# Ocneanu's Magic Garden Canvas: Syllabus: [https://mathpicture.fas.harvard.edu/files/mathpicture/files/syllabus.pdf](/file_url/194) Sort ![Adrian with a few models](/sites/g/files/omnuum6611/files/styles/hwp_1_1__360x360_scale/public/mathpicture/files/screen_shot_2017-08-18_at_3.47.46_am.png?itok=Xs9cNp-6) ![Adrian Ocneanu](/sites/g/files/omnuum6611/files/styles/hwp_1_1__360x360_scale/public/mathpicture/files/adrian90s.png?itok=LLPUGvZ2) *Left: Adrian Ocneanu in his office at Harvard in 2017.* *Right: This photo taken in 1999 shows Adrian holding Misner-Thorne-Wheeler in one hand, and some models in the other hand. He was celebrating the fact that he realized intertwiners, and coefficients like the 6j symbols, are made of a network of small permutohedra, in frames subject to Riemann curvature, namely gravity-like conditions.* In 2017, Professor Adrian Ocneanu, visiting from Penn State's mathematics department, taught a course introducing completely new work in higher representation theory. Cross-listed in Harvard's physics and mathematics departments, the course will cover the construction of higher (category) simple Lie groups, their roots, weights and representations, and Dynkin and Young diagrams - all encoded by discrete Riemann curvature. Transcriptions of the course lectures are posted on this website. Videos can be obtained from A. Ocneanu. **Relevant papers and talks** A. Ocneanu, [The classification of subgroups of quantum SU(N)](https://cel.archives-ouvertes.fr/cel-00374414/document). In: *Bariloche* (Argentine), pp. 26, 2000. A. Ocneanu, [Chirality for operator algebras](https://tqft.net/web/projects/taniguchi/Chirality%20for%20operator%20algebras%20-%20Adrian%20Ocneanu%20-%20Subfactors%20(Kyuzeso,%201993)%2039-63%20-%20MR1317353.pdf). In: H. Araki, Y. Kawahigashi and H. Kosaki (eds.): *Subfactors*. pp. 39-63. World Scientific Publ., 1994. A. Ocneanu, [Operator algebras, topology and subgroups of quantum symmetry— construction of subgroups of quantum groups](https://tqft.net/other-papers/subfactors/Subgroups%20of%20Quantum%20Groups%20-%20Ocneanu.pdf). In: Taniguchi Conference on Mathematics Nara 1998, 235–263, *Adv. Stud. Pure Math.*, 31, Math. Soc. Japan, Tokyo, 2001. A. Ocneanu, [Paths on Coxeter diagrams: From platonic solids and singularities to minimal models and subfactors](https://www.researchgate.net/publication/248790709_Paths_on_Coxeter_diagrams_From_Platonic_solids_and_singularities_to_minimal_models_and_subfactors), (Notes by S. Goto) in “Lectures on operator theory”, *Fields Inst. Monographs* 13, Amer. Math. Soc., Providence, 1999. A. Ocneanu, [Quantized groups, string algebras and Galois theory for algebras](https://www.cambridge.org/core/books/operator-algebras-and-applications/quantized-groups-string-algebras-and-galois-theory-for-algebras/61DFE87D2B960EB9DDD1F7AE8BD9C5AD). In: *Operator algebras and applications*, Vol. 2, pp. 119-172, Cambridge Univ. Press, 1988. A. Ocneanu, [Quantum Subgroups and Higher McKay Correspondences](https://www.youtube.com/watch?v=TzsJ2WZN9do). Talk given at workshop "Generalized McKay Correspondences and Representation Theory", MSRI, Berkeley, 2006. ![Higher rep course poster](/sites/g/files/omnuum6611/files/styles/hwp_1_1__720x720_scale/public/mathpicture/files/hrt_poster.png?itok=5A6B2rfE) --- Attachments- [ picture\_as\_pdf Syllabus ](/sites/g/files/omnuum6611/files/mathpicture/files/syllabus.pdf) - [ picture\_as\_pdf lecture\_1\_23.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_1_23.pdf) - [ picture\_as\_pdf lecture\_24\_20171025.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_24_20171025.pdf) - [ picture\_as\_pdf lecture\_25\_20171027.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_25_20171027.pdf) - [ picture\_as\_pdf lecture\_26\_20171030.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_26_20171030.pdf) - [ picture\_as\_pdf lecture\_27\_20171101.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_27_20171101.pdf) - [ picture\_as\_pdf lecture\_28\_20171103.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_28_20171103.pdf) - [ picture\_as\_pdf lecture\_29\_20171106.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_29_20171106.pdf) - [ picture\_as\_pdf lecture\_30\_20171108.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_30_20171108.pdf) - [ picture\_as\_pdf lecture\_31\_20171110.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_31_20171110.pdf) - [ picture\_as\_pdf lecture\_32\_20171113.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_32_20171113.pdf) - [ picture\_as\_pdf lecture\_33\_20171115.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_33_20171115.pdf) - [ picture\_as\_pdf lecture\_34\_20171117.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_34_20171117.pdf) - [ picture\_as\_pdf lecture\_35\_20171120.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_35_20171120.pdf) - [ picture\_as\_pdf lecture\_36\_20171127.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_36_20171127.pdf) - [ picture\_as\_pdf lecture\_37\_20171129.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_37_20171129.pdf) - [ picture\_as\_pdf lecture\_38\_20171201.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_38_20171201.pdf) - [ picture\_as\_pdf lecture\_39\_20171204.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_39_20171204.pdf) - [ picture\_as\_pdf lecture\_40\_20171206.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_40_20171206.pdf) - [ picture\_as\_pdf lecture\_41\_20171208.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_41_20171208.pdf) - [ picture\_as\_pdf lecture\_42\_20171213.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/lecture_42_20171213.pdf) ---