Rovelli's talk at Perimeter 4/4/12: video online, comment?

[TrickyDicky]

Also, as far as references go, I would say that these lectures should be regarded as the primary and canonical reference right now. These are the clearest, pedagogical and most concise (that is, unburdened by the tortuous route of history) presentation of the theory that exist.

Ok, that's great, I'll watch them.

 

[marcus]

Ok, that's great, I'll watch them.

FWIW I'll tell you my experience. I started with Lecture 3 and in retrospect I would do that again and invite you to do likewise, if it works for you. Lectures 3 and 4 present the "timeless path integral" formalism on which the rest is built.
Alternatively, if you have read "On the Structure..". http://arxiv.org/abs/1108.0832, since that is what Lectures 3 and 4 cover, you could start with Lecture 5, which is where the development of GR and QG starts.

The second thing is I've found it helpful to download the "slides" PDFs and have all 7 icons on my desktop. Actually they are a series of blackboard "stills", not slides. So now I can click immediately on the stills PDF of any of the Lectures 3-9 whenever I want to be reminded of what was covered in that lecture. It takes a couple of minutes to download each PDF, but then it's done.

Lecture 3 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040021
Lecture 4 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040022

Lecture 5 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040026
Lecture 6 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040027
Lecture 7 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040028
Lecture 8 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040029
Lecture 9 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040030

I think scrolling down the fifty to hundred still-frame shots of the blackboard, from a given lecture, could have been baffling or meaningless to me before I actually watched the lecture. The stills hardly speak for themselves. But once having watched and listened, I find that looking back at the blackboard stills is an easy way to recall the main points.

Lectures 3 (resp. 4) review a neat way of treating classical (resp. quantum) mechanics without a preferred time. It is for a general system, not yet specialized to gravity. Lecture 3, classical mechanics without time, is about the Hamilton function (of initial and final configurations of the system). Lecture 4, quantum mechanics without time, is about transition amplitudes (from initial to final states of the system).

In case anyone is new to it, in rough terms the classical Hamilton function, given initial and final, tells you a quantity which is the least action given that choice of initial and final. In other words it gives you the action associated with whatever the classical solution is, if one exists given that choice. Happily it carries over to the "generally covariant" case of classical GR---with very little trouble it can be formulated without preferred time. This gives a clean way of describing both classical and quantum evolution relationally, without commitment to anybody's clock.

In a sense, the Hamilton function (like the transition amplitude) is a function of system boundary variables, like input and output, rather than what happens in between. It is the classical object most closely analogous to the path integral transition amplitude---when quantum mechanics is done without preferred time, in a generally covariant way.

These two things, Hamilton function and transition amplitude, are central to what's being presented, so for anyone not familiar with their treatment without preferred time (On the Structure... http://arxiv.org/abs/1108.0832) Lectures 3 is a good place to start. What then follows in Lecture 5 is to define Palatini and Holst actions for gravity (and starting at minute 40, work out the simplified 3d gravity case.)

It could be that another person would find it better to start with the first two lectures---which give motivation, historical perspective, and a possible intuitive answer to "what is quantum gravity about?".
Reduced to the most basic elementary level, the answer could be paraphrased as follows: Take what you should have learned about the tetrahedron in high school (volume, face areas, normals...), subject that to just one quantum ansatz, the Heisenberg uncertainty principle, and see what a circus erupts from this simple opening move. I listened to Lectures 1 and 2 mostly after watching the formal development in the other talks.

 

[TrickyDicky]

Thanks for the advice and the links, Marcus, really interesting stuff.

 

[marcus]

I have to say, I think this lecture series is fantastic. Nevermind whether the 4D Lorentzian theory is actually true, I think this might be the largest "airing" of the work that the loop community has done. There are *lots* of mathematical theorems which are interesting in and of themselves --- the structure of covariant/parameterised systems, fun facts about group theory and representations and functions on them, historical fun (the latest lecture had a line about "then magic, magic and magic" regarding the semiclassical expansion of the 6j symbol)...

I completely agree! I find I gain understanding of some math tools better after seeing them used ingeniously in geometry (Wigner matrices, j-symbols, representations, quantum groups). This context adds motivation and interest. You referred to Lecture 8 here---the excited exclamation about the 6j symbol was around minute 44.

