Emily Peters has compiled a collection of LaTexed notes for these talks; you can find them here.

Monday, August 16th (112 Lillis)

9:00 André Henriques

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]

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

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]

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

8:00 Discussion in dormitory lounge

Tuesday, August 17th (185 Lillis)

9:00 André Henriques

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

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

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

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

4:30 Christoph Solveen (Gottingen)
The Bisognano-Wichman theorem

8:00 Discussion in dormitory lounge

Wednesday, August 18th (112 Lillis)

9:00-9:30 André Henriques

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

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

1:20 hike

7:00 reception

Thursday, August 19th (185 Lillis)

9:00 André Henriques

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]

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

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

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

8:00 Discussion in dormitory lounge

Friday, August 20th (112 Lillis)

9:00 André Henriques

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

11:30 André Henriques
Transport formula, Connes fusion with the vector representation
Reference: [Wa, section 31]

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

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

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]

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

11:30 André Henriques

References are to the following works:

[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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