Email from Jorge Pullin about this seminar ilqgs

[ccdantas]

Hi,

I have just received an email from Jorge Pullin about this seminar:
"[URL
International Loop Quantum Gravity Seminar[/URL]

I apologise in case this has already been posted here.

Best wishes,
Christine

 

[selfAdjoint]

What a neat resource! Thanks Christine!

 

[william donnelly]

Great find Christine, thanks. I particularly recommend Oeckl's presentation. I think he has provided a very compelling solution to some very important conceptual problems of quantum gravity.

 

[marcus]

Time to post the ILQGS talks scheduled so far for Spring 2007
Notice that there were four organizers of the KITP january workshop on quantum resolution of spacetime singularities----Martin Bojowald was one.

At the end another of the organizers, we heard Gary Horowitz (string), give a summary of the workshop.

We didn't hear Martin Bojowald's summary which would have been from a non-string point of view. He might have emphasized different things about the workshop.

Pullin, who runs ILQGS, has apparently invited M.B. to give a seminar talk this month, and present just such a summary. Pullin was also at the KITP workshop and gave a presentation.

====================
SPRING 2007

NOTE: All seminars will be held at 9:00 AM Central Time

Feb 13 UV properties of N=8 supergravity: is it finite? Radu Roiban PennState

Feb 20 KITP program on singularities summary Martin Bojowald PennState

Feb 27 Diffeomorphism invariance in loop quantum gravity Abhay Ashtekar PennState

Mar 13 Kapppa Poincare space-time symmetries Michele Arzano Perimeter Institute

Mar 20 TBA Kirill Krasnov Perimeter Institute

Mar 27 Loop quantization of spherically symmetric spacetimes Jorge Pullin Louisiana State University

Apr 3 TBA (about Trinions) Lee Smolin Perimeter Institute

So what are trinions?

here is the URL for the Spring 2007 schedule of the International LQG Seminar,
http://relativity.phys.lsu.edu/ilqgs/schedulesp07.html
we should check it periodically to see what other talks are put into the other slots.

 

[william donnelly]

You're wearing a trinion right now! (at least I hope so). A trinion is sphere with 3 disks cut out, also known as a "pair of pants" or "3-punctured sphere".

They were used in Lee's paper with Fotini and Sundance to decompose manifolds into "ribbon graphs". The interesting thing in this context is that you can build any 2-dimensional manifold by gluing together trinions. The trinion is also relevant to TQFT because it's one of the simplest non-identity cobordisms.

If you google for "trinion quantum gravity" or "trinion topology" you will find some discussion of Lee's paper and some relevant TWF's that talk about them.

 

[francesca]

So what are trinions?

A trinion would be a decomposition of Riemann surfaces.
To figure it, you can think that it's topologically isomorphic to the letter Y.

In the image from Smolin-Marcopoulu-Sundance's papers
http://arxiv.org/hep-th/0603022"
there are a trinion and a trinion and a trinion decomposition of a 2-surface S.
We start with a compact three manifold \Sigma. Given a two-dimensional surface S in \Sigma, we can regard S as a union of trinions: 2-surfaces with three punctures that connect to other trinions.

The idea is that any surface can be glued out of 3-holed spheres, sometimes called trinions. (see Louis Crane, Kirill Krasnov and others)

[...] the unitary operator which describes the change of representation factorizes into operators associated to the individual three holed spheres (trinions) which appear in a pants decomposition. (http://arxiv.org/abs/math.QA/0510174" )

So what is a pants decomposition? :uhh: Think about pants, it has three exits...

A pants decomposition of an orientable surface S is a collection of simple cycles that partition S into pants, i.e., surfaces of genus zero with three boundary cycles. (http://arxiv.org/abs/cs.CG/0602080" )

...oh, it's enough for me! by now...

 

[marcus]

Thanks franscesca and william,
actually it is the morning
and I am having coffee in my bathrobe.

But the bathrobe is probably a trinion because it is a flat piece of fabric with two sleeves for the arms---thus topologically equivalent to (though practically useless as) a pair of pants

 

[rtharbaugh1]

I was going to correct you, Marcus, but on further reflection I think you are in fact correct already. if you flatten out a three-hole spere, it is indeed a two hole surface...the other hole becomes the outer edge of the flat space! Thanks! I needed to think about that.

By the way, what kind of mathematical object do you have if you glue two trinions together by the edges of two of the holes? As if sewing two bathrobes together by the sleeve cuffs, keeping the freedom to pass an arm through both at once. Ouch. I am having trouble trying to flatten that.

I alternate between studying math and writing my novel. The novel has current precedence...But I'll be around.

R.