I think Lectures 8 and 9 are the finest so far---fast clear illuminating delivery. I feel as if I should make a brief outline, of at least those two, maybe Lecture 5 as well, to deepen my understanding, maybe our shared understanding as well.

 

[marcus]

Since we're on a new page I'll recopy links to Rovelli's online video course in LQG, which goes along with the colloquium talk Transition Amplitudes in QG that we are considering in this thread. It's expected to run three weeks: 14 lectures through 20th April. http://pirsa.org/C12012 If you have watched the lectures, feel welcome to emend my summary/outline or contribute your own.

Lecture 1 http://pirsa.org/12040019 what are Q theory and geometry basically about?, the quantum tetrahedron.
Lecture 2 http://pirsa.org/12040020 historical and philosophical perspective on QG.
Lecture 3 http://pirsa.org/12040021 Hamilton function, classical physics w/o preferred time coord.
Lecture 4 http://pirsa.org/12040022 quantum physics w/o time: transition amplitudes.

Lecture 5 http://pirsa.org/12040026 putting GR in the picture. deriving and motivating Palatini&Holst actions. overview of how discretized, quantized in 4d. At minute 40, begin working out toy model (3D Euclidean case) which will be copied in Lecture 9 to get the "real world" case.
Lecture 6 http://pirsa.org/12040027 continue simple worked example: quantizing 3D Euclidean case. How to get from Palatini/Holst classical continuous action to the spin foam.
Lecture 7 http://pirsa.org/12040028 math tools: specific graph Hilbert space&operators, SU(2) reps, spinnet basis.
Lecture 8 http://pirsa.org/12040029 concluding the 3D Euclidean example: defining transition amplitudes. Minute 18 = partition function (which give transition amplitudes when boundary is introduced). Minute 30 - 34= Wigner 6j appear. Minute 44=Ponzano&Regge recover GR! Minute 48=how bubble divergence can arise. How Turaev-Viro cured that using the quantum group of SU(2). How cosmological constant appears in the theory.
Lecture 9 http://pirsa.org/12040030 Beginning "the real world" 4D Lorentzian case.

Lecture 10 http://pirsa.org/12040033 (Eugenio Bianchi) M 16
Lecture 11 http://pirsa.org/12040034 (Eugenio Bianchi) T 17
Lecture 12 http://pirsa.org/12040035 W 18
Lecture 13 http://pirsa.org/12040036 Th 19
Lecture 14 http://pirsa.org/12040037 F 20

The first 9 lectures are now online.
For reference:
On the Structure... http://arxiv.org/abs/1108.0832
Colloquium Transition Amplitudes...http://pirsa.org/12040059
Background Zakopane Lectures... http://arxiv.org/abs/1102.3660

If anyone wants to download blackboard still shots PDF for some of the lectures, to have for reference and review, here are the PDF links.

Lecture 5 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040026
Lecture 6 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040027
Lecture 7 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040028
Lecture 8 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040029
Lecture 9 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040030

I put them on my desktop to have handy. Once I've listened to a lecture, looking back at the stills is an easy way to recall the main points.

 

[marcus]

Lecture 10 is now online as well:
http://pirsa.org/12040033 (topics=spin network basis in 4D, and the spectrum of the volume operator)
http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040033 (the blackboard stills PDF)
As announced earlier, Eugenio Bianchi gives this one, and I believe he will tomorrow's as well.
The focus is on the real world (4D Lorentzian) case--I had time to watch only the first part so far--he seems to be giving a careful thorough formal development, illustrated by working out a number of examples.

Deriving the spin network basis and demonstrating its key properties only takes the first 25 minutes of Lecture 10.
Then starting at minute 25 the topic is the volume operator spectrum. Some of what is being presented may be new, because there have been some differences about the V spectrum and recent research clarifying the issues regarding it.

Btw around minute 48 EB makes efficient use of diagram manipulation in calculating the matrix elements of the V operator. It shows how a few diagram moves can replace (and be more comprehensible than) some possibly lengthy algebra. Also btw around minute 50 he employs an area formula discovered by Hero of Alexandria (10-70 AD).

The topic of Lecture 11 announced at the end of Monday's lecture is Coherent (spin network) States.

 

[marcus]

Lecture 11 is now online too.
http://pirsa.org/12040034
two topics this time:
1) coherent states (up to minute 42)
2) unitary irreducible representations of SL(2,C) (minute 42 to end at minute 72)
Students asked a bunch of questions during, and then applauded at end, it seems they approved.
Feel free to contribute your own comment/summary.

