Ocneanu's Magic Garden

Canvas: https://canvas.harvard.edu/courses/31194
Syllabus: https://mathpicture.fas.harvard.edu/files/mathpicture/files/syllabus.pdf

Adrian with a few models Adrian Ocneanu

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.


This fall term, Professor Adrian Ocneanu, visiting from Penn State's mathematics department, will be teaching 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.

The course will be held Monday, Wednesday, and Friday at 11AM in Jefferson 250. 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). In: Bariloche (Argentine), pp. 26, 2000.
A. Ocneanu, Chirality for operator algebras. 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. 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, (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. In: Operator algebras and applications, Vol. 2, pp. 119-172, Cambridge Univ. Press, 1988.
A. Ocneanu, Quantum Subgroups and Higher McKay Correspondences. Talk given at workshop "Generalized McKay Correspondences and Representation Theory", MSRI, Berkeley, 2006.

 

Higher rep course poster

Syllabus571 KB
lecture_1_23.pdf301 KB
lecture_24_20171025.pdf1.58 MB
lecture_25_20171027.pdf728 KB
lecture_26_20171030.pdf173 KB
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lecture_29_20171106.pdf7.27 MB
lecture_30_20171108.pdf7.35 MB
lecture_31_20171110.pdf644 KB
lecture_32_20171113.pdf390 KB
lecture_33_20171115.pdf880 KB
lecture_34_20171117.pdf1.08 MB
lecture_35_20171120.pdf1.27 MB
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lecture_38_20171201.pdf636 KB
lecture_39_20171204.pdf690 KB
lecture_40_20171206.pdf788 KB
lecture_41_20171208.pdf619 KB
lecture_42_20171213.pdf1.04 MB