 

[marcus]

By the way, what kind of mathematical object do you have if you glue two trinions together by the edges of two of the holes?

R.

a quad-nion or quanion

a sphere with four holes cut out

a novel by you might be amusing---I am glad to hear that such a thing has precedence.

 

[f-h]

More familiarly: a torus with two holes in it.

 

[marcus]

More familiarly: a torus with two holes in it.

As I imagine it, f-h, this is not right. Richard is asking what if you have TWO trinions and you join them

By the way, what kind of mathematical object do you have if you glue two trinions together by the edges of two of the holes?

R.

Richard says you have two separate spheres each with 3 holes, so there are 6 holes to start with-----then you join two of the holes (each on a different trinion) together----so now their are 4 holes

the boundary of Richard's thing consists of 4 circles-----or 4 separate components.

But your torus with two holes punched in it has a boundary with only 2 components----the two rims of the two holes---so it doesn't seem right. Am I missing something?

--------------------------------------------

I am trying to figure out where your torus with two holes punched in it is coming from and I don't immediately see.
Richard was talking about two trinions but if you just have ONE trinion and you sew two of its holes together then you get a torus with ONE hole.

OK then you take another trinion and sew it on. THEN you have what you said, a torus with two holes.
But it takes two joinings. Now I see.

 

[Chronos]

I object to all the topological trivia. Until some model of it reproduces the observable universe, it is pure speculation.

 

[f-h]

Oh I read it to state that you glue them together by two holes each. You are of course right, I simply misread the original statement.

 

[rtharbaugh1]

I thought it through and I think the torus with two holes in its surface (plus the one in the middle) is correct.

First flatten each of the trinians so that they each resemble a disk with two holes. The disk with two holes is a trinion, like the bathrobe, because contracting the outer edge of the disk results in the third hole of the trinion.

Then layer the two disks so that the holes match up, and stitch around each set of matched holes. Now you have the odd thing I first was trying to imagine. Between these two joinings is a hole that didn't exist until they were sewn together. It isn't a hole through either surface, but a new hole which passes between the two disks and between the two sewn holes without piercing anything. If you stuck your arm through it, you wouldn't have your arm through either of the two original disk surfaces, but you would pass through between the two disks, with a joining on either side of your arm.


Then if you contract the outer edges of each of the disks until they are each holes, you have a single closed surface possessing two exits (the contracted edges) and two passages through the interior, one through each set of the stitched holes. Smooth this out and the result is a shape like a bicycle tire inner tube with two seams around the short circumfrence through the middle hole and two holes in its surface, just as if joining two plain tubes by their ends, each tube having one hole through its surface.

So, another shape for a trinion must be a simple tube with a single hole in its surface. You can go in either end of the tube, and then either out through the other end, or out through the hole in the surface. A y shaped tube or a tube with a hole in it or a disk with two holes are all the same topological shape.

It seems funny to think of a bathrobe as a tube with a hole in the surface, but it seems easier to distort the tube with a hole in its surface into a pair of pants.

Now my relentless imagination won't leave me alone until I sew two pairs of pants together by stitching around the belt line. Seems simple enough. A sphere with four holes in its surface: which is a tube with two holes in its surface and two ends: which is a disk with three holes, the fourth hole having become an outer edge.

SelfAdjoint set us a puzzle once. If you have a torus with a single hole in its surface, and you turn it inside out through that hole, what does the resulting object look like? Try it with a bicycle inner tube.

R.

 

[francesca]

SelfAdjoint set us a puzzle once. If you have a torus with a single hole in its surface, and you turn it inside out through that hole, what does the resulting object look like? Try it with a bicycle inner tube.

If I've well understood, you obtain a torus with an hole in the surface! the action is topologically invariant... but it can be wrong because I haven't try with the inner tubes of my bike!

 

[rtharbaugh1]

Yes, that is what I got. I never tried it with an actual innertube, but was able to imagine my way through it. I don't recall if sA ever gave an answer.

I want to go to ILQGS at LSU Baton Rouge. I think I can get myself there. Anybody know of someone there with a spare room? I can sleep on couches, floors, in garages or even pool cabanas.

You can read about my adventures at KITP UCSB singularities mini-program in this link: https://www.physicsforums.com/showthread.php?t=153285.

Any ideas?

R

 

[marcus]

for anyone who just dropped in on this discussion, the international seminar is an unusual hookup.
like "teleconferencing"

for any give seminar the participants could be in several places around the world, I guess Jorge Pullin at LSU is the one operating the switchboard
and posting the PDF lecture notes ahead of time

 

[rtharbaugh1]

How dissappointing. In my view the side discussions were the best part of the program. Not to say being at the seminar was anything less than a huge treat for me. Oh well. Thanks for the update.

R