In part 2) was discussed the map Y_γ from representations of SU(2) to those of SL(2,C), which will play a role in defining the dynamics of the theory and appear in the next three lectures.

 

[marcus]

Lecture 12 (full 4D theory, dynamics) is online
http://pirsa.org/12040035/
The first 19 minutes are a discussion of a student's question about the issue of uniqueness.
Rovelli's response is essentially that it's premature--first we must be sure we have *a* theory (at least one)
which is general covariant (diff-invariant) quantum with the right classical limit. In the history of physics the issue of uniqueness has always been secondary. First there was the guess (Maxwell eqn, Einstein GR eqn...), intuiting *a* theory that could work, and then later people could investigate was it the only one, and how it could be varied.
If one is not concerned about the uniqueness issue, then one might, I suppose, skip the first 19 minutes.

Here is the blackboard stills PDF
Lecture 12 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040035
The main lecture stills start with #17, skipping the first 16 stills corresponds to skipping the first 19 minutes.

In a sense the core of the course of lectures occurs starting at minute 46 or so. Until that point the partition function is with a general group G and it is simply a quantization of a the "BF" theory based on that group.
At minute 46, he says now introduce gravity.

At minute 50 you see where the map Y is introduced, and you see clearly where and why it must enter.
This map Y was defined by Eugenio in Lecture 11 when he was presenting the math tools---irreducible unitary reps of SL(2,C). This is the focal point because it is the non-obvious guess move that distinguishes the theory. Up to that point we are basically seeing what could be expected from the well known and well studied examples of the 3D gravity (which is worked out) and the BF theory. You could say it is a "rubicon" step. So that happens at minute 50.

Around minute 62:30 he sums up: this now is the definition of the full theory. A partition function Z which becomes a transition amplitude W when you designate part of the 2-complex as boundary. Analogies with the 3D theory are made. The q-deformed version is finite.
Around minute 64 or 65 is described why the classical limit is Regge (for large j, in a fixed triangulation). More on that in the next Lecture.

 

[marcus]

Lecture 13 is online.
http://pirsa.org/12040036/
wrapup of the full theory.
redundancy of one SL(2,C) integration. finiteness. (first 17 minutes)
relation to Regge-with-cosmological-constant (for large j).
thinking about refinement of 2-complex by analogy with QED Feynman diagrams.
alternative ways of looking at theory e.g. quantum polyhedra, e.g. sum over histories involving elementary geometric moves...

Lecture 14 is planned to discuss what we can calculate (I hope it may include some mention of application to cosmology, but it may not) and is expected to leave time for questions.

About the general question "what do we want to calculate with QG?" you might want to take a look at the thread
https://www.physicsforums.com/showthread.php?t=597933
which Lapidus started recently. It mentions some things to calculate and compare with observation. If you think of others you could add them to Lapidus' thread.

 

[genneth]

Lecture 12 (full 4D theory, dynamics) is online
http://pirsa.org/12040035/
The first 19 minutes are a discussion of a student's question about the issue of uniqueness.
Rovelli's response is essentially that it's premature--first we must be sure we have *a* theory (at least one)
which is general covariant (diff-invariant) quantum with the right classical limit. In the history of physics the issue of uniqueness has always been secondary. First there was the guess (Maxwell eqn, Einstein GR eqn...), intuiting *a* theory that could work, and then later people could investigate was it the only one, and how it could be varied.
If one is not concerned about the uniqueness issue, then one might, I suppose, skip the first 19 minutes.

I had a comment on that if only I was there! The student is confused about whether small or large gamma is the classical limit. He thinks that since the "classical" Lagrangian is without the topological term, the correct limit is with gamma going to infinity (since it appears as a 1/gamma prefactor). This is incorrect!

First, whatever the value of gamma it does not affect the classical equations of motion. It only weights off-shell paths in the quantum theory. Second, taken on its own, the topological term is enforcing the Bianci identity --- so in the absence of the first term, it is with gamma equal to zero that the Bianci identity is actually enforced! In other words, the smaller gamma is, the *less* weight we put on off-shell paths, and the closer the quantum theory is to a classical saddle-point.

With that out of the way, I hope it is clear in what sense the theory is "unique" up to the motivating classical Lagrangian --- it is polynomial in the variables, and of low(est) order.

