argument I saw assumed S was positive definite, and mine isn’t

Ted Shifrin

Can you make a perturbative argument?

Semiclassical

Dunno.

The awkward thing is that I have an example for S, but I’m not sure how I should be generalizing it

The example has S being symmetric and orthogonal.

Tobias Kildetoft

7:15 PM

@TedShifrin These programs do feel a bit slow at times, since I already know the rules and a bit about bidding. But on the other hand, they do teach some fundamentals I did not know. Just went through a chapter on finessing, which is not something I had really considered before.

Ted Shifrin

Yeah, and if you have a choice of finessing either way, do you have information from which to infer which way is more likely? (Bidding/counting points that have shown up in the respective hands, signals, etc.)

Tobias Kildetoft

@TedShifrin This is before anything about bidding. But it did make a point of having you play as many cards as you could safely do before choosing which finess to take.

Ted Shifrin

Yup, lots to learn.

Semiclassical

in that example I can do a Cauchy-Schwarz argument (since that trace can be understood as the Frobenius inner product) in order to deduce a bound

Tobias Kildetoft

indeed

Semiclassical

7:17 PM

So I like that.

The weird thing, which I feel like I should understand, is that the bound should only be saturated when $U=US$

Where U is 3-by-4 and S is 4-by-4 in my example

Obviously, the rank of U is at most 3. But i feel like I should be able to say more than that.

Alessandro Codenotti

@TedShifrin yup

we got the second pset today

Ted Shifrin

Excitement.

anon

It's $\sum_{i,j}\langle u_i,u_j\rangle s_{ji}$, which is a kind of dot product if you interpret them as vectors with $n^2$ entries.

Ted Shifrin

mr @anon!

Semiclassical

Right.

You can view it as the Frobenius inner product of U and US with S orthogonal

Or, well

In the case I understand, S is orthogonal

I’m not sure I really need that but for now I don’t know how to dispense with it

gian

7:25 PM

Is anyone here familiar with intersection homology?

Helmut

I am new to Math.SE. I have seen an accepted answer to some question that contains a fundamental mistake. Can you tell me what to do? If this is not the right location to ask this question, please excuse me and tell me ahere to look.