Notes

These are LiveTeXed notes from the talks and are likely to contain errors. (Things which I'm pretty sure are wrong or incomplete appear in blue.) If you have any interest in editing them, please go ahead! Don't forget to send the results to eep@math.mit.edu when you're done.

If you're helping to liveTeX talks, you might want to use this template.

Recent Updates:

13 September 2010 -- Christoph significantly improved and extended the notes from his Tuesday afternoon talk, and also updated his slides.

25 August 2010 -- Scott Carnahan and Dmitri Pavlov both wrote their own, TeXed notes for the workshop, and kindly offered to share them.
Dmitri's notes (tarred; each talk is its own separate file)
Scott's notes (in a single LaTeX file)

Monday, August 16th (112 Lillis)

9:00 André Henriques
notes (pdf), LaTeX source

10:15 Hiro Tanaka (Northwestern)
Representation theory of SU(N), the Pieri rule, fusion rules for representations of LSU(N)
References: [Wa, sections 2 and 34], [FH]
notes (pdf), LaTeX source

11:30 Min Ro (Oregon)
Hilbert spaces, polar decomposition, spectral theorem, von Neumann algebras
References: [Wa, section 10], [RS], [Ta]
notes (pdf), LaTeX source

2:45 Ryan Grady (Notre Dame)
Segal's quantization criterion, actions of LSU(N) and of Diff(S^1) on the fermionic Fock space
References: [Wa, sections 3 and 4], [PS]
notes (pdf), Ryan's notes

4:00 Owen Gwilliam (Northwestern)
The central extension of LG, positive energy representations, Lie algebra cocycles
References: [Wa, sections 5-8], [PS]
notes (pdf), LaTeX source

8:00 Discussion in dormitory lounge


Tuesday, August 17th (185 Lillis)

9:00 André Henriques
notes (pdf), LaTeX source

10:15 James Tener (Berkeley)
Classification of LG-reps, weight polytopes for the characters of LG-reps
References: [Wa, section 9], [KMKS], [Ka]
notes (pdf), LaTeX source

11:30 Michael Hartglass (Berkeley)
Tomita Takesaki theory and the KMS condition
References: [Wa, sections 11-12], [RvD], [Y1], [Lo]
notes (pdf), LaTeX source

2:00 Dmitri Pavlov (Berkeley)
Tomita Takesaki theory for fermions
References: [Wa, sections 13-15]
notes (pdf), LaTeX source

3:15 Corbett Redden (Michigan State)
Conformal nets
notes (pdf), LaTeX source
References: [Wa, section 17], [Lo], [GF]

4:30 Christoph Solveen (Gottingen)
The Bisognano-Wichman theorem
Christoph's Slides edited notes (pdf), LaTeX source

8:00 Discussion in dormitory lounge


Wednesday, August 18th (112 Lillis)

9:00-9:30 André Henriques
Blackboard 1, Blackboard 2, Blackboard 3,

9:45 Anatoly Preygel (MIT)
The Knizhnik-Zamolodchikov equation
References: [Wa, section 18], [EFK]
notes (pdf), LaTeX source

11:00 Daniel Moseley (Oregon)
The hypergeometric function
References: [Wa, sections 18-24], [BE]
notes (pdf), LaTeX source

1:20 hike View Eugene Squirrel

7:00 reception


Thursday, August 19th (185 Lillis)

9:00 André Henriques
notes (pdf), LaTeX source

10:15 Nick Rozenblyum (MIT)
Sugawara's formula and the action of Diff(S^1) on positive energy representation
References: [Wa, sections 5 and 27], [FBZ], [Ka, section 12.8]
notes (pdf), LaTeX source

11:30 Arturo Prat-Waldron (Max Planck)
Primary fields, boundedness of smeared primary fields
Reference: [Wa, section 25], [To]
notes (pdf), LaTeX source

2:45 Yoh Tanimoto (Rome)
Connes fusion
References: [Wa, section 30], [Y2], [Co]
notes (pdf), LaTeX source

4:00 Josiah Thornton (Oregon)
Quantum dimension
References: [LRo], [LRe1]
notes (pdf), LaTeX source

8:00 Discussion in dormitory lounge


Friday, August 20th (112 Lillis)

9:00 André Henriques
notes (pdf), LaTeX source

10:15 Scott Carnahan (MIT)
Braiding of smeared primary fields
Reference: [Wa, sections 26, 28, 29]
notes (pdf), LaTeX source

11:30 André Henriques
Transport formula, Connes fusion with the vector representation
Reference: [Wa, section 31]
notes (pdf), LaTeX source

2:45 Orit Davidovich (Texas)
Modularity of the category of representations of a conformal net (Part 1)
References: [KLM], [Mu]
notes (pdf), LaTeX source

4:00 Emily Peters (New Hampshire / MIT)
Boundary CFTs and their classification via Frobenius algebras
References: [Pe], [LRe1], [LRe2]
notes (pdf), LaTeX source

8:00 Discussion in dormitory lounge


Saturday, August 21st (221 McKenzie)

9:00 Marcel Bischoff (Rome)
Modularity of the category of representations of a conformal net (Part 2)
References: [KLM], [Mu]
notes (pdf), LaTeX source

10:15 Braxton Collier (Texas)
The 3-category of conformal nets
Reference: [BDH], [DH]
notes (pdf), LaTeX source

11:30 André Henriques
notes (pdf), LaTeX source


References are to the following works. If links are broken, please visit the official workshop page, which I stole this code from!

[BDH] Barthels, Douglas, and Henriques, Conformal nets and local field theory.
[BE] Beukers, Notes on differential equations and hypergeometric functions.
[Co] Connes, Noncommutative geometry.
[DH] Douglas and Henriques, Geometric string structures.
[EFK] Etingof, Frenkel, and Kirillov, Lectures on representation theory and Knizhnik-Zamolodchikov equations.
[FBZ] Frenkel and Ben Zvi, Vertex algebras and algebraic curves.
[FH] Fulton and Harris, Representation theory: a first course.
[GF] Gabiani and Frohlich, Operator algebras and conformal field theory.
[Ka] Kac, Infinite dimensional Lie algebras.
[KMKS] Kass, Moody, Katera, and Slansky, Affine Lie algebras, weight multiplicities, and branching rules.
[KLM] Kawahigashi, Longo, and Muger, Multi-interval subfactors and modularity of representations in conformal field theory.
[Ko] Kosaki, Type III factors and index theory.
[Lo] Longo, Lecture notes.
[LRe1] Longo and Rehren, Nets of subfactors.
[LRe2] Longo and Rehren, Local fields in boundary conformal QFT.
[LRo] Longo and Roberts, A theory of dimension.
[Mu] Mueger, notes.
[Pe] Pennig, Sektorstruktur und Klassifikation von zweidimensionalen, konformen Quantenfeldtheorien auf dem Halbraum.
[PS] Pressley and Segal, Loop Groups.
[RS] Reed and Simon, Functional Analysis.
[RvD] Rieffel and van Daele, A bounded operator approach to Tomita-Takesaki theory.
[Ta] Takesaki, Theory of operator algebras, I.
[To], Toledano Laredo, Fusion of Positive Energy Representations of LSpin(2n).
[Wa] Wasserman, Operator algebras and conformal field theory III.
[Y1] Yamagami, Algebraic aspects in modular theory.
[Y2] Yamagami, Modular theory for bimodules.

Back to the main workshop page.