 

[atyy]

I had a comment on that if only I was there! The student is confused about whether small or large gamma is the classical limit. He thinks that since the "classical" Lagrangian is without the topological term, the correct limit is with gamma going to infinity (since it appears as a 1/gamma prefactor). This is incorrect!

First, whatever the value of gamma it does not affect the classical equations of motion. It only weights off-shell paths in the quantum theory. Second, taken on its own, the topological term is enforcing the Bianci identity --- so in the absence of the first term, it is with gamma equal to zero that the Bianci identity is actually enforced! In other words, the smaller gamma is, the *less* weight we put on off-shell paths, and the closer the quantum theory is to a classical saddle-point.

With that out of the way, I hope it is clear in what sense the theory is "unique" up to the motivating classical Lagrangian --- it is polynomial in the variables, and of low(est) order.

But is the Hilbert space the same as that for the LOST theorem? If it isn't, then isn't it the wrong sort of uniqueness?

 

[genneth]

But is the Hilbert space the same as that for the LOST theorem? If it isn't, then isn't it the wrong sort of uniqueness?

It is not truly unique in any precise sense at the moment. I was simply addressing the concerns that student had. The broader picture was given by Rovelli --- we're looking for *a* theory, not *the* theory.

Guess, then check with experiments.

 

[atyy]

It is not truly unique in any precise sense at the moment. I was simply addressing the concerns that student had. The broader picture was given by Rovelli --- we're looking for *a* theory, not *the* theory.

Guess, then check with experiments.

Is that really Rovelli's view or your view? I do think that's a very sensible view, and that indeed is how I view "LQG". But one should admit then that LOST is lost, no?

Lecture 12 (full 4D theory, dynamics) is online
http://pirsa.org/12040035/
The first 19 minutes are a discussion of a student's question about the issue of uniqueness.
Rovelli's response is essentially that it's premature--first we must be sure we have *a* theory (at least one)
which is general covariant (diff-invariant) quantum with the right classical limit. In the history of physics the issue of uniqueness has always been secondary. First there was the guess (Maxwell eqn, Einstein GR eqn...), intuiting *a* theory that could work, and then later people could investigate was it the only one, and how it could be varied.
If one is not concerned about the uniqueness issue, then one might, I suppose, skip the first 19 minutes.

If I read marcus's summary correctly, it isn't a goal just to have a theory - the goal is to have a "general covariant" quantum theory. Doesn't the LOST theorem say that the canonical LQG state space is the only state space of such a theory? If the new spin foams don't have that state space, doesn't that mean they are not "general covariant" quantum theories?

 

[genneth]

Is that really Rovelli's view or your view? I do think that's a very sensible view, and that indeed is how I view "LQG". But one should admit then that LOST is lost, no?

It's my understanding of Rovelli's view.

If I read marcus's summary correctly, it isn't a goal just to have a theory - the goal is to have a "general covariant" quantum theory. Doesn't the LOST theorem say that the canonical LQG state space is the only state space of such a theory? If the new spin foams don't have that state space, doesn't that mean they are not "general covariant" quantum theories?

As far as theorems go, one should always be very careful. I'm not perfectly intimate with said theorem, but let me outline one possible "get out clause". The spin foams are not generally covariant when one considers any truncation, i.e. any graph/2-complex. It is expected that in the refinement/continuum limit true general covariance is recovered. This is exactly analogous to Rovelli's toy covariant harmonic oscillator example, where any discretisation breaks the general covariance.

 

[marcus]

Rovelli's Lecture 14 is online now
http://pirsa.org/12040037/
last in the series. He goes to Princeton now to give a talk 23 April at the Institute for Advanced Studies--I don't think they record and post their Seminar talks online.

There is not just one "LOST" theorem. At least two based on different assumptions, maybe more. It is a class of theorems which apply only to kinematics and which show that a certain algebra (a *-algebra or C*-algebra) is unique up to the appropriate isomorphism, based on various sets of assumptions.

When we talk about the current LQG theory or about finding *a* QG theory we are mainly talking about the DYNAMICS. That's how it comes across to me anyway.

I don't see what guidance the 2004-2005 "LOST"-type theorems could possibly give to the construction of LQG dynamics. I don't think they had an influence on the reformulation of dynamics that happened 2007-2010.

