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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)

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

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

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

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

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

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.

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