@LeakyNun What do you mean by hyperbolic in this context?

nonzero derivative

guten Abend @Ted

guten Tag, @Leaky

Punks.

weist du andre Bedeutungen des "hyperbolisch"? @Ted

There are lots of meanings, in dynamical systems, for example.

As usual, I have no idea what ultra is talking about, so I really don't want to think about it.

ok

Watch whom you're calling punks, @anakhro.

ich bin ein Punkt

Punktenburger*

Ganz komisch.

Going to make this cauliflower pea chutney recipe tonight.

Math-wise, I might start typing out some notes for my classes.

Or I should pick out a book to read.

Or you should tell Ted about the normal vector field on the knot.

By the way, my argument works for any knot at all.

A cute problem I found the other month that I didn't get to share here was the following: Consider a spherical loaf of bread of radius $r$ which is cut into $n$ even slices of equal thickness, $2r/n$. Which slice has the most bread? Which slice has the most crust?

well depends on how you cut it obviously

Oh, this is one of the famous properties characterizing the sphere. It's the only surface of revolution with the property that the surface area between parallel planes (perpendicular to the axis of revolution) depends only on the distance between the planes.

I've actually used this property in talks to middle-school and high-school students.

@TedShifrin :)

(ok you cut it in parallel)

@TedShifrin does your argument work for wild knots?

One of my old diff geo friends wrote a cute little paper on this, @anakhro.

Do you want me to find the reference?

@TedShifrin sure!

(for some reason I was considering cutting concentrically, because I was thinking mathematically)

@anakhro: I'm definitely using smoothness.

No you weren't, @Leaky.

I'd argue that thinking of anything but parallel would be "unmathematically".

Most mathematicians I know are idealists. :P

I didn't think of a knife at all

@anakhro: It's particularly good for you because it's a symplectic approach. Here is the paper.

Thanks!

looks very formal to me

Hi all, short question about Matsubara frequency summations

Warning: Probably no one knows what you're talking about.

Haha nobody? :(

Ok rewind then

Suppose I'm using contour integration to perform some integral

The integral contains say, 20 poles on the real axis

say, 18 of these are roots of unity by virtue of some Bose-Einstein distribution type thing, and 2 of them are not

Suppose now I'm taking one contour around the 18 roots of unity

My book claims this is exactly equal to the minus the sum of the two other poles, plus an integral over the real axis of the function I'm integrating over, excluding this distribution

Excuse me? You have 18 roots of unity on the real axis?

They are Wick rotated in my system

No clue.

yeah, (-1), (-1), (-1),....,(-1) and (-1)

perhaps he means the residua are roots of unity

At any rate, I'll throw out the comment that you can often sum all the residues in the plane by computing a single residue at $\infty$. Maybe that trick is involved here — if the residue at $\infty$ happens to be $0$.

@s.harp: "contour around the 18 roots of unity"

@1010011010 this looks like an application of one of the "move part of the contour to infinity to wrap around the other poles" type of trick

Yes sorry this is poorly phrased, what I'm trying to say is that some distribution has poles at the values 2\pi m of my integration variable, so it's like 1/(1-exp(i*x)) for example

@s.harp I get that, but shouldnt it contain $\pi i$ times the other residues? I'm integrating over the real axis now. Should I argue that I can shift these poles slightly away from the real axis?

i think i calculated a matsubara frequency integral thing once, though i got the wrong answer

I am trying to find the focus of a hyperbola

i think what ted remakred upon is what you have to do here @1010011010 , you may also see your contour around your line as a countour around the two poles outside of the line and around the pole at ininity en.wikipedia.org/wiki/Residue_at_infinity

Snap! Found it

I could shift my distribution function by assuming the imaginary part was infinitesimally positive, then I would automatically enclose the other poles, and integrate along the real axis :-)

Any measure theorist in the room?

(wanted an opinion)