Mathematical theorems always involve some artificial rigorous assumptions (not about nature but about a mathematical structure that one wants to prove the theorem about). For instance a compact differential manifold, embeddings of 1 and 2 dimensional submanifolds which are analytic (or in Fleischhack's theorem semianalytic, not sure what the difference is). So one proves that such and such an abstract algebra is unique up to some abstract equivalence.

It would be naive to imagine that the importance of these theorems has been lost or is being ignored! Uniqueness theorems like that do not tell you how you must construct a physical theory, their role is to guide intelligent conjecture and give confidence.

I think one way to say it might be that the technical assumptions of this or that abstract theorem do not give you a prescription that you must slavishly follow about how your Hilbertspace must be constructed. IOW, what you learn from such a theorem will necessarily involve intuition and interpretation.

Rather than being lost or ignored, I think you can see the important influence that the uniqueness theorems of Fleischhack, Lewandowski and the rest, if you just look at the way kinematics is formulated in the 2011 Zakopane lectures, and in these Perimeter lectures.
I would say that it is in part thanks to the confidence gained from those 2004-2005 theorems, people moved boldly into a "group field theory" or abstract graph Hilbertspace formulation of the kinematics. The mathematical structures are quite different (from those prevalent 8 years ago) but they are analogous. So the assurance carries over and reinforces current work.

 

[marcus]

If I remember right, about 4 minutes into Lecture 14 there is a reference to new work on black hole entropy which has not been posted on arxiv yet. It sounds interesting because it gets the right coefficient---the 1/4---without having to adjust the Immirzi parameter.
http://pirsa.org/12040037/

This would be a landmark because in String one only gets the 1/4 in some unrealistic extremal or near-extremal case. This would be the first time, in any type of QG, that one gets the 1/4 in general.

If I have understood right, and if this new work holds up under scrutiny. So that's kind of exciting. Yes, the mention starts around minute 4:20. I hope it all checks out and we see the paper soon!

(There was also the Ghosh-Perez paper last year, but I haven't heard so much followup on that, so I don't know if it has been confirmed or not. This new result is by someone else. We'll see.)

 

[genneth]

If I remember right, about 4 minutes into Lecture 14 there is a reference to new work on black hole entropy which has not been posted on arxiv yet. It sounds interesting because it gets the right coefficient---the 1/4---without having to adjust the Immirzi parameter.
http://pirsa.org/12040037/

This would be a landmark because in String one only gets the 1/4 in some unrealistic extremal or near-extremal case. This would be the first time, in any type of QG, that one gets the 1/4 in general.

If I have understood right, and if this new work holds up under scrutiny. So that's kind of exciting. Yes, the mention starts around minute 4:20. I hope it all checks out and we see the paper soon!

(There was also the Ghosh-Perez paper last year, but I haven't heard so much followup on that, so I don't know if it has been accepted. This new result is by someone else. We'll see.)

I thought that was a reference to Ghosh-Perez...? Do you know which paper that is referring to?

 

[marcus]

He says the author is Eugenio Bianchi and the work was done there at Perimeter, which means in the past 3 or 4 months. He says EB just showed him how the proof goes on the blackboard, he has not reviewed it on paper.
So it is not yet final, we have to wait and see.

 

[atyy]

As far as theorems go, one should always be very careful. I'm not perfectly intimate with said theorem, but let me outline one possible "get out clause". The spin foams are not generally covariant when one considers any truncation, i.e. any graph/2-complex. It is expected that in the refinement/continuum limit true general covariance is recovered. This is exactly analogous to Rovelli's toy covariant harmonic oscillator example, where any discretisation breaks the general covariance.

Yes, my impression is that the continuum limit is supposed to do that. But I believe it has to be the continuum limit without q-deformation.

 

[marcus]

Since we're on a new page I'll recopy links to Rovelli's online video course in LQG. It ran three weeks: 14 lectures through 20th April. http://pirsa.org/C12012
Lecture 1 http://pirsa.org/12040019 what are quantum theory and geometry basically about? quantum tetrahedron.
Lecture 2 http://pirsa.org/12040020 historical and philosophical perspective on QG.
Lecture 3 http://pirsa.org/12040021 classical physics w/o preferred time coord: Hamilton function
Lecture 4 http://pirsa.org/12040022 quantum physics w/o time: transition amplitudes.

Lecture 5 http://pirsa.org/12040026 putting GR in the picture. deriving and motivating Palatini&Holst actions. overview of how discretized, quantized in 4d. At minute 40, begin working out toy model (3D Euclidean case) which will be copied in Lecture 9 to get the "real world" case.
Lecture 6 http://pirsa.org/12040027 continue simple worked example: quantizing 3D Euclidean case. How to get from Palatini/Holst classical continuous action to the spin foam.
Lecture 7 http://pirsa.org/12040028 math tools: specific graph Hilbert space&operators, SU(2) reps, spinnet basis.
Lecture 8 http://pirsa.org/12040029 concluding the 3D Euclidean example: defining transition amplitudes. Minute 18 = partition functions (which give transition amplitudes when boundaries are introduced). Minute 30 - 34= Wigner 6j appear. Minute 44=Ponzano&Regge recover GR! Minute 48=how bubble divergence can arise. How Turaev-Viro cured that using the quantum group of SU(2). How cosmological constant appears in the theory.
Lecture 9 http://pirsa.org/12040030 Beginning "the real world" 4D Lorentzian case.
Lecture 10 http://pirsa.org/12040033 First 25 minutes: deriving the spin network basis and demonstrating its key properties. Starting at minute 25 the topic is the volume operator spectrum. Around minute 48 Bianchi makes efficient use of diagram manipulation in calculating the matrix elements of the V operator.
Lecture 11 http://pirsa.org/12040034 Bianchi covered two topics:
1) up to minute 42---coherent (spin network) states
2) minute 42-72---unitary irreducible representations of SL(2,C). The map Y_γ from representations of SU(2) to those of SL(2,C), which will appear in the next three lectures and play a role in defining the dynamics of the theory. The students asked a bunch of questions during the lecture and applauded at end.

Lecture 12 http://pirsa.org/12040035 Full 4D theory, dynamics.
The first 19 minutes are a discussion of a student's question about the issue of uniqueness. This question may be premature--first we must be sure we have *a* background independent theory (at least one) with the right classical limit. The issue of uniqueness has been secondary in major historical advances (Maxwell, Einstein...) If one is not concerned about the uniqueness issue, then one might skip the first 19 minutes of this lecture. In the blackboard stills PDF the main lecture starts with #17, skipping the first 16 stills corresponds to skipping the first 19 minutes.
In a sense the core of the course starts around minute 46. Until that point the partition function is with a general group G and it is simply a quantization of a the "BF" theory based on that group. At minute 46, he says now introduce gravity. At minute 50 you see where the map Yγ is introduced, and you see clearly where and why it must enter. This map Yγ was defined in Lecture 11 while presenting math tools---irreducible unitary reps of SL(2,C). Around minute 62:30 he sums up: this is the definition of the full theory. A partition function Z which becomes a transition amplitude W when you designate part of the 2-complex as boundary. Analogies with the 3D theory are drawn. The q-deformed version is finite. Around minute 64 or 65: why the classical limit is Regge (for large j, in a fixed triangulation). More on that in the next Lecture.
Lecture 13 http://pirsa.org/12040036 Conclusion of the full theory.
First 17 minutes---redundancy of one SL(2,C) integration. Finiteness. Relation to Regge-with-cosmological-constant (for large j). Thinking about refinement: analogy of 2-complexes with QED Feynman diagrams.
Alternative ways of looking at theory e.g. quantum polyhedra, e.g. sum over histories involving elementary geometric moves...
Lecture 14 http://pirsa.org/12040037 Calculations with the theory: bounce cosmology, early universe, black hole features. Starting around minute 4 mention is made of some new work by Banchi on black hole entropy.

General references:
Zakopane Lectures... http://arxiv.org/abs/1102.3660
On the Structure... http://arxiv.org/abs/1108.0832
Transition Amplitudes... Colloquium http://pirsa.org/12040059

In case anyone wants to download blackboard still shots PDF for some of the lectures, to have for reference and review, here are the PDF links.
Lecture 5 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040026
Lecture 6 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040027
Lecture 7 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040028
Lecture 8 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040029
Lecture 9 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040030
Lecture 10 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040033
Lecture 11 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040034
Lecture 12 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040035
Lecture 13 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040036
Lecture 14 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040037
I put them on my desktop to have handy. Once I've listened to a lecture, looking back at the stills is an easy way to recall